Jee Mains 25 February 2021 Shift-II Previous Year Paper

PHYSICS

SECTION A

Q. 1: An electron with kinetic energy K1 enters between parallel plates of a capacitor at an angle ‘α’ with the plates. It leaves the plates at angle ‘β’ with kinetic energy K2. Then the ratio of kinetic energies K1 : K2 will be:

(A) sin2β/cos2α

(B) cos2β/cos2α

(C) cosβ/sinα

(D) cosβ/cosα

Answer: (B)
Physics JEE Main 2021 Paper Solutions For Shift 2 Feb 25
∵v1cosα = v2cosβ [electric field inside a parallel plate capacitor is perpendicular to the plates, hence, there will be no change in parallel component of velocity]
v1/v2 = cosβ/cosα
Then the ratio of kinetic energies
k1/k2 = ½ mv12/ ½ mv22 = (v1/v2)2 = (cosβ/cosα)2
k1/k2 = cos2β/cos2α

 

Q. 2: Two identical springs of spring constant ‘2K’ are attached to a block of mass m and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. Then, time period of oscillations of this system is:

Shift 2 Physics JEE Main 2021 Paper Solutions For Feb 25

(A) π√(m/k)

(B) π√(m/2k)

(C) 2π√(m/k)

(D) 2π√(m/2k)

Answer: (A)
Shift 2 Physics Solved Paper JEE Main 2021 For Feb 25
Springs are in parallel combination.
Hence, Keff = 2k + 2k = 4k
∵ T = 2π √(m/keff)
 = 2π√(m/4k)
T  = π √(m/k)

 

Q. 3: The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 2 to n = 1 state is:

(A) 194.8 nm

(B) 490.7 nm

(C) 913.3 nm

(D) 121.8 nm

Answer: (D)
∆E = 10.2 eV is the energy difference between the state n = 2 & n = 1
∆E = –3.4 – (–13.6) = 10.2 eV
hc/λ = 10.2 ev
λ = hc/(10.2)e (in meters) where ‘e’ = 1.6 × 10–19 J/V
= 12400/10.2 Å (because hc = 12400 eV nm)
= 121.56 nm
≃ 121.8 nm

 

Q. 4: In a ferromagnetic material below the Curie temperature, a domain is defined as:

(A) a macroscopic region with consecutive magnetic dipoles oriented in opposite directions.

(B) a macroscopic region with zero magnetization.

(C) a macroscopic region with saturation magnetization.

(D) a macroscopic region with randomly oriented magnetic dipoles.

Answer: (C)
In a ferromagnetic material below the Curie temperature, the domain is defined as a macroscopic region with saturation magnetization.

 

Q. 5: The point A moves with a uniform speed along the circumference of a circle of radius 0.36m and covers 30o in 0.1s. The perpendicular projection ‘P’ form ‘A’ on the diameter MN represents the simple harmonic motion of ‘P’. The restoring force per unit mass when P touches M will be:

Shift 2 JEE Main 2021 Feb 25 Paper With Solutions Physics

(A) 100 N

(B) 50 N

(C) 9.87 N

(D) 0.49 N

Answer: (C)
Shift 2 Physics JEE Main 2021 Paper With Solutions Feb 25
The point covers 30o in 0.1 sec.
Means
π/6 → 0.1sec.
1 → 0.1/(π/6)
2π = → 0.1×6×2π/π
T = 1.2 sec.
We know that ω = 2π/T
ω = 2π/1.2
Restoring force (F) = mω2A
Then, Restoring force per unit mass (F/m) = ω2A
F/m = (2π/1.2)2×0.36
≃ 9.87 N

 

Q. 6: Match List I with List II.

List I List II
(a) Rectifier (i) Used either for stepping up or stepping down the A.C.voltage
(b) Stabilizer (ii) Used to convert A.C. voltage into D.C. voltage
(c) Transformer (iii) Used to remove any ripple in the rectified output voltage
(d) Filter (iv) Used for constant output voltage even when the input voltage or load current change

Choose the correct answer form the options given below:

(A) (a)-(ii), (b)- (i), (c)-(iv), (d)-(iii)

(B) (a)-(ii), (b)- (iv), (c)-(i), (d)-(iii)

(C) (a)-(ii), (b)- (i), (c)-(iii), (d)-(iv)

(D) (a)-(iii), (b)- (iv), (c)-(i), (d)-(ii)

Answer: (B)
(a) Rectifier:- used to convert A.C voltage into D.C. Voltage.
(b) Stabilizer:- used for constant output voltage even when the input voltage or load current change
(c) Transformer:- used either for stepping up or stepping down the A.C. voltage.
(d) Filter:- used to remove any ripple in the rectified output voltage.

 

Q. 7: Y = A sin(ωt + ϕ) is the time – displacement equation of an SHM, At t = 0, the displacement of the particle is Y = A/2 and it is moving along negative x-direction. Then, the initial phase angle ϕ will be.

(A) π/6

(B) π/3

(C) 2π/3

(D) 5π/6

Answer: (D)
Shift 2 Physics JEE Main 2021 Paper With Solutions For Feb 25
y = A sin (ωt + ϕ)
t = 0, x = A/2
1/2 = sin ϕ
ϕ = π/6, 5π/6
v = dy/dt = A ωcos(ωt + ϕ)
t = 0, v = A ωcosϕ
ϕ = π/6, for v (positive)
ϕ = 5π/6, for v (negative)
∴ϕ = 5π/6

 

Q. 8: A sphere of radius ‘a’ and mass ‘m’ rolls along horizontal plane with constant speed v0. It encounters an inclined plane at angle θ and climbs upwar(D) Assuming that it rolls without slipping how far up the sphere will travel (along the incline)?

Shift 2 JEE Main Feb 25 2021 Physics Paper With Solution

(A) (⅖) v02/g sin θ

(B) 10v02/7gsin θ

(C) v02/5gsin θ

(D) 7v02/10gsin θ

Answer: (D)
Shift 2 Feb 25 JEE Main 2021 Physics Papers With Solutions
From energy conservation
mgh = ½ mv2 + ½ Iω2
mgh = ½ mv2 + ½×(⅖)ma2× v02/a2
gh = ½ v02+ ⅕ v02
gh = (7/10)v02
h = (7/10)v02/g
From triangle, sinθ = h/l
Then, h = lsinθ
l sinθ = (7/10) (v02/g)
l = (7/10) (v02/g sin θ)

 

Q. 9: Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter 0.1 μm. If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that:

(A) its size decreases, but intensity increases

(B) its size increases, but intensity decreases

(C) its size increases, and intensity increases

(D) its size decreases, and intensity decreases

Answer: (A)
For diffraction through a single slit, for first minimum.
sin θ = 1.22λ/D
If D is increased, then sinθ will decrease i.e θ will decrease
∴ size of circular fringe will decrease but intensity increases.

 

Q. 10: An electron of mass me and a proton of mass mp = 1836 me are moving with the same speed. The ratio of their de Broglie wavelength λelectronProton will be:

(A) 918

(B) 1836

(C) 1/1836

(D) 1

Answer: (B)
Given mass of electron = me
Mass of proton = mp
∴ given mp = 1836 me
From de-Broglie wavelength
λ = h/p = h/mv
λep = mp/me [v is same]
= 1836me/me
λep= 1836

 

Q. 11: The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is 1.43 V. The new wavelength is:

(A) 400 nm

(B) 382 nm

(C) 309 nm

(D) 329 nm

Answer: (B)
From the photoelectric effect equation
hc/λ = ϕ + evs
where Vs is the stopping potential and ϕ is work function of the metal.
So, evs1 = hc/λ1 – ϕ ……(i)
evs2 = hc/λ2 – ϕ …..(ii)
Subtract equation (i) from equation (ii)
evs1 – evs2 = hc/λ1– hc/λ2
vs1 – vs2 = (hc/e) (1/λ1 – 1/λ2)
(0.710 – 1.43) = 1240 (1/491 – 1/λ2)
(because hc = 1240 eV nm)
-0.72/1240 = 1/491 – 1/λ2
1/λ2 = 1/491 + 0.72/1240
1/λ2 = 0.00203 + 0.00058
1/λ2 = 0.00261
λ2 = 383.14
λ2 ≃ 382 nm

 

Q. 12: The truth table for the following logic circuit is:

Physics Feb 25 Solved Paper JEE Main 2021 For Shift 2

Answer: (D)
Physics Solved Feb 25 Paper Shift 2 JEE Main 2021
If A = B = 0 then output y = 1
If A = B = 1 then output y = 1

 

Q. 13: If e is the electronic charged, c is the speed of light in free space and h is planck’s constant, the quantity (1/4πε0) |e|2/hc has dimensions of:

(A) [ LC-1]

(B) [M0 L0 T0]

(C) [ M L T0]

(D) [M L T-1]

Answer: (B)
Given
e = electronic charge
c = speed of light in free space
h = planck’s constant
(1/4πε0) e2/hc = (ke2/hc)× λ22 [multiply and divide by lambda = wavelength]
= F×λ/E [ke22 has dimensions of force and hc/λ = E]
= E/E [F× λ has dimension of E]
= dimensionless
= [ M0 L0 T0]

 

Q. 14: A charge ‘q’ is placed at one corner of a cube as shown in figure. The flux of electrostatic field E through the shaded area is:

Feb 25 Shift 2 JEE Main 2021 Physics Paper With Solutions

(A) q/48ε0

(B) q/8ε0

(C) q/24ε0

(D) q/4ε0

Answer: (C)
Total flux through the cube = (q/ε0)× ⅛ = q/8ε0
Total flux through one “outer” face of the cube = (q/8ε0)×1/3 = q/24ε0
[Because there is flux only through 3 faces]
Hence, total flux through shaded area
ϕT = (q/24ε0 + q/24ε0)×1/2 [half of each face is shaded]
ϕT = q/24ε0

 

Q. 15: Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V2 = 2V1 then the ratio of temperature T2/T1 is:

Feb 25 Shift 2 JEE Main 2021 Solved Paper For Physics

(A) 1/√2

(B) 1/2

(C) 2

(D) √2

Answer: (D)
Shift 2 JEE Main 2021 Solved Paper Physics Feb 25
From P-V diagram,
Given PV1/2 = constant …..(i)
We know that
PV = nRT
P ∝ (T/V) [for 1 mole]
Put in equation (i)
(T/V) (V)1/2 = constant
T ∝V1/2
T2/T1 = √(V2/V1)
T2/T1 = √(2V1/V1)
T2/T1 = √2

 

Q. 16: Given below are two statements:

Statement I: In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell’s distribution.

Statement II: In a diatomic molecule, the rotational energy at a given temperature equals the transnational kinetic energy for each molecule.

In the light of the above statements, choose the correct answer from the options given below:

(A) Both statement I and statement II are false.

(B) Both statement I and statement II are true.

(C) Statement I is false but statement II is true.

(D) Statement I is true but statement II is false.

Answer: (D)
The translational kinetic energy & rotational kinetic energy both obey Maxwell’s distribution independent of each other.
T.K.E. of diatomic molecules = (3/2) kT [3 translational D.O.F.]
R.K.E. of diatomic molecules = (2/2) kT = [2 rotational D.O.F.]
So statement I is true but statement II is false.

 

Q. 17: An LCR circuit contains resistance of 110 Ω and a supply of 220 V at 300 rad/s angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by 450. If on the other hand, only inductor is removed the current leads by 450 with the applied voltage. The rms current flowing in the circuit will be:

(A) 2.5 A

(B) 2 A

(C) 1 A

(D) 1.5 A

Answer: (B)
When L and C are connected with R in series the circuit will come in resonance So, current in the circuit will be:
Irms = Vrms/R
= 220/110
= 2 A

 

Q. 18: For extrinsic semiconductors: when doping level is increased;

(A) Fermi–level of p and n-type semiconductors will not be affected.

(B) Fermi–level of p-type semiconductors will go downward and Fermi–level of n-type semiconductor will go upward.

(C) Fermi–level of both p–type and n–type semiconductors will go upward for T >TFK and downward for T<TFK, where TF is Fermi temperature.

(D) Fermi–level of p-type semiconductor will go upward and Fermi–level of n–type semiconductors will go downward.

Answer: (B)
In n-type semiconductor, pentavalent impurity is added Each pentavalent impurity donates a free electron. So the Fermi-level of n-type semiconductor will go upward and in p-type semiconductor, trivalent impurity is added. Each trivalent impurity creates a hole in the valence band So the Fermi-level of p-type semiconductor will go downward.

 

Q. 19: A stone is dropped from the top of a building. When it crosses a point 5m below the top, another stone starts to fall from a point 25m below the top, both stones reach the bottom of the building simultaneously. The height of the building is: [Take g = 10 m/s2]

(A) 45 m

(B) 35 m

(C) 25 m

(D) 50 m

Answer: (A)
Physics JEE Main Feb 25 2021 Paper With Solutions For Shift 2
Velocity of particle (1) at 5m below top u1 = √2gh = √(2×10×5) =10 m/s
For particle (1), using 2nd equation of motion
20+h = 10t + ½ gt2 …..(i)
For particle (2), using 2nd equation of motion
h = ½ gt2 …..(ii)
Put equation (ii) in equation (i)
20 + ½ gt2 = 10t + ½ gt2
t = 2 sec.
Put in equation (ii)
h = ½ gt2
= ½ ×10 × 22
h = 20m
The height of the building = 25 + 20 = 45m

 

Q. 20: If a message signal of frequency ‘fm’ is amplitude modulated with a carrier signal of frequency ‘fc’ and radiated through an antenna, the wavelength of the corresponding signal in air is:

[Given, C is the speed of electromagnetic waves in vacuum/air]

(A) c/(fc+fm)

(B) c/(fc-fm)

(C) c/fm

(D) c/fc

Answer: (A)
Equation of amplitude modulated wave y = (Ac + Am sin ωmt) sin ωct
Here angular frequency of modulated signal = ωc
Thus frequency of modulated signal = fc
Thus wavelength = c/fc

Section B

Q. 1: The initial velocity v1 required to project a body vertically upward from the surface of the earth to just reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity ve such that vi = √(x/y) ve. The value of x will be_______.

Answer: 20
Physics Feb 25 JEE Main 2021 Paper Solution For Shift 2
Here R = radius of the earth
From energy conservation
-Gmem/R + ½ mvi2 = -Gmem/11R + 0
½ mvi2 = (10/11)Gmem/R
vi = √(20Gme/11R)
vi = √(20/11) ve {∵escape  velocity  ve = √(Gme/R)}
Then the value of x = 20

 

Q. 2: The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4% will be ___%.

Answer: 2
Speed of transverse wave is
V = √(T/μ)
Taking log on both sides
ln v = ½ lnT – ½ ln μ
Δv/v = ½ ΔT/T ⇒ (Δv/v)×100 = 1/2 ( ΔT/T)×100
= ½ ×4 [ μ is constant for a string]
(Δv/v)×100 = 2%

 

Q. 3: The peak electric field produced by the radiation coming from the 8 W bulb at a distance of 10 m is (x/10) √(µ0c/π) V/m. The efficiency of the bulb is 10% and it is a point source. The value of x is ___.

Answer: 2
Intensity I = ½ c∈0E02
Intensity = Power / Area = 8 /(4π × 102)
(8/4π×102) ×½ =¼ × c ×(1/µ0c2) ×E02 [Multiply by ½ and ∈0 =1/μ0c2]
E0 = (2/10)√(µ0c/π)
⇒ x = 2

 

Q. 4: Two identical conducting spheres with negligible volume have 2.1nC and -0.1nC charges, respectively. They are brought into contact and then separated by a distance of 0.5 m. The electrostatic force acting between the spheres is _______× 10-9 N. [Given : 4πε0 = 1/9×109 SI unit]

Answer: 36
Physics Solved Feb 25 Paper Shift 2 JEE Main 2021
When they are brought into contact & then separated by a distance = 0.5 m. Then charge distribution will be
Physics JEE Main Shift 2 Feb 25 2021 Paper Solution
The electrostatic force acting b/w the sphere is
Fe = kq1q2/r2
= 9×109×1×10-9×1×10-9/(0.5)2
= (900/25) × 10-9
Fe = 36 ×10-9 N

 

Q. 5: A current of 6A enters one corner P of an equilateral triangle PQR having 3 wires of resistance 21Ω each and leaves by the corner R. The currents i1 in ampere is______.

25 Feb 2021 JEE Main Physics Solved Paper Shift 2

Answer: 2
25 Feb JEE Main Shift 2 2021 Physics Solved Paper
The current i1 = (R2/(R1 + R2))i
= (2/(4+2))×6
i1 = 2A

 

Q. 6: The wavelength of an X-ray beam is 10 Å. The mass of a fictitious particle having the same energy as that of the X-ray photons is (x/3) h kg. The value of x is _______.

Answer: 10
Given wavelength of an X-ray beam = 10 Å
∵E = hc/λ = mc2
m = hc/λ will be the mass of a particle having the same energy
The mass of a fictitious particle having the same energy as that of the X-ray photons = (x/3)h kg
(x/3) h = h/cλ
x = 3/cλ
= 3/3×108×10×10-10
x = 10

 

Q. 7: A reversible heat engine converts one- fourth of the heat input into work. When the temperature of the sink is reduced by 52 K, its efficiency is doubled The temperature in Kelvin of the source will be_______.

Answer: 208
∵ n = W/Qin = 1/4
¼ = 1 – T2/T1 [for reversible heat engine]
T2/T1 = 3/4
When the temperature of the sink is reduced by 52k then its efficiency is doubled.
1/2 = 1 -(T2 – 52)/T1
(T2– 52)/T1 = 1/2
T2/T1 – 52/T1 = 1/2
¾ – 52/T1 = 1/2
52/T1 = 1/4
T1 = 208 K is the source temperature.

 

Q. 8: If P× Q= Q× P , the angle between P and Q is θ(0o<θ< 360o). The value of ‘θ’ will be ____.

Answer: 180
25 Feb Shift 2 JEE Main 2021 Solved Paper Physics

 

Q. 9: Two particles having masses 4g and 16g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n:2. The value of n will be_____.

Answer: 1
Relation b/w kinetic energy & momentum is
p = √(2mKE) (∵KE = same)
p1/p2 = √(m1/m2)
n/2 = √(4/16)
n = 1

 

Q. 10 : Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m. Then charge on each of the sphere is (a/21)×10-8C. The value of ‘a’ will be________. [Take g = 10 m/s2]

Answer: 20
Physics JEE Feb 25 Main 2021 Solved Paper Shift 2
From FBD, T sinθ = kq2/d2 and T cosθ = mg
Dividing them,
mg tanθ = kq2/d2
q = √(mg tanθ)/25k
= √(10×10-6×10×1/√24(25)9×109)
= √(10-4×4/√24×25×4×9×109)
= (⅔)√(10-4/√24×1011)
Thus (a/21)×10-8 = ⅔ √(10-15/√24)
= ⅔ √(10-16/0.49)
a = 2×21/3×0.7
= 20

CHEMISTRY

SECTION A

Q. 1. What is ‘X’ in the given reaction?

JEE Main 25th Feb Shift 2 Chemistry Paper Question 6

Answer: (A)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 6 solution

Q. 2. The major product of the following reaction:

Answer: (D)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 8 solution

Q. 3. Given below are two statements:

Statement I: The identification of Ni2+ is carried out by dimethylglyoxime in the presence of NH4OH

Statement II: The dimethylglyoxime is a bidentate neutral ligand.

In the light of the above statements, choose the correct answer from the options given below:

(A) Both statement I and statement II are true

(B) Both statement I and statement II are false

(C) Statement I is false but statement II is true

(D) Statement I is true but statement II is false

Answer: (D)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 1 solution
Dimethylglyoxime is a negative bidentate legend.

 

Q. 4. Carbylamine test is used to detect the presence of a primary amino group in an organic compound Which of the following compounds is formed when this test is performed with aniline?

Answer: (B)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 2 solution

 

Q. 5. The correct order of bond dissociation enthalpy of halogen is:

(A) F2>Cl2>Br2>I2

(B) Cl2>F2>Br2>I2

(C) Cl2>Br2>F2>I2

(D) I2>Br2>Cl2>F2

Answer: (C)
Fact based
F2 has F — F, F2 involves repulsion of non-bonding electrons & more over its size is small and hence due to high repulsion its bond dissociation energy is very low.

Q. 6. Which one of the following statements is FALSE for hydrophilic sols?

(A) These sols are reversible in nature

(B) The sols cannot be easily coagulated

(C) They do not require electrolytes for stability

(D) Their viscosity is of the order of that of H2O

Answer: (D)
Fact based

Q. 7. Water does not produce CO on reacting with

(A) C3H8

(B) C

(C) CH4

(D) CO2

Answer: (D)
H2O + CO2 H2CO3

 

Q. 8: The correct sequence of reagents used in the preparation of 4-bromo-2-nitroethyl benzene from benzene is:

(A) CH3COCl/AlCl3, Br2/AlBr3, HNO3/H2SO4, Zn/HCl

(B) CH3COCl/AlCl3, Zn-Hg/HCl, Br2/AlBr3, HNO3/H2SO4

(C) Br2/AlBr3, CH3COCl/AlCl3, HNO3/H2SO4, Zn/HCl

(D) HNO3/H2SO4, Br2/AlCl3, CH3COCl/AlCl3, Zn-Hg/HCl

Answer: (B)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 9 solution

 

Q. 9. Given below are two statements:

Statement I: α and β forms of sulphur can change reversibly between themselves with slow heating or slow cooling.

Statement II: At room temperature the stable crystalline form of sulphur is monoclinic sulphur.

In the light of the above statements, choose the correct answer from the options given below.

(A) Both statement I and statement II are false

(B) Statement I is true but statement II is false

(C) Both statement I and statement II are true

(D) Statement I is false but statement II is true

Answer: (B)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 16 solution

 

Q. 10. Correct statement about the given chemical reaction is:

JEE Main 25th Feb Shift 2 Chemistry Paper Question 17

(A) Reaction is possible and compound (A) will be a major product.

(B) The reaction will form a sulphonated product instead of nitration.

(C) NH2 group is ortho and para directive, so product (B) is not possible.

(D) Reaction is possible and compound (B) will be the major product.

Answer: (A)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 17 solution

Q. 11. Which of the following compounds is added to the sodium extract before addition of silver nitrate for testing of halogens?

(A) Nitric acid

(B) Sodium hydroxide

(C) Hydrochloric acid

(D) Ammonia

Answer: (A)
NaCN + HNO3 → NaNO3 + HCN ↑
Na2S + HNO3 → NaNO3 + H2S ↑
Nitric acid decomposes NaCN & Na2S, else they precipitate in test & misguide the resolve.

 

Q. 12: Given below are two statements:

Statement I: The pH of rain water is normally ~5.6.

Statement II: If the pH of rain water drops below 5.6, it is called acid rain.

In the light of the above statements, choose the correct answer from the option given below.

(A) Statement I is false but Statement II is true

(B) Both statement I and statement II are true

(C) Both statement I and statement II are false

(D) Statement I is true but statement II is false

Answer: (B)
Both statements are correct

 

Q. 13. The solubility of Ca(OH)2 in water is:

[Given: The solubility product of Ca(OH)2 in water = 5.5×10-6]

(A) 1.11 ×10-6

(B) 1.77 ×10-6

(C) 1.77×10-2

(D) 1.11×10-2

Answer: (D)
Ca(OH)2 ⇌ Ca+2 + 2OH
s (2s + 10-7)
s(2s+10-7)2 = 55×10-7
4s3 = 55×10-7
s3 = 5500 / 4 × 10-9

s = (2250/2) 1/3× 10-3

s = (1125)⅓ × 10-3
s = 1.11 × 10-2

 

Q. 14. The major components of German Silver are:

(A) Cu, Zn and Mg

(B) Ge, Cu and Ag

(C) Zn, Ni and Ag

(D) Cu, Zn and Ni

Answer: (D)
Fact
German silver is alloy which does not have silver.
Cu-50%; Ni-30%; Zn-20%

 

Q. 15. The method used for the purification of Indium is:

(A) Van Arkel method

(B) Vapour phase refining

(C) Zone refining

(D) Liquation

Answer: (C)
Fact
Ga, In, Si, Ge are refined by zone refining or vacuum refining.

 

Q. 16. Which of the following is correct structure of α-anomer of maltose

Answer: (D)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 12

Q. 17. The major product of the following reaction is:

JEE Main 25th Feb Shift 2 Chemistry Paper Question 13

(A) CH3CH2CH2CHO

(B) CH3CH2CH=CH–CHO

(C) CH3CH2CH2CH2CHO

(D) JEE Main 25th Feb Shift 2 Chemistry Paper Question 13

Answer: (C)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 13 solution

 

Q. 18. The correct order of acid character of the following compounds is:

JEE Main 25th Feb Shift 2 Chemistry Paper Question 14

(A) II>III>IV>I

(B) III>II>I>IV

(C) IV>III>II>I

(D) I>II>III>IV

Answer: (A)
Acidity of carboxylic acid α-R>-H>-I
1 / α + R > + H > + I
JEE Main 25th Feb Shift 2 Chemistry Paper Question 14 solution

Q. 19. Which among the following species has unequal bond lengths?

(A) XeF4

(B) SiF4

(C) BF4-

(D) SF4

Answer: (D)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 15 solution

 

Q. 20. If which of the following orders the given complex ions are arranged correctly with respect to their decreasing spin only magnetic moment?

(i) [FeF6]3-

(ii) [Co(NH3)6]3+

(iii) [NiCl4]2-

(iv) [Cu(NH3)4]2+

(A) (ii)>(i)>(iii)>(iv)

(B) (iii)>(iv)>(ii)>(i)

(C) (ii)>(iii)>(i)>(iv)

(D) (i)>(iii)>(iv)>(ii)

Answer: (D)
[FeF6]3-: Fe3+ 3d5 → 5-unpaired electrons as F- is weak field legend
[Co(NH3)6]3+: Co3+ 3d6→ No-unpaired electron as NH3 is strong field light and causes pairing
[NiCl4]2-: Ni2+ 3d8 → 2-unpaired electrons
[Cu(NH3)4]2+: Cu2+ 3d9 → 1-unpaired electrons

 

SECTION B

Q. 1. Consider titration of NaOH solution versus 1.25 M oxalic acid solution. At the end point following burette readings were obtained.

(i) 4.5 mL (ii) 4.5 mL (iii) 4.4 mL (iv) 4.4 mL (v) 4.4 mL

If the volume of oxalic acid taken was 10.0 ml. then the molarity of the NaOH solution is ____M. (Rounded-off to the nearest integer)

Answer: 6
Eq. of NaOH = Eq. of oxalic acid
[NaOH] × 1 × 4.4 = 5/4 × 2 ×10
[NaOH] = 100 / 4 × 4.4 = 25 / 4.4 = 5.68
Nearest integer = 6 M

 

Q. 2. Electromagnetic radiation of wavelength 663 nm is just sufficient to ionize the atom of metal A. The ionization energy of metal A in kJ mol—1 is____. (Rounded off to the nearest integer)

[h=6.63×10-34Js, c = 3.00×108ms-1, NA=6.02×1023 mol-1]

Answer: 180
Energy required to ionize an atom of metal ‘A’ = hc / λ = hc / 663 nm for 1 mole atoms of ‘A’
Total energy required = NA × hc / λ

[6.023 × 1023  × 6.63 × 10-34  × 3  × 108]/[663 × 10-9]

= 6.023 × 3 × 1023-34+8+7
= 18.04 × 104 J/mol
= 180.4 kJ/mol
Nearest Integer = 180 kJ/Mol.

 

Q. 3. Copper reduces into NO and NO2 depending upon the concentration of HNO3 in solution. (Assuming fixed [Cu2+] and PNO=PNO2), the HNO3 concentration at which the thermodynamic tendency for reduction of into NO and NO2 by copper is same is 10x M.

The value of 2x is ______. (Rounded-off to the nearest integer)

[Given: 

E0(Cu2+ /Cu) = 0.34V, E0 (No3 / NO) = 0.96V, E0(No3 / NO2 = 0.79V and at 298 K, 

RT/F(2.303)= 0.059

Answer: 4
Anode
Cu(s) → Cu+2 + 2e
Cathode (1)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 7 solution
JEE Main 25th Feb Shift 2 Chemistry Paper Question 7 solution
JEE Main 25th Feb Shift 2 Chemistry Paper Question 7 solution
log (HNO3) = 2.16
[HNO3] = 102.16 = 10x
x = 2.16 ⇒ 2x = 4.32 ≈ 4

 

Q. 4. Five moles of an ideal gas at 293 K is expanded isothermally from an initial pressure of 2.1 MPa to 1.3 MPa against a constant external 4.3 MP(A) The heat transferred in this process is ____kJ mol-1. (Rounded-off of the nearest integer)

[Use R = 8.314 J mol-1 K-1]

Answer: 15
Moles (n) = 5
T = 293 K
Process = Iso T. → Irreversible
Pini = 2.1 M Pa
Pt = 1.3 M Pa
Pext = 4.3 mPa
Work = – Pext Δv

=−4.3×(5×293R / 1.3 − 5×293/2.1)

=−5×293×8.314×43(1/13 −1/21)

=(5×293×8.314×43×8)/(21×13)

= -15347.7049 J
= – 15.34 kJ
Isothermal process, so ΔU = 0
w = – Q
Q = 15.34 kJ / mol
So, answer is 15.

 

Q. 5. Among the following, the number of metal/s which can be used as electrodes in the photoelectric cell is _____(Integer answer).

Answer: (A)
Cs is used in photoelectric cells due to its very low ionization potential.

 

Q. 6. The rate constant of a reaction increases by five times on increasing temperature from 270 C to 520C. The value of activation energy in kJ mol-1 is ______.

(Rounded off to the nearest integer)

[R=8.314 J K-1 mol-1]

Answer: 52
JEE Main 25th Feb Shift 2 Chemistry Paper Question 7
Ea = 51524.96 J/mol
Ea = 51.524 kJ/mol
52 Ans.

 

Q. 7. If a compound AB dissociates to the extent of 75% in an aqueous solution, the molality of the solution which shows a 2.5 K rise in the boiling point of the solution is ______molal.

Answer: 3
AB → A+ + B
1 – α α α
α = 3 / 4
N = 2
i = [1+(2-1)α]
2.5 = [1+(2-1)3/4] × 0.52 × m

m = 2.5/0.52 × 7/4 = 10/3.64 = 2.747
m= 2.747≈ 3 mol/kg

 

Q. 8. The spin only magnetic moment of a divalent ion in aqueous solution (atomic number 29) is ____BM.

Answer: 2
29Cu+2 → [Ar]183d9
JEE Main 25th Feb Shift 2 Chemistry Paper Question 2
No. of unpaired e = 1
Magnetic moment = μ = √n(n + 2)
μ = √(1)(1 + 2) = √3B.M.
= 1.73 B.M

 

Q. 9. The number of compound/s given below which contain/s —COOH group is ______

(A) Sulphanilic acid

(B) Picric acid

(C) Aspirin

(D) Ascorbic acid

Answer: (A)
JEE Main 25th Feb Shift 2 Chemistry Paper Question 3 solution

 

Q. 10. The unit cell of copper corresponds to a face centered cube of edge length 3.596 Å with one copper atom at each lattice point. The calculated density of copper in kg/m3 is ______.

Answer: 9077
a = 3.596 Å

d = Z × GMM / NA × a3

d = (Z4 × 63.54 × 10-3)/ 6.022 × 1023 ×  (3.956 × 10-10)3

d = 0.9076 × 104 = 9076.2 kg/m3

MATHS 

SECTION A

Q. 1: If the curve x2 + 2y2 = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is:

(A) 𝜋/2 + tan–1(1/4)

(B) 𝜋/2 – 𝑡𝑎𝑛–1(1/4)

(C) 𝜋/2 + 𝑡𝑎𝑛–1(1/3)

(D) 𝜋/2 – 𝑡𝑎𝑛–1(1/3)

Answer: (A)
JEE Main Feb 2021 Solved Maths Paper
Using homogenization
x2 + 2y2 = 2(1) 2
⇒x2 + 2y2 = 2(x + y) 2
⇒x2 + 2y2 = 2x2 + 2y2 + 4xy
⇒x2 + 4xy = 0
for ax2 + 2hxy + by2 = 0, obtuse angle between lines θ is
tan θ = ±(2√(h2–ab))/(a+b)
⇒tan θ = ±4
⇒tan θ = –4
cot θ = -1/4
θ = cot–1(–1/4)
θ = π – cot–1 (1/4)
θ = π – (π/2– tan–1(1/4) )
θ = π/2 + tan-1(1/4)

 

Q. 2:

JEE Main Feb 2021 Maths Solved Question 8

(A) loge|x2 + 5x – 7| + c

(B) (1/4) loge |x2 + 5x – 7| + c

(C) 4 loge|x2 + 5x – 7| + c

(D) loge √(x2 + 5x – 7) + c

Answer: (C)
JEE Main Feb 2021 Maths Question 8 Solution

 

Q. 3: A hyperbola passes through the foci of the ellipse x2/25 + y2/16 = 1 and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is:

(A) x2/9 – y2/4 = 1

(B) x2/9 – y2/16 = 1

(C) x2 – y2 = 9

(D) x2/9 – y2/25 = 1

Answer: (B)
For ellipse, e1 = √(1–16/25)=3/5
Foci = (±3,0)
Let equation of hyperbola be x2/A2 – y2/B2 = 1, passes through (±3, 0)
A2 =9, A=3, e2=5/3
e22 = 1 + B2/A2
25/9 = 1 + B2/9 ⇒B2 = 16
x2/9 – y2/16 = 1

 

Q. 4: limn→∞[1/n + n/(n+1)2 + n/(n+2)2 + …….. + n/(2n-1)2] is equal to:

(A) 1

(B) 1/3

(C) 1/2

(D) 1/4

Answer: (C)
JEE Main Feb 2021 Maths Solved Question 10

 

Q. 5: In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarians and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are 35%, 20% and 10% respectively. A person is chosen from the group at random and is found to be suffering from chest disorder. The probability that the selected person is a smoker and non-vegetarian is:

(A) 7/45

(B) 8/45

(C) 14/45

(D) 28/45

Answer: (D)
Based on Bayes’ theorem
Probability = ((160/400×35/100))/((160/400×35/100)+(100/400×20/100)+(140/400×10/100) )
= 5600/9000
= 28/45

 

Q. 6: The following system of linear equations

2x + 3y + 2z = 9

3x + 2y + 2z = 9

x – y + 4z = 8

(A) does not have any solution

(B) has a unique solution

(C) has a solution (α, β, γ) satisfying α + β2 + γ3 = 12

(D) has infinitely many solutions

Answer: (B)
Determinant of given system = -20 ≠ 0
It has a unique solution.

 

Q. 7: The minimum value of f(x) = a^ax + a^(1-ax) where a, x ∈ R and a > 0, is equal to:

(A) a + 1/a

(B) a + 1

(C) 2a

(D) 2√a

Answer: (D)
Using AM ≥ GM inequality, we get

 

Q. 8: A function f(x) is given by f(x) = 5x/(5x+5), then the sum of the series f(1/20) + f(2/20) + f(3/20) + …… + f(39/20) is equal to:

(A) 19/2

(B) 49/2

(C) 39/2

(D) 29/2

Answer: (C)
f(x) = 5x/(5x + 5)….(i)
⇒ f(2–x) = 52–x/(52–x +5)
⇒f(2–x) = 5/(5x+5)……(ii)
Adding equation(i)and(ii)
f(x)+f(2–x)=1
f(1/20)+f(39/20)=1
f(2/20)+f(38/20)=1
……
…..
f(19/20) + f(21/20)=1
and f(20/20) = f(1) = 1/2
Therefore, f(1/20) + f(2/20) + f(3/20) + …… + f(39/20) = 19 + 1/2 = 39/2

 

Q. 9: A plane passes through the points A(1,2,3), B(2,3,1) and C(2,4,2). If O is the origin and P is (2,–1,1), then the projection of vector(OP) on this plane is of length:

(A) √(2/5)

(B) √(2/3)

(C) √(2/11)

(D) √(2/7)

Answer: (C)
A(1,2,3),B(2,3,1),C(2,4,2),O(0,0,0)
Equation of plane passing through A, B, C will be
JEE Main 2021 Feb Shift 2 Maths Solutions
(x – 1)(–1 + 4) – (y – 2)(–1 + 2) + (z – 3)(2 – 1) = 0
(x – 1)(3) – (y – 2)(1) + (z – 3)(1) = 0
3x – 3 – y + 2 + z – 3 = 0
3x – y + z – 4 = 0, is the required plane equation
Now, given O(0,0,0) & P(2,–1,1)
Plane is 3x – y + z – 4 = 0
Let O’ & P’ be the foot of perpendiculars.
JEE Main 2021 Feb Shift 2 Maths Solution
JEE Main 2021 Feb Shift 2 Maths Solved Paper

 

Q. 10: The contra positive of the statement “If you will work, you will earn money” is:

(A) If you will not earn money, you will not work

(B) You will earn money, if you will not work

(C) If you will earn money, you will work

(D) To earn money, you need to work

Answer: (A)
Contrapositive of p → q is ~q →~p
p: you will work
q: you will earn money
~q: you will not earn money
~p: you will not work
~q →~p: if you will not earn money, you will not work

 

Q. 11: The shortest distance between the line x – y = 1 and the curve x2 = 2y is:

(A) 1/2

(B) 0

(C) 1/(2√2)

(D) 1/√2

Answer: (C)
Shortest distance must be along common normal
JEE Main Feb 2021 Maths Solved Question 17
m1 (slope of line x–y = 1) = 1 ⇒slope of perpendicular line =–1
m2 = 2x/2 = x ⇒ m2 = h ⇒slope of normal = –1/h
–1/h=–1 ⇒h=1
So, the point is (1,1/2)
Therefore, Shortest distance (D) =|(1–1/2–1)/√(1+1)|=1/(2√2)

 

Q. 12: Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is:

(A) 1/5

(B) 2/9

(C) 97/297

(D) 122/297

Answer: (C)
Total cases
= 4C1 × 9 × 9 × 9 – 3C1 × 9 × 9
(as 4 digit number having 0 at thousands place have to be excluded)
For a number to have a remainder 2 when divided by 5 it’s unit digit should be 2 or 7
Case 1: when unit digit is 2
Number of four-digit number = 3C1×9×9 – 2C1×9
Case 2: when unit digit is 7
Number of four digits number = 8 × 9 × 9
So total number favorable cases = 3×92 – 2×9 + 8×92
Required Probability = ((3×9×9)–(2×9)+(8×9×9))/((4×93) – (3×92))
= 97/297

 

Q. 13: cosec[2 cot–1( 5) + cos–1(4/5) ] is equal to:

(A) 75/56

(B) 65/56

(C) 56/33

(D) 65/33

Answer: (B)
cosec[2 cot–1( 5) + cos–1(4/5) ]
JEE Main Feb 2021 Maths Solved Question 19

 

Q. 14: If 0 < x, y < π and cos x + cos y – cos (x + y) = 3/2, then sin x + cos y is equal to:

(A) (1+√3)/2

(B) (1–√3)/2

(C) √3/2

(D) 1/2

Answer: (A)
JEE Main Feb 2021 Maths Solved Question 20

 

Q. 15: If α, β∈ R are such that 1 – 2i (here i2 = –1) is a root of z2 + αz + β = 0, then (α – β) is equal to:

(A) 7

(B) -3

(C) 3

(D) -7

Answer: (D)
1-2i is a root of z2 + αz + β = 0.
(1-2i) 2 + α(1-2i)+β=0
⇒1-4-4i+α-2iα+β=0
⇒(α+β-3)-i(4+2α)=0
⇒α+β-3=0 & 4+2α=0
So, α=-2, β=5
Therefore, α-β=-7

 

Q. 16: If , then

(A) 1/(I2 + I4 ) , 1/(I3 + I5 ), 1/(I4 + I6) are in G.P.

(B) 1/(I2 + I4 ) , 1/(I3 + I5 ), 1/(I4 + I6) are in A.P.

(C) I2 + I4 , I3 + I5 , I4 + I6) are in A.P.

(D) I2 + I4 , I3 + I5 , I4 + I6) are in G.P.

Answer: (B)

In+2 + In = 1/(n+1)
I2 + I4 =1/3, I3 + I5 =1/4 and I4 + I6 =1/5
So, 1/(I2 + I4 ) , 1/(I3 + I5 ) and 1/(I4 + I6) are in A.P.

Q. 17: If for the matrix, A= AAT = I2, then the value of α4 + β4 is:

(A) 1

(B) 3

(C) 2

(D) 4

Answer: (A)
JEE Main Feb 2021 Shift 2 Maths Solutions

 

Q. 18: Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions from the set A to the set A × B. Then:

(A) y = 273x

(B) 2y = 91x

(C) y = 91x

(D) 2y = 273x

Answer: (B)
Number of elements in A = 3
Number of elements in B = 5
Number of elements in A × B = 15
Number of one-one function is x = 5 × 4 × 3
⇒x = 60
Number of one-one function is y = 15 × 14 × 13
⇒y = 15 × 4 × 14/4 × 13
⇒y = 60 × 7/2 × 13
⇒2y = (13)(7x)
⇒2y = 91x

 

Q. 19: Let α and β be the roots of x2 – 6x – 2 = 0. If an = αn – βn for n ≥ 1, then the value of (a10–2a8)/(3a9 ) is:

(A) 4

(B) 1

(C) 2

(D) 3

Answer: (C)
α and β be the roots of x2–6x–2=0.
So,
α2–6α–2=0⇒α2–2=6α
β2–6β–2=0⇒β2–2=6β
Now,
JEE Main Feb 2021 Maths Solved Question 15

 

Q. 20: Let A be a 3 × 3 matrix with det(A) = 4. Let Ri denote the ith row of A. If a matrix B is obtained by performing the operation R2→ 2R2 + 5R3 on 2A, then det(B) is equal to:

(A) 64

(B) 16

(C) 80

(D) 128

Answer: (A)
JEE Main Feb 2021 Maths Question 16 Solution

Section B

Q. 1: Let . If the area of the parallelogram whose adjacent sides are represented by the vectors a and a is 8√3 square units, then 

a.bis equal to ______.

Answer: 2
Area of parallelogram = 

|a × b|


(64)(3) = 16α2 + 64 + 16α2
⇒ α2 = 4
Now, 

a.b = 3 – α2 + 3
= 6 – α2
= 6 – 4
= 2

 

Q. 2: If the curve y = y(x) represented by the solution of the differential equation (2xy2 – y)dx + xdy = 0, passes through the intersection of the lines, 2x – 3y = 1 and 3x + 2y = 8, then |y(1)| is equal to ______.

Answer:1
Given,
(2xy2 – y)dx + xdy = 0
⇒ dy/dx + 2y2 – y/x = 0
⇒ (–1/y2) . dy/dx + (1/y) (1/x) = 2
Let, 1/y = z
(–1/y2) dy/dx = dz/dx
⇒dz/dx + z(1/x) = 2
Feb 2021 Maths JEE Main Paper Solutions
As it passes through P(2, 1)
[Point of intersection of 2x – 3y = 1 and 3x + 2y = 8]
Therefore, 2/1 = 4 + c
⇒c = –2
⇒x/y = x2 – 2
Put x = 1
1/y = 1 – 2 = –1
⇒y(1) = –1
⇒|y(1)| = 1

 

Q. 3: If limx→0 ax−(e4x−1) / ax(e4x−1) exists and is equal to b, then the value of a – 2b is ______.

Answer: 5

limx→0 ax−(e4x−1) / ax(e4x−1)

Applying L’Hospital Rule

limx→0 a−4e4x / a(e4x−1)+ax(4e4x) So for limit to exist,a=4
Applying L’Hospital Rule

limx→0 −16e4x / a(4e4x) + a(4e4x) + ax(16e4x)

(-16)/(4a+4a)=(–16)/32=–1/2=b
a-2b = 4–2((–1)/2) = 4+1 = 5

 

Q. 4: A line L passing through origin is perpendicular to the lines

Solved JEE Main Feb 2021 Maths Paper Questions

If the co-ordinates of the point in the first octant on L2 at the distance of √17 from the point of intersection of L and L1 are (a, b, c), then 18(a+b+c) is equal to ______.

Answer: 44
Solved JEE Main Maths Feb 2021 Paper Question
D.R. of L is parallel to (L1 × L2) ⇒ (-2, 3, -2)
Equation of l : x/2 = y/(–3) = z/2
Solving L & L1
(2λ, –3λ, 2λ) = (µ + 3, 2µ – 1, 2µ + 4)
µ = – 1 , λ = 1
So, intersection point P(2, –3, 2)
Let, Q(2ν + 3, 2ν + 3, ν + 2) be required point on L2
Solved JEE Main Maths Feb 2021 Exam Questions

 

Q. 5: A function f is defined on [–3,3] as

JEE Main Maths Feb 2021 Paper Question

where [x] denotes the greatest integer ≤ x. The number of points, where f is not differentiable in (–3,3) is ______.

Answer: (5)
Feb 2021 JEE Main Maths Paper Question
Points of non-differentiable in (–3, 3) are at x = –2, –1, 0, 1, 2.
i.e. 5 points.

 

Q. 6: A line is a common tangent to the circle (x – 3)2 + y2 = 9 and the parabola y2 = 4x. If the two points of contact (a, b) and (c, d) are distinct and lie in the first quadrant, then 2(a+c) is equal to ______.

Answer: 9
Sol. Circle: (x – 3)2+ y2= 9
Parabola: y2 = 4x
Let common tangent equation be y = mx + a/m
⇒y = mx + 1/m
⇒m2x – my + 1 = 0
The above line is also tangent to circle
(x – 3)2 + y2= 9
Therefore, the perpendicular from (3, 0) to line = 3
⇒|(3m2 – 0 + 1)/√(m2+m4 )| = 3
⇒(3m2 + 1)2 = 9(m2 + m4)
⇒m = ±1/√3
Tangent is
y = 1/√3x + √3 (it will be used)
=> m = 1/√3
or y = –1/√3x – √3 (rejected)
JEE Main Feb 2021 Maths Solved Question Problems
For Parabola, point of contact is (a/m2 , 2a/m)= (3, 2√3) = (c, d)
Solving Circle (x – 3)2 + y2 = 9 & line equation y = (1/√3) x + √3
(x – 3)2 + ((1/√3) x + √3)2 = 9
⇒x2 + 9 – 6x + (1/3)x2 + 3 + 2x = 9
⇒(4/3)x2 – 4x + 3 = 0
⇒x = 3/2=a
∴ 2(a + c) = 2(3/2+3)= 9

 

Q. 7: The value of is ______.

Answer: 19

x2-x-2=(x–2)(x+1)

Solved JEE Main Feb 2021 Maths Paper Question

 

Q. 8: If the remainder when x is divided by 4 is 3, then the remainder when (2020+x)2022 is divided by 8 is ______.

Answer: 1
Let x = 4k + 3
(2020 + x)2022
= (2020 + 4k + 3)2022
= (2024 + 4k – 1)2022
= (4A – 1)2022
=2022C0(4A)2022(–1)0 + 2022C1(4A)2021(–1)1 + ……+2022C2021(4A)1(–1)2021+ 2022C2022(4A)0(–1)2022
Which will be of the form 8λ+1
So, Remainder is 1.

 

Q. 9: If the curves x = y4 and xy = k cut at right angles, then (4k)6 is equal to ______.

Answer: 4
Feb 2021 JEE Main Maths Exam Question

 

Q. 10: The total number of two digit numbers ‘n’, such that 3n+7n is a multiple of 10, is ______.

Answer: 45
Feb 2021 JEE Main Maths Paper Solutions
Let n = 2t; t ∈ N
3n = 32t = (10 – 1)t
=10p + (–1)t
= 10p ± 1
If n = even then 7n + 3n will not be multiple of 10
So, if n is odd then only 7n + 3n will be a multiple of 10
Therefore, n = 11,13,15,………..,99
Therefore, the answer is 45

Jee Mains 25 February 2021 Shift-I Previous Year Paper

PHYSICS

SECTION A

Q. 1: Match List-I with List-II:

List-I List-II
(A)h (Planck’s constant) (i) [MLT–1]
(B)E (Kinetic energy) (ii) [ML2T–1]
(C)V (Electric potential) (iii) [ML2T–2]
(D)P (Linear momentum) (iv) [ML2I–1T–3]

Choose the correct answer from the options given below:

(A) (A) → (ii), (B) →(iii), (C) → (iv), (D) → (i)

(B) (A) →(i), (B) → (ii), (C) →(iv), (D) → (iii)

(C) (A) → (iii), (B) → (ii), (C) →(iv), (D) →(i)

(D) (A) → (iii), (B) → (iv), (C) →(ii), (D) →(i)

Answer: (A)
K.E. = [ML2T–2]
P (Linear momentum) = [MLT–1]
h (Planck’s constant) = [ML2T–1]
V (Electric potential) = [ML2T–3I–1]

 

Q. 2: The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lines 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while the 72nd division on circular scale coincides with the reference line. The radius of the wire is:

(A) 1.64 mm

(B) 1.80 mm

(C) 0.82 mm

(D) 0.90 mm

Answer: (C)
Least count. = pitch/no. of div.
= 1 mm/100
= 0.01 mm
+ve zero error = 8 × L.C. = +0.08 mm
Measured reading = 1mm + 72 × L.C.
= 1mm + 0.72 mm
= 1.72 mm
True reading = 1.72 – 0.08
= 1.64 mm
Radius = 1.64/2 = 0.82 mm

 

Q. 3: If the time period of a two meter long simple pendulum is 2 s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is:

(A) 2π2 ms–2

(B) 16 m/s2

(C) 9.8 ms–2

(D) π2 ms–2

Answer: (A)
T = 2π√(l/g)
T2 = 4π2l/g
g = 4π2l/T2
= 4π2×2/(2)2 = 2π2 ms–2

 

Q. 4: An α particle and a proton are accelerated from rest by a potential difference of 200 V. After this, their de Broglie wavelengths are λα and λp respectively. The ratio λp/λα is:

(A) 8

(B) 2.8

(C) 3.8

(D) 7.8

Answer: (B)
λ = h/p
= h/√(2mqV)
λp/λα = √(mαqα/mpqp)
= √(4×2/1×1)
= 2√2 = 2.8

 

Q. 5: Given below are two statements: one is labelled as Assertion A and the other is labelled as reason R.

Assertion A: The escape velocities of planet A and B are same. But A and B are of unequal masses.

Reason R: The product of their masses and radii must be same. M1R1 = M2R2

In the light of the above statements, choose the most appropriate answer from the options given below:

(A) Both A and R are correct but R is NOT the correct explanation of A

(B) A is correct but R is not correct

(C) Both A and R are correct and R is the correct explanation of A

(D) A is not correct but R is correct

Answer: (B)
Ve = escape velocity
ve = √(2GM/R)
So, for same ve, M1/R1 = M2/R2
A is true but R is false

 

Q. 6: A diatomic gas, having Cp = (7/2)R and Cv = (5/2)R, is heated at constant pressure. The ratio dU : dQ : dW

(A) 3 : 7 : 2

(B) 5 : 7 : 2

(C) 5 : 7 : 3

(D) 3 : 5 : 2

Answer: (B)
Since the gas is diatomic in nature and the process is isobaric, we have
Cp = (7/2)R
Cv = (5/2)R
dU = nCvdT
dQ = nCpdT
dW = nRdT
dU : dQ : dW
Cv : Cp : R
(5/2) R : (7/2) R : R
5 : 7 : 2

 

Q. 7: Statement I: A speech signal of 2 kHz is used to modulate a carrier signal of 1 MHz. The bandwidth requirement for the signal is 4 kHz.

Statement II: The side band frequencies are 1002 kHz and 998 kHz.

In the light of the above statements, choose the correct answer from the options given below:

(A) Both statement I and statement II are false

(B) Statement I is false but statement II is true

(C) Statement I is true but statement II is false

(D) Both statement I and statement II are true

Answer: (D)
Side band = (fc – fm) to (fc + fm)
= (1000 – 2) kHz to (1000 + 2) kHz
= 998 kHz to 1002 kHz
Band width = 2fm
= 2 ×2kHz
= 4 kHz
Both statements are true.

 

Q. 8: The current (i) at time t = 0 and t = ∞ respectively for the given circuit is:

Shift 1 Physics Solved Paper JEE Main 2021 For Feb 25

(A) 18E/55,5E/18

(B) 5E/18,18E/55

(C) 5E/18,10E/33

(D) 10E/33,5E/18

Answer: (C)
Shift 1 JEE Main 2021 Feb 25 Paper With Solutions Physics
At t = 0, inductor is open
Initial-state equivalent of the circuit shown in figure -1 is
Shift 1 Physics JEE Main 2021 Paper With Solutions Feb 25
Req = 6×9/(6+9) = 54/15
I (t = 0) = E×15/54 = 5E/18
At t = ∞, For steady state inductor is replaced by plane wire
Steady state equivalent of the circuit shown in figure-1 is
Shift 1 JEE Main Feb 25 2021 Physics Paper With Solution
Equivalent circuit diagram is given by
Shift 1 Feb 25 JEE Main 2021 Physics Papers With Solutions
Req =1×4/(1+4) + 5×5/(5+5)
= 4/5 + 5/2
= (8 + 25)/10
= 33/10
I = E/Req = 10E/33

 

Q. 9: Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively.

If TA and TB are the time periods of A and B respectively then the value of TB – TA:

Shift 1 JEE Main 2021 Solved Paper Physics Feb 25

[Given: Radius of earth = 6400 km, mass of earth = 6×1024 kg]

(A) 4.24× 102 s

(B) 3.33 × 102 s

(C) 1.33 × 103 s

(D) 4.24 × 103 s

Answer: (C)
Feb 25 Shift 1 JEE Main 2021 Solved Paper For Physics
V = √(GMe/r)

T = 2​𝜋r/ (√(GMe/r)) = 2​𝜋r/ (√(r/GMe))

T =√(4𝜋2r3/GMe) = √(4𝜋2r3/GMe)
T2 – T1 = √(4𝜋2(8000×103)3/G×6×1024 ) – √(4𝜋2(7000×103)3/G×6×1024 )
≅ 1.33 ×103 s

 

Q. 10: An engine of a train, moving with uniform acceleration, passes the signal post with velocity u and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is:

(A) √(v2 – u2)/2

(B) (v – u)/2

(C) √(v2 + u2)/2

(D) (u + v)/2

Answer: (C)
Feb 25 Shift 1 JEE Main 2021 Solved Paper For Physics
a = uniform acceleration
u = velocity of first compartment
v = velocity of last compartment
l = length of train
v2 = u2 + 2as (3rd equation of motion)
v2 = u2 + 2al …..(1)
v2 middle = u2 + 2al/2
∴ v 2middle = u2 + al ….(2)
From equation (1) and (2)
v2middle = u2 + (v2 – u2)/2
= (v2 + u2)/2
∴ vmiddle = √(v2 + u2)/2

 

Q. 11: A 5V battery is connected across the points X and Y. Assume D1 and D2 to be normal silicon diodes. Find the current supplied by the battery if the +ve terminal of the battery is connected to point X.

Shift 1 Physics JEE Main 2021 Paper With Solutions For Feb 25

(A) ~0.86 A

(B) ~0.5 A

(C) ~0.43 A

(D) ~1.5 A

Answer: (C)
Since silicon diode is used so 0.7 Volt is drop across it, only D1 will conduct so current through cell.
I = (5 – 0.7)/10 = 0.43 A

 

Q. 12: A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force F1. Now a spherical cavity of radius R/2 is made in the sphere (as shown in figure) and the force becomes F2. The value of F1: F2 is:

Shift 1 Physics JEE Main 2021 Paper Solutions For Feb 25

(A) 41 : 50

(B) 36 : 25

(C) 50 : 41

(D) 25 : 36

Answer: (A)
Gravitational field intensity g1 = GM/(3R)2 = GM/9R2 …(1)
Gravitational field intensity g2 = GM/9R2 – G(M/8)/(5R/2)2
= GM/9R2 – GM/R250
= (41/9×50) GM/R2….(2)
Implies , g1/g2 = 41/50
⇒ F1/F2 = mg1/mg2 = 41/50

 

Q. 13: A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m/s. The zero of the metre scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is:

(A) 13 cm

(B) 14.8 cm

(C) 16.6 cm

(D) 18.4 cm

Answer: (B)
λ = v/f
= 336/504 = 66.66cm
λ/4 = l + e = l + 0.3d
= l + 1.8
16.66 = l + 1.8 cm
l = 14.86 cm

 

Q. 14: A proton, a deuteron and an α particle are moving with the same momentum in a uniform magnetic fiel(D) The ratio of magnetic forces acting on them is _______ and their speeds are in the ratio______.

(A) 2 : 1 : 1 and 4 : 2 : 1

(B) 1 : 2 : 4 and 2 : 1 :1

(C) 1 : 2 : 4 and 1 : 1 : 2

(D) 4 : 2 : 1 and 2 : 1 : 1

Answer: (A)
As v = p/m & F = qvB
∴ F = qpB/m
F1 = qpB/m, v1 = p/m
F2 = qpB/2m, v2 = p/2m
F3 = 2qpB/4m, v3 = p/4m
F1 : F2 : F3 & V1 : V2 : V3
1 : ½ : ½  & 1 : ½ :¼
2 : 1 : 1 & 4 : 2 : 1

 

Q. 15: Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: When a rod lying freely is heated, no thermal stress is developed in it.

Reason R: On heating, the length of the rod increases

In the light of the above statements, choose the correct answer from the options given below:

(A) A is true but R is false

(B) Both A and R are true and R is the correct explanation of A

(C) Both A and R are true but R is NOT the correct explanation of A

(D) A is false but R is true

Answer: (C)
If a rod is free and it is heated then there is no thermal stress produced in it.
The rod will expand due to increase in temperature.
So, both A & R are true.

 

Q. 16: In an octagon ABCDEFGH of equal side, what is the sum of

Physics JEE Main 2021 Paper With Solutions For Shift 1 Feb 25

Answer: (A)

Physics Feb 25 Solved Paper JEE Main 2021 For Shift 1
Physics Solution Feb 25 Paper Shift 1 JEE Main 2021

 

Q. 17: Two radioactive substances X and Y originally have N1 and N2 nuclei respectively. Half-life of X is half of the half-life of Y. After three half-lives of Y, numbers of nuclei of both are equal. The ratio N1/N2 will be equal to:

(A) 8/1

(B) 1/8

(C) 3/1

(D) 1/3

Answer: (A)
After n half-life no of nuclei undecayed = No/2n
Given, t(1/2)x= t(1/2y)/2
So 3 half-life of y = 6 half-life of x
Given, Nx = Ny after 3t(½)y
N1/26 = N2/23
N1/N2 = 26/23 = 23= 8/1

 

Q. 18: The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

Physics Feb 25 Shift 1 JEE Main 2021 Solved Paper

(A) 0.8 H and 250 μF

(B) 0.8 H and 150 μF

(C) 1.33 H and 250 μF

(D) 1.33 H and 150 μF

Answer: (A)
Physics JEE Main 2021 Feb 25 Solved Papers Shift 1
Since key is open, circuit is series L-C-R circuit
15 = irms (60)
∴irms = ¼ A
Now, 20 = ¼ XL = ¼ (ωL)
∴ L = 4/5 = 0.8 H
& 10 = ¼ 1/(100C)
C = (1/4000) F
= 250 μF

 

Q. 19: Two coherent light sources having intensities in the ratio 2x produce an interference pattern. The ratio (Imax – Imin)/(Imax + Imin) will be:

(A) 2√(2x)/(x + 1)

(B) √(2x)/(2x + 1)

(C) 2√(2x)/(2x + 1)

(D) √(2x)/(x + 1)

Answer: (C)
Let I1 = 2x
I2 = 1
Imax = (√I1 + √I2)2
Imin = (√I1 – √I2)2

(Imax-Imin)/ (Imax+ Imin) = [(√2x + 1)2 -(√2x – 1)2] / [(√2x + 1)2 +​(√2x – 1)2]

= 4√(2x)/(2 + 4x)
= 2√(2x)/(2x + 1)

 

Q. 20: Magnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and 0.2 m from the centre are in the ratio 8 : 1. The radius of coil is ______

(A) 0.15 m

(B) 0.2 m

(C) 0.1 m

(D) 1.0 m

Answer: (C)
Physics JEE Main Feb 25 2021 Paper Solution For Shift 1
B = μ0NiR2/2(R2 + x2)3/2
at x1 = 0.05m, B1 = μ0NiR2/2(R2 + (0.05)2)3/2
at x2 = 0.2m, B2 = μ0NiR2/2(R2 + (0.2)2)3/2
B1/B2 = (R2 + 0.04)3/2/(R2 + 0.0025)3/2
(8/1)2/3 = (R2 + 0.04)/(R2 + 0.0025)
4 (R2 + 0.0025) = R2 + 0.04
3R2 = 0.04 – 0.01
R2 = 0.03/3 = 0.01
R = √0.01 = 0.1 m

Section – B

Q. 1: The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as U= α/r10– β/r5 – 3. Where, a and b are positive constants. The equilibrium distance between two atoms will (2α/β)a/(B) Where a =_______

Answer: 1
F = -dU/dr
F = -[-10α/r11 + 5β/r6]
for equilibrium, F = 0
10α/r11 = 5β/r6
2α/β = r5
r = (2α/β)1/5
a = 1

 

Q. 2: A small bob tied at one end of a thin string of length 1m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position is ______ m/s. (take g = 10 m/s2)

Answer: 5
Shift 1 Physics 2021 JEE Main Solution Paper For Feb 25
By conservation of energy,
v2min = V2 – 4gl ….(1)
Tmax = mg + mv2/l ….(2)
Tmin = mv2min/l – mg ….(3)
from equation (1) and (3)
Tmin = (m/l) (v2 – 4gl) – mg
Tmax/Tmin = (v2/l + g)/(v2/l – 5g)
5/1 = (v2/1 + 10)/ (v2/1 – 50)
5v2 – 250 = v2 + 10
v2 = 65 ….(4)
from equation (4) and (1)
v2min = 65 – 40 = 25
vmin = 5 m/s

 

Q. 3: In a certain thermodynamic process, the pressure of a gas depends on its volume as kV3. The work done when the temperature changes from 1000 C to 3000 C will be ____ nR, where n denotes the number of moles of a gas.

Answer: 50
P = kv3
pv–3 = k
x = –3
w = nR(T1 – T2)/(x – 1)
= nR(100-300)/(-3 -1)
= nR(-200)/-4
= 50nR

 

Q. 4: In the given circuit of potentiometer, the potential difference E across AB (10 m length) is larger than E1 and E2 as well. For key K1 (closed), the jockey is adjusted to touch the wire at point J1 so that there is no deflection in the galvanometer. Now the first battery (E1) is replaced by the second battery (E2) for working by making K1 open and E2 close(D) The galvanometer gives then null deflection at J2. The value of E1/E2 is the smallest fraction of a/b, Then the value of a is ____.

Shift 1 Physics Solved Papers JEE Main 2021 Feb 25

Answer: 1
E1/E2 = l1/l2
= 3×100 cm + (100 – 20)cm)/(7×100 cm + 60 cm)
= 380/760
= ½
= a/b
a = 1

 

Q. 5: The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of a convex lens is ______ cm.

Answer: 15
1/v – 1/u = 1/f …(1)
m = v/u ….(2)
from (1) and (2) we get
m = f/(f + u)
Given conditions
m1 = -m2
f/(f – 10) = -f/(f – 20)
f – 20 = –f + 10
2f = 30
f = 15 cm

 

Q. 6: A transmitting station releases waves of wavelength 960 m. A capacitor of 256 μF is used in the resonant circuit. The self inductance of coil necessary for resonance is _____ × 10–8H.

Answer: 10
At resonance
ωr = 1/√(Lc)
∴ 2πf = 1/√(Lc)
∴ 4π2c22 = 1/Lc
∴4π2×3×108×3×108/960×960 = 1/L×2.56×10-6
L = 375×960/10-6×4×π2×9×1016 = 103/1010
= 10–7 H
= 10 × 10–8 H

 

Q. 7: The electric field in a region is given by . The ratio of flux of reported field through the rectangular surface of area 0.2 m2 (parallel to y-z plane) to that of the surface of area 0.3 m2(parallel to x-z plane) is a : 2, where a = ________

[Here i, j and k are unit vectors along x, y and z-axes respectively]

Answer: 1

Shift 1 Physics JEE Main 2021 Solution Paper For Feb 25
Therefore, a = 1

 

Q. 8: 512 identical drops of mercury are charged to a potential of 2 V each. The drops are joined to form a single drop. The potential of this drop is ____ V.

Answer: 128
Let charge on each drop = q
Radius = r
V = kq/r
2 = kq/r
Radius of bigger
4πR3/3 = 512 × (4/3) πr3
R = 8r
V = k(512)q/R = (512/8) (kq/r)
= (512/8) × 2
= 128 V

 

Q. 9: A monatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with a velocity 30 m/s. If the container is suddenly stopped then the change in temperature of the gas (R=gas constant) is x/3R. Value of x is ______.

Answer: 3600
ΔKE = ΔU
ΔU = nCVΔT
½ mv2 = (3/2) nRΔT
mv2/3nR = ΔT
4×(30)2/3×1×R = ΔT
ΔT = 4×(30)2/3×1×R
x/3R = 1200/R
x = 3600

 

Q. 10: A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V = 3t volt. (where t is in second). If the voltage is applied when t = 0, then the energy stored in the coil after 4 s is _______ J.

Answer: 144
L di/dt = ε
= 3t
L ∫di = 3 ∫t dt
Li = 3t2/2
i = 3t2/2L
Energy stored in the coil, E = ½ Li2
= ½ L (3t2/2L)2
= ½ × 9t4/4L
= 9/8 × (4)4/2
= 144 J

Chemistry

SECTION A

Q. 1. The hybridization and magnetic nature of [Mn(CN)6]4– and [Fe(CN)6]3–, respectively are:

(A) d2sp3 and paramagnetic

(B) sp3d2 and paramagnetic

(C) d2sp3 and diamagnetic

(D) sp3d2 and diamagnetic

Answer: (A)
JEE Main 25th Feb Shift 1 Chemistry Paper Question 17 solution

 

Q. 2. Identify A and B in the chemical reaction.

JEE Main 25th Feb Shift 1 Chemistry Paper Question 18

Answer: (D)
JEE Main 25th Feb Shift 1 Chemistry Paper Question 18 solution

 

Q. 3. Compound(s) which will liberate carbon dioxide with sodium bicarbonate solution is/are:

JEE Main 25th Feb Shift 1 Chemistry Paper Question 19

(A) 2 and 3 only

(B) 1 only

(C) 2 only

(D) 3 only

Answer: (A)
Compounds that are more acidic than H2CO3, gives CO2 gas in reaction with NaHCO3. Compound B i.e. Benzoic acid and compound C i.e. picric acid both are more acidic than H2CO3.

 

Q. 4. Ellingham diagram is a graphical representation of:

(A) ΔG vs T

(B) (ΔG – TΔS) vs T

(C) ΔH vs T

(D) ΔG vs P

Answer: (A)
Ellingham diagram tells us about the spontaneity of a reaction with temperature.

 

Q. 5. Which of the following equations depicts the oxidizing nature of H2O2?

(A) Cl2 + H2O2 → 2HCl + O2

(B) KlO4 + H2O2 → KlO3 + H2O + O2

(C) 2l + H2O2 + 2H+ → I2 + 2H2O

(D) I2 + H2O2 + 2OH → 2I + 2H2O + O2

Answer: (C)
2l + H2O2 + 2H+ → I2 + 2H2O
Oxygen reduces from –1 to –2
So, its reduction will take place. Hence it will behave as oxidising agent or it shows
oxidising nature.

 

Q. 6. In Freundlich adsorption isotherm at moderate pressure, the extent of adsorption (x/m) is directly proportional to Px. The value of x is:

(A) ∞

(B) 1

(C) zero

(D) 1/n

Answer: (D)
x / m = px
The formula is x / m = px
Hence, x= 1 / n. The value of ‘n’ is any natural number.

 

Q. 7. According to molecular orbital theory, the species among the following that does not exist is:

(A) He2

(B) He2+

(C) O22-

(D) Be2

Answer: (D)
B.O. of Be2 is zero, so it does not exist.

 

Q. 8. In which of the following pairs, the outermost electronic configuration will be the same?

(A) Fe2+ and Co+

(B) Cr+ and Mn2+

(C) Ni2+ and Cu+

(D) V2+ and Cr+

Answer: (B)
Cr+ → [Ar]3d5
Mn2+ → [Ar]3d5

 

Q. 9. Given below are two statements:

Statement-I: An allotrope of oxygen is an important intermediate in the formation of reducing smog.

Statement-II: Gases such as oxides of nitrogen and Sulphur present in the troposphere contribute to the formation of photochemical smog.

(A) Statement I and Statement II are true

(B) Statement I is true about Statement II is false

(C) Both Statement I and Statement II are false

(D) Statement I is false but Statement II is true

Answer: (C)
Reducing smog acts as a reducing agent and the reducing character is due to presence of sulphur dioxide and carbon particles.

 

Q. 10. The plots of radial distribution functions for various orbitals of hydrogen atom against ‘r’ are given below:

JEE Main 25th Feb Shift 1 Chemistry Paper Question 13
JEE Main 25th Feb Shift 1 Chemistry Paper Question 13

(A) (4)

(B) (2)

(C) (1)

(D) (3)

Answer: (A)
3s orbital
Number of radial nodes = n – λ – 1
For 3s orbital n = 3, λ = 0
Number of radial nodes = 3 – 0 – 1 = 2
It is correctly represented in graph of option 4

 

Q. 11. Identify A in the given chemical reaction.

Answer: (D)


JEE Main 25th Feb Shift 1 Chemistry Paper Question 5 solution
Aromatization reaction or hydroforming reaction.

 

Q. 12. Given below are two statements:

Statement-I: CeO2 can be used for oxidation of aldehydes and ketones.

Statement-II: Aqueous solution of EuSO4 is a strong reducing agent.

(A) Statement I is true, statement II is false

(B) Statement I is false, statement II is true

(C) Both Statement I and Statement II are false

(D) Both Statement I and Statement II are true

Answer: (D)
CeO2 can be used as an oxidizing agent like seO2. Similarly, EuSO4 is used as a reducing agent.

 

Q. 13. The major product of the following chemical reaction is:

JEE Main 25th Feb Shift 1 Chemistry Paper Question 7

(A) (CH3CH2CO)2O

(B) CH3CH2CHO

(C) CH3CH2CH3

(D) CH3CH2CH2OH

Answer: (B)
JEE Main 25th Feb Shift 1 Chemistry Paper Question 7 solution

Q. 14. Complete combustion of 1.80 g of an oxygen-containing compound (CxHyOz) gave 2.64 g of CO2 and 1.08 g of H2O. The percentage of oxygen in the organic compound is:

(A) 63.53

(B) 51.63

(C) 53.33

(D) 50.33

Answer: (C)
n(CO2) = 2.64 / 44 = 0.06
nc = 0.06
weight of carbon = 0.06 × 12 = 0.72 gm
n(H2O) = 1.08 / 1.8 = 0.06
nH = 0.06 × 2 = 0.12
weight of H = 0.12 gm
∴ Weight of oxygen in CxHyOz
= 1.8 – (0.72 + 0.12)
= 0.96 gram
% weight of oxygen = 0.96/18 × 100 = 53.3%

 

Q. 15.The correct statement about B2H6 is:

(A) All B–H–B angles are 120°.

(B) Its fragment, BH3, behaves as a Lewis base.

(C) Terminal B–H bonds have less p-character when compared to bridging bonds.

(D) The two B–H–B bonds are not of the same length.

Answer: (C)
The terminal bond angle is greater than that of bridge bond angle
Bond angle ∝ S-character

α  1/ pcharacter

 

Q. 16. Which of the glycosidic linkage galactose and glucose is present in lactose?

(A) C-1 of glucose and C-6 of galactose

(B) C-1 of galactose and C-4 of glucose

(C) C-1 of glucose and C-4 of galactose

(D) C-1 of galactose and C-6 of glucose

Answer: (B)
JEE Main 25th Feb Shift 1 Chemistry Paper Question 14

 

Q. 17. Which one of the following reactions will not form acetaldehyde?

Answer: (A)
JEE Main 25th Feb Shift 1 Chemistry Paper Question 14 solution

 

Q. 18. Which of the following reactions will not give p-amino azobenzene?

JEE Main 25th Feb Shift 1 Chemistry Paper Question 16

(A) 2 only

(B) 1 and 2

(C) 3 only

(D) 1 only

Answer: (A)
JEE Main 25th Feb Shift 1 Chemistry Paper Question 16 solution

 

Q. 19. The solubility of AgCN in a buffer solution of pH = 3 is x. The value of x is: [Assume: No cyano complex is formed; Ksp(AgCN) = 2.2 × 10–16 and Ka (HCN) = 6.2 × 10–10]

(A) 0.625 × 10-6

(B) 1.6 × 10-6

(C) 2.2 × 10-16

(D) 1.9 × 10-5

Answer: (D)
Let solubility is x
AgCN ⇌ Ag+ + CNKsp = 2.2 × 10–16
x x
H+ + CN ⇌ HCN

K = 1/ Ka

K= 1/ 6.2 × 10–10

Ksp × 1/ka = [Ag+] [CN] × [HCN] / [H+][CN]
2.2 × 10-16 × 1 / 6.2 × 10-10 = [S][S] / 10-3
S2 = 2.2 / 6.2 × 10-9
S2 = 3.55 × 10–10
S = √3.55 × 10–10
S = 1.88 × 10–5 ⇒ 1.9 × 10–5

 

Q. 20. Which statement is correct?

(A) Buna-S is a synthetic and linear thermosetting polymer

(B) Neoprene is an addition copolymer used in plastic bucket manufacturing

(C) Synthesis of Buna-S needs nascent oxygen

(D) Buna-N is a natural polymer

Answer: (C)
Synthesis of Buna-S needs nascent oxygen.

SECTION B

Q. 1. A car tire is filled with nitrogen gas at 35 psi at 27°C. It will burst if pressure exceeds 40 psi. The temperature in °C at which the car tyre will burst is ______. (Rounded-off to the nearest integer)

Answer: 69.85°C ≃ 70°C
P1 / T1 = P2 / T2
35 / 300 = 40 / T2
T2 = 40 × 300 / 35
= 342.86 K
= 69.85°C ≃ 70°C

 

Q. 2. The reaction of cyanamide, NH2CN(s) with oxygen was run in a bomb calorimeter and ΔU was found to be –742.24 kJ mol–1. The magnitude of ΔH298 for the reaction NH2CN (s) + 3/2 O2 (g) → N2 (g) + O2 (g) + H2O(l) is______kJ. (Rounded off to the nearest integer). [Assume ideal gases and R = 8.314 J mol–1 K–1]

Answer: 741 kJ/mol
NH2CN(s) + 3/2 O2(g) → N2(g) + CO2(g) + H2O(λ)
Δng = (1 + 1) – 3/2 = ½
ΔH = ΔU + Δng RT
= -742.24 + ½ × 8.314 × 298 / 1000
= -742.24 + 1.24
= 741 kJ/mol

 

Q. 3. The ionization enthalpy of Na+ formation from Na(g) is 495.8 kJ mol–1, while the electron gain enthalpy of Br is –325.0 kJ mol–1. Given the lattice enthalpy of NaBr is –728.4 kJ mol–1. The energy for the formation of NaBr ionic solid is (–)_____ × 10–1 kJ mol–1.

Answer: 5576 kJ
Na(s) → Na+(g) ΔH = 495.8
½ Br2(λ) + e → Br(g) ΔH = 325
Na+(g) + Br(g) → NaBr(s) ΔH = –728.4
Na(s) + ½ Βr2(λ) → NaBr(s). ΔH =?
ΔH = 495.8 – 325 – 728.4
–557.6 kJ = –5576 × 10–1 kJ

 

Q. 4. Consider the following chemical reaction.

Answer: 7
JEE Main 25th Feb Shift 1 Chemistry Paper Question 6 solution
All carbon atoms in benzaldehyde are sp2 hybridized.

 

Q. 5. Among the following, the number of halide(s) which is/are inert to hydrolysis is ______.

(A) BF3

(B) SiCl4

(C) PCl5

(D) SF6

Answer: 1
Due to crowding, SF6 is not hydrolyzed.

 

Q. 6. In basic medium CrO42– oxidizes S2O32– to form SO24 and itself changes into Cr(OH)4–. The volume of 0.154 M CrO42– required to react with 40 mL of 0.25 M S2O32– is ______ mL. (Rounded-off to the nearest integer)

Answer: 173 mL
17H2O + 8CrO4 + 3S2O3 → 6SO4 + 8Cr(OH)4– + 2OH
Applying mole-mole analysis
0.154 × v / 8 = 40 × 0.25 / 3
V = 173 mL

 

Q. 7. 1 molal aqueous solution of an electrolyte A2B3 is 60% ionise(D) The boiling point of the solution at 1 atm is _____ K. (Rounded-off to the nearest integer). [Given Kb for (H2O) = 0.52 K kg mol–1]

Answer: 375 K
A2B3 → 2A+3 + 3B–2
No. of ions = 2 + 3 = 5
wi = 1 + (n – 1) ∝
= 1 + (5 – 1) × 0.6
= 1 + 4 × 0.6 = 1 + 2.4 = 3.4
ΔTb = Kb × m × i
= 0.52 × 1 × 3.4 = 1.768°C
ΔTb = (Tb)solution – [(TbH2O)]solution
1.768 = (Tb)solution – 100
(Tb)solution = 101.768 °C
= 375 K

 

Q. 8. Using the provided information in the following paper chromatogram:

JEE Main 25th Feb Shift 1 Chemistry Paper Question 10

The calculated Rf value of A ______ × 10–1.

Answer: 4

Rr = Distance Travelled By Solvent / Distance Travelled By Compound

On chromatogram distance travelled by compound is → 2 cm
Distance travelled by solvent = 5 cm
So Rf = 2 / 5 = 4 × 10–1 = 0.4

 

Q. 9. For the reaction, aA + bB → cC + dD, the plot of log k vs 1/T is given below:

JEE Main 25th Feb Shift 1 Chemistry Paper Question 3

The temperature at which the rate constant of the reaction is 10–4s–1 is ________ K. [Rounded off to the nearest integer)

[Given: The rate constant of the reaction is 10–5 s–1 at 500 K]

Answer: 526 K

log10 K = log10 A – E0/2.303RT

Slope = E0/2.203 = -10000

log10 K1/K2 = ​E0/2.203 × (1/T1 – 1/T2)

log10 10-4/10-5 = 1000 × (1/500 -1/T)

1 = 1000 × (1/500 -1/T)

1/10000 = 1/500 = 1/T

1/T = 1/500 = 1/10000

1/T = 20-1 / 10000 = 19/10000

T = 10000 / 19
T= 526 K

 

Q. 10. A 0.4g mixture of NaOH, Na2CO3 and some inert impurities was first titrated with N / 10HCl using phenolphthalein as an indicator, 17.5 mL of HCl was required at the end point. After this methyl orange was added and titrate(D) 1.5 mL of the same HCl was required for the next end point. The weight percentage of Na2CO3 in the mixture is ______. (Rounded-off to the nearest integer)

Answer: 3%
1st end point reaction
NaOH + HCl → NaCl + H2O
nf = 1
NaCO3 + HCl → NaHCO3
nf = 1
Eq of HCl used = n(NaOH) × 1 + n(Na2CO3) × 1
17.5 × 1/10 × 10-3 = n(NaOH) + n(Na2CO3)

2nd end point
NaHCO3 + HCl → H2CO3
1.5 × 1/10 × 10-3 = n(NaHCO3) × 1 = n(NaHCO3)
0.15 mmol = n(Na2CO3)
0.15 = n(Na2CO3)

W(Na2CO3) = 0.15×106×10-3 × 100 × 10
= 3 × 106 × 10–2
= 3 × 1.06 = 3.18%

Maths

SECTION A

Q. 1: A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A, with uniform spee(D) At that point, the angle of depression of the boat with the man’s eye is 30° (Ignore man’s height). After sailing for 20 seconds towards the base of the tower (which is at the level of water), the boat has reached point B, where the angle of depression is 45°. Then the time taken (in seconds) by the boat from B to reach the base of the tower is :

(A) 10(√3-1)

(B) 10√3

(C) 10

(D) 10(√3+1)

Answer: (D)
JEE MAIN 2021 Feb 25 Shift 1 Solution 4
x + y = √3h ….…….(1)
Also,
h/y = tan 45o
h = y …….(2)
put in (1)
x + y = √3y
x = (√3 – 1)y
x/20=v (speed)
Therefore, time taken to reach
Foot from B
= y/V
= x/(√3-1)x . 20
= 10 (√3 + 1)

 

Q. 2:

JEE MAIN 2021 Feb 25 Shift 1 Solution 5

(A) xyz = 4

(B) xy – z = (x + y)z

(C) xy + yz + zx = z

(D) xy + z = (x+y)z

Answer: (D)
JEE MAIN 2021 Feb 25 Shift 1 Solved Question 5

 

Q. 3: The equation of the line through the point (0,1,2) and perpendicular to the line (x-1)/2 = (y+1)/3 = (z-1)/-2 is :

(A) ​x/-3 = (y-1)/ 4 = (z-2)/3

(B) x/3 = (y-1)/ 4 = (z-2)/3

(C) x/3 = (y-1)/ -4 = (z-2)/3

(D) x/3 = (y-1)/ 4 = (z-2)/-3

Answer: (A)

(x-1)/2 = (y+1)/3 = (z-1)/-2 =λ
Any point on this line (2λ + 1, 3λ – 1, -2λ + 1)
Direction ratio of given line d1 ≡ (2, 3, -2)
Direction ratio of the line to be found  d2 ≡(2λ+1,3λ−2,−2λ−1)

 ∴ d1 d2 = 0

λ = 2 / 17
Direction ratio of line (21, -28, -21) (3, -4, -3) ≡ (-3, 4, 3)

 

Q. 4: The coefficients a,b and c of the quadratic equation, ax2 + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is :

(A) 1/54

(B) 1/72

(C) 1/36

(D) 5/216

Answer: (D)
ax2 + bx + c = 0
a,b,c ∈ {1,2,3,4,5,6}
n(s) = 6 × 6 × 6 = 216
D=0 ⇒ b2 = 4ac
ac = b2/4, If b = 2, ac = 1 ⇒ a = 1,c = 1
If b = 4, ac = 4 ⇒ a = 1, c = 4
a = 4, c = 1
a = 2, c = 2
If b = 6, ac = 9 ⇒ a = 3, c = 3
Therefore, probability = 5/216

 

Q. 5: Let α be the angle between the lines whose direction cosines satisfy the equations l +m – n = 0 and l2 + m2 – n2 = 0. Then the value of sin4 α + cos4 α is :

(A) 3/4

(B) 1/2

(C) 5/8

(D) 3/8

Answer: (C)
Given that l+m=n ….(1)
l2 + m2 – n2 = 0 ….(2)
Squaring equation (1)
l2 + m2 + 2lm = n2 ….(3)
From equations (2) and (3)
lm=0 ⇒ l = 0 or m = 0
Case (1) : l = 0
⇒ m=n
⇒ l2 + m2 + n2 = 0
⇒ m=n = ±1/(√2 )
∴(l,m,n) = (0, 1/√2, 1/√2) or (0, -1/√2, -1/√2)
Case (2): m = 0
⇒ l = n
⇒ l2 + m2 + n2 = 0
JEE MAIN 2021 Feb 25 Shift 1 Solution 2

 

Q. 6: The value of the integralJEE MAIN 2021 Feb 25 Shift 1 Solution 3

(where c is a constant of integration)

(A) 1/18[9 – 2 sin6θ – 3 sin4θ – 6 sin2θ ](3/2) + c

(B) 1/18[11 – 18 sin2θ + 9 sin4θ – 2 sin6θ ](3/2) + c

(C) 1/18[11 – 18 cos2θ + 9 cos4θ – 2 cos6θ ](3/2) + c

(D) 1/18[9 – 2 cos6θ – 3 cos4θ – 6 cos2θ ](3/2) + c

Answer: (C)
Using trig identities, sin2A = 2sinAcosA and 1-cos2A = 2sin2A
JEE MAIN 2021 Feb 25 Shift 1 Solved Question 3

 

Q. 7: The statement A→ (B → A) is equivalent to:

(A) A → (A ᐱ B)

(B) A → (A ᐯ B)

(C) A → (A → B) 

(D) A → (A ↔ B)

Answer: (B)
A → (B → A)
⇒ A → (∼ B ᐯ A)
⇒ ∼ A ᐯ (∼ B ᐯ A)
⇒ ∼ B ᐯ (∼ A ᐯ A)
⇒ ∼ B ᐯ t
= t (tautology)
From options:
(B) A → (A ᐯ B)
⇒ ∼ A ᐯ (A ᐯ B)
⇒ (∼ A ᐯ A) ᐯ B
⇒ t ᐯ B
⇒ t

 

Q. 8: The integer k, for which the inequality x2 – 2(3k – 1)x + 8k2 – 7 >0 is valid for every x in R is :

(A) 3

(B) 2

(C) 4

(D) 0

Answer: (A)
D < 0
(2(3k-1))2 – 4(8k2 – 7) < 0
4(9k2 – 6k + 1) – 4(8k2 – 7) < 0
k2 – 6 k + 8 < 0
(k–4)(k–2)<0
2< k < 4
then k = 3

 

Q. 9: All possible values of θ ∈ [0, 2π] for which sin2θ + tan2θ > 0 lie in

a.(0,π/2)∪(π,3π/2)

(B) (0,π/4)∪(π/2,3π/4)∪(π,5π/4)∪(3π/2,7π/4)

(C) (0,π/2)∪(π/2,3π/4)∪(π,7π/4)

(D) (0,π/4)∪(π/2,3π/4)∪(3π/2,11π/6)

Answer: (B)
JEE MAIN 2021 Feb 25 Shift 1 Solved Problem 12

 

Q. 10: The image of the point (3,5) in the line x – y + 1 = 0, lies on :

(A) (x – 2)2 + (y – 4) 2 =4

(B) (x – 4) 2 + (y + 2)2 =16

(C) (x – 4)2 + (y – 4)2 = 8

(D) (x – 2)2 + (y – 2)2 =12

Answer: (A)
Image of P(3, 5) on the line x – y + 1 = 0 is

(x-3)/1 = (y-5)/-1 = (-2(3-5+1))/ 2 = 1

x = 4, y = 4
Image is (4, 4)
Which lies on (x – 2)2 + (y – 4)2 = 4

 

Q. 11: If Rolle’s theorem holds for the function f(x) = x3 – ax2 + bx – 4, x ∈ [1, 2] with f'(4/3) = 0, then ordered pair (a, b) is equal to :

(A) (–5, 8)

(B) (5, 8)

(C) (5, –8)

(D) (–5, –8)

Answer: (B)
f(1) = f(2)
⇒ 1 – a + b –4 = 8 – 4a + 2b –4
3a – b = 7 …(1)
f’(x) = 3x2 – 2ax + b
⇒f’(4/3) = 0 ⇒ 3 x 16/9 – 8a/3 + b =0
⇒–8a + 3b = –16 …(2)
a = 5, b = 8

 

Q. 12: If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is (x2-4x+y+8)/(x-2), then this curve also passes through the point :

(A) (4, 5)

(B) (5, 4)

(C) (4, 4)

(D) (5, 5)

Answer: (D)

dy/dx = [(x-2)2 +y+4]/(x-2) = (x-2) + (y+4)/(x-2)

Let x – 2 = t ⇒ dx = dt
and y + 4 = u ⇒dy = du
dy/dx = du/dt
du/dt = t + u/t ⇒ du/dt – u/t = t
Here, IF = 1/t
u. (1/t) = ∫ t.(1\t) dt
⇒ u/t = t + c
⇒ (y+4)/(y-2) = (x – 2) + c
Passing through (0, 0)
c = 0
⇒ (y + 4) = (x – 2)2

 

Q. 13: The value of  ∫1-1 x2 ex^3 dx where [t] denotes the greatest integer ≤ t,is :

(A) (e+1)/3

(B) (e-1)/3e

(C) (e+1)/3e

(D) 1/3e

Answer: (C)
JEE MAIN 2021 Feb 25 Shift 1 Solution 19

 

Q. 14: When a missile is fired from a ship, the probability that it is intercepted is 1/3 and the probability that the missile hits the target, given that it is not intercepted, is 3/4. If three missiles are fired independently from the ship, then the probability that all three hit the target, is:

(A) 1/8

(B) 1/27

(C) 3/4

(D) 3/8

Answer:(A)
Probability of not getting intercepted = 2/3
Probability of missile hitting target = 3/4
Probability that all 3 hit the target = (2/3 x3/4)3 = ⅛

 

Q. 15: If the curves, x2/a + y2/b  and x2/c + y2/d intersect each other at an angle of 90°, then which of the following relations is true ?

(A) a + b = c + d

(B) a- b = c – d

(C) ab = (c+d)/(a+b)

(D) a-c = b+d

Answer: (B)

x2/a + y2/b ………(1)

diff : 

2x/a +2y/b dx/dy =0

y/b . dx/dy = -x/a

dx/dy = -bx/ay……(2)

x2/c + y2/d………(3)

Diff : 

dy/dx = -dx/cy ………(4)

m1m2 = –1 

⇒ -bx/ay × -dx/cy​ =−1

⇒ bdx2 = – acy2…….(5)
(1)–(3) ⇒ (1/a – 1/c)x2 + (1/b – 1/d) y2 = 0
Solve above equation using 5
⇒ (c – a) – (d – b) = 0
⇒ c – a = d – b
⇒ c – d = a – b

 

Q. 16: A tangent is drawn to the parabola y2 = 6x which is perpendicular to the line 2x + y =1. Which of the following points does NOT lie on it?

(A) (0,3)

(B) (-6,0)

(C) (4,5)

(D) (5,4)

Answer: (D)
Equation of tangent : y = mx + 3/(2m)
mT = (1/2) (Because perpendicular to line 2x + y = 1)
Therefore, tangent is: y = x/2 + 3 ⇒ x – 2y + 6 = 0

 

Q. 17: Let f, g: N→N such that f(n + 1)= f(n)+ f(1) for all n ∈ N and g be any arbitrary function. Which of the following statements is NOT true ?

(A) f is one-one

(B) If fog is one-one, then g is one-one

(C) If g is onto, then fog is one-one

(D) If f is onto, then f(n) = n for all n ∈ N

Answer: (C)
f(n + 1) = f(n) +f(1)
⇒ f(n + 1)- f(n)= f(1) → A.P. with common difference = f(1)
General term = Tn = f(1) + (n-1)f(1) = nf(1)
⇒f(n) = nf(1)
Clearly f(n) is one-one.
For fog to be one-one, g must be one-one.
For f to be onto, f(n) should take all the values of natural numbers.
As f(x) is increasing, f(1)=1
⇒f(n)=n
If g is many one, then fog is many one. So “if g is onto, then fog is one-one” is incorrect.

 

Q. 18: Let the lines (2 – i)z = (2 + i)zˉ and (2 + i)z + (i – 2)zˉ– 4i = 0, (here i2 = –1) be normal to a circle C. If the line iz + zˉ+ 1 + i = 0 is tangent to this circle C, then its radius is :

(A) 3/√2

(B) 3√2

(C) 3/(2√2)

(D) 1/(2√2)

Answer: (C)
(2–i)z = (2+i)zˉ

⇒(2–i)(x+ iy)=(2+i)(x–iy)
⇒2x–ix + 2iy + y=2x+ ix–2iy+y
⇒2ix –4iy=0
L1 ∶ x–2y=0
⇒(2+i)z+(i –2)zˉ–4i=0.
⇒(2+i) (x + iy)+(i –2)(x–iy)– 4i = 0.
⇒2x +ix + 2iy – y + ix – 2x + y +2iy – 4i =0
⇒2ix + 4iy – 4i =0
L2 ∶ x+2y–2 = 0
Solve L1 and L2
4y=2 or y=1/2
∴ x = 1
Centre(1, 1/2)
L3∶ iz + zˉ+ 1 + i = 0
⇒i(x+iy)+x–iy+1+i=0
⇒ix–y+x–iy+1+i=0
⇒(x–y+1)+i(x–y+1)=0
Radius = distance from (1, 1/2) to x – y + 1 = 0
r = (1-1/2+1)/ √2
r = 3/2√2

 

Q. 19:

JEE MAIN 2021 Feb 25 Shift 1 Solution 16

(A) 1/2

(B) 1/e

(C) 1

(D) 0

Answer: (C)
JEE MAIN 2021 Feb 25 Shift 1 Solved Problem 16

 

Q. 20: The total number of positive integral solutions (x, y, z) such that xyz = 24 is

(A) 36

(B) 45

(C) 24

(D) 30

Answer: (D)
x.y.z = 24
x.y.z= 23 × 31
x=2(a1) ⋅3(b1)
y = 2(a2) ⋅3(b2)
z = 2(a3)⋅3(b3)
a1, a2, a3 ∈ {0,1,2,3}
b1, b2, b3 ∈ {0,1}
Case 1: a1 + a2 + a3 =3
Non negative solution = (3+3-1) C(3-1) = 5C2 = 10
Case 2: b1 + b2 + b3 = 1
Non negative solution = (1+3-1) C(3-1) = 3C2 = 3
∴ Total solutions =10×3=30

Section B

Q. 1: Let A is a matrix where x, y and z are real numbers such that x + y + z > 0 and xyz = 2. If A2 = l3, then the value of x3 + y3 + z3 is ______.

Answer: 7
Maths JEE MAIN 2021 Shift 1 Feb 25 Solutions

 

Q. 2: Let A1, A2, A3,…. be squares such that for each n ≥ 1, the length of the side of An equals the length of diagonal of An+1. If the length of A1 is 12 cm, then the smallest value of n for which area of An is less than one is ____________.

Answer: (9)
JEE MAIN 2021 Feb 25 Shift 1 Solutions

 

Q. 3: The locus of the point of intersection of the lines (√3)kx + ky – 4√3 = 0 and √3x – y – 4√3 k = 0 is a conic, whose eccentricity is _________.

Answer: (2)
(√3)kx + ky – 4√3 = 0 …(1)
√3kx -ky= 4√3 k2 …(2)
Adding equation (1) & (2)
2√3 kx = 4√3(k^2 + 1)
x = 2 (k + 1/k) ….(3)
Subtracting equation (1) & (2)
y = 2√3(1/k – k) ………(4)
x2/4 – y2/12 = 4
x2/16 – y2/48 = 1 – Hyperbola
e2 = 1 + 48/16
or e = 2

 

Q. 4:

JEE MAIN 2021 Feb 25 Shift 1 Maths Problems Solution

Answer: 13
Maths JEE MAIN 2021 Feb 25 Shift 1 Solutions
|I2 + A|=|I2 – A|
From equation (1)
∴a2 + b2 = 1
⇒13(a2 + b2) = 13

 

Q. 5: The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area A. Then A4 is equal to ___________

Answer: (64)
JEE MAIN 2021 Feb 25 Shift 1 Maths Solutions

 

Q. 6: The number of points, at which the function f(x) = |2x + 1| – 3|x+2|+|x2 + x–2|, x ∈ R is not differentiable, is ________.

Answer: 2
Maths JEE MAIN 2021 Feb 25 Shift 1 Problem Solution
Check at 1, –2 and -1/2
Non-Differentiable at x = 1 and -1/2

 

Q. 7: If the system of equations

kx + y + 2z = 1

3x – y – 2z = 2

–2x – 2y – 4z = 3

has infinitely many solutions, then k is equal to __________.

Answer: 21
D = D1 = D2 = D3 = 0
Choose D2 = 0
k(–8+6)–1(–12–4)+2(9+4)=0
–2k + 16 + 26 = 0
2k = 42
k = 21

 

Q. 8: The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3, 4,5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5 is ________.

Answer: 32
Maths JEE MAIN 2021 Shift 1 Feb 25 Paper Solutions

 

Q. 9: Let f(x) be a polynomial of degree 6 in x, in which the coefficient of x6 is unity and it has extrema at x = –1 and x = 1. If limx→0 f(x)/x3 =1, then 5.f(2) is equal to _________.

Answer: (144)
f(x) = x6 + ax5 + bx4 + x3
f’(x) = 6x5 + 5ax4 + 4bx3 + 3x2
Roots 1 & – 1
Therefore, 6 + 5a + 4b + 3 = 0 & – 6 + 5a – 4b + 3 = 0 solving
a = -3/5 and b = -3/2
f(x) = x6 – (3/5)x5 – (3/2)x4 + x3
5.f(2) = 5 [64 – 96/5 – 24 + 8] = 144

 

Q. 10: Let  and be three given vectors. If r is a vector such that and r.b =0, then 

r.a =0 is equal to _______

Answer: 12
Maths 2021 JEE MAIN Feb 25 Shift 1 Solutions

Jee Mains 24 February 2021 Shift-II Previous Year Paper

[tabs title=”JEE MAINS Previous Year Paper” type=”centered”]

[tab title=”PHYSICS”]

PHYSICS

SECTION A

Q 1: A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator?

[Use g = GM/R2 = 9.8 ms-2 and radius of earth, R = 6400 km.]

(A) 49 N

(B) 49.83 N

(C) 49.17 N

(D) 48.83 N

Answer: (D)
At North Pole, weight
Mg = 49
Now, at equator
g’ = g – ω2R
⇒ Mg’ = M(g – ω2R)
⇒ weight will be less than Mg at equator.
Alter:
g is maximum at the poles.
Hence from options only (D) has lesser value than 49N.

Q 2: The logic circuit shown below is equivalent to :

Shift 2 JEE Main 2021 Feb 24 Paper With Solutions Physics
Shift 2 Physics JEE Main 2021 Paper With Solutions Feb 24

Answer: (2)
Feb 24 Shift 2 JEE Main 2021 Feb 24 Physics Paper With Solutions

Q 3: If one mole of an ideal gas at (P1, V1) is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value (B→C). Then it is restored to its initial state by a reversible adiabatic compression (C to A). The net work done by the gas is equal to:

Shift 2 JEE Main Feb 24 2021 Physics Paper With Solution

(A) 0

(B) -RT/2( γ – 1)

(C) RT [ln2 -1/2( γ -1)]

(D) RT ln2

Answer: (C)
AB → Isothermal process
WAB = nRT ln2 = RT ln2
BC → Isochoric process
WBC = 0
CA → Adiabatic process
WCA = P1V1 – (P1/4)X2V1)/(1 – γ)
= P1V1/2(1 – γ)
= RT/2(1 – γ )
WABCA = RT ln2 + RT/2(1 – γ)
= RT [ln2 – 1/2(γ – 1)]

Q 4: Match List – I with List – II.

List – I List – II
(a) Source of microwave frequency (i) Radioactive decay of nucleus
(b) Source of infrared frequency (ii) Magnetron
(c) Source of Gamma Rays (iii) Inner shell electrons
(d) Source of X-rays (iv) Vibration of atoms and molecules
(v) LASER
(vi) RC circuit

Choose the correct answer from the options given below:

(A) (a)-(ii),(b)-(iv),(c)-(i),(d)-(iii)

(B) (a)-(vi),(b)-(iv),(c)-(i),(d)-(v)

(C) (a)-(ii),(b)-(iv),(c)-(vi),(d)-(iii)

(D) (a)-(vi),(b)-(v),(c)-(i),(d)-(iv)

Answer: (A)
(a) Source of microwave frequency – (ii) Magnetron
(b) Source of infrared frequency – (iv) Vibration of atom and molecules
(c) Source of gamma ray – (i) Radioactive decay of nucleus
(d) Source of X-ray – (iii) inner shell electron

Q 5: The period of oscillation of a simple pendulum is T = 2π√(L/g). Measured value of ‘L’ is 1.0 m from meter-scale having a minimum division of 1 mm and time of one complete oscillation is 1.95 s measured from stopwatch of 0.01 s resolution. The percentage error in the determination of ‘g’ will be:

(A) 1.33 %

(B) 1.30 %

(C) 1.13 %

(D) 1.03 %

Answer: (C)
T = 2π√(L/g)
T2 = 4𝜋2 [L/g]
g = 4𝜋2 [L/T2]
Δg/g = ΔL/L + 2ΔT/T
= [1mm/1m + 2(10×10-3)/1.95]×100
= 1.13 %

Q 6: When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is:

(A) elliptical

(B) parabolic

(C) straight line

(D) circular

Answer: (A)
We know that in SHM;
V = ω√(A2 – x2)
Shift 2 Physics Solved Paper JEE Main 2021 For Feb 24
Elliptical
Alternate:
x = A sinωt ⇒ sin ωt = x/A
v = Aω cos ωt ⇒ cos ωt = v/Aω
Hence (x/A)2 + (v/Aω)2 = 1
Which is the equation of an ellipse.

Q 7: In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant k, the frequency of oscillation of given body is:

Shift 2 Feb 24 JEE Main 2021 Physics Papers With Solutions

(A) (1/2π) √(2K/Mg sin α)

(B) (1/2π) √(K/Mg sin α)

(C) (1/2π) √(2K/M)

(D) (1/2π) √(K/2M)

Answer: (A)
Equivalent K = K + K = 2K
Now, T = 2π √(M/Keq)
⇒ T = 2π √(M/2K)
∴f = (1/2π) √(2K/M)

Q 8: Given below are two statements:

Statement I: PN junction diodes can be used to function as transistor, simply by connecting two diodes, back to back, which acts as the base terminal.

Statement II: In the study of transistor, the amplification factor β indicates ratio of the collector current to the base current.

In the light of the above statements, choose the correct answer from the options given below.

(A) Statement I is false but Statement II is true.

(B) Both Statement I and Statement II are true.

(C) Statement I is true but Statement II is false.

(D) Both Statement I and Statement II are false.

Answer: (A)
S-1
Statement 1 is false because in case of two discrete back to back connected diodes, there are four doped regions instead of three and there is nothing that resembles a thin base region between an emitter and a collector.
S-2
Statement-2 is true, as
β = IC/IB

Q 9: Figure shows a circuit that contains four identical resistors with resistance R = 2.0 Ω. Two identical inductors with inductance L = 2.0 mH and an ideal battery with emf E = 9.V. The current ‘i’ just after the switch ‘s’ is closed will be:

Feb 24 Shift 2 JEE Main 2021 Solved Paper For Physics

(A) 9A

(B) 3.0 A

(C) 2.25 A

(D) 3.37 A

Answer: (C)
Just when switch S is closed, inductor will behave like an infinite resistance. Hence, the circuit will be like
Shift 2 JEE Main 2021 Solved Paper Physics Feb 24
Given: V = 9 V
From V = IR
I = V/R
Req. = 2 + 2 = 4 Ω
i = 9/4 = 2.25 A

Q 10: A circular hole of radius (a/2) is cut out of a circular disc of radius ‘a’ shown in figure. The centroid of the remaining circular portion with respect to point ‘O’ will be:

Shift 2 Physics JEE Main 2021 Paper With Solutions For Feb 24

(A) (10/11)a

(B) (⅔)a

(C) (⅙)a

(D) (⅚)a

Answer: (D)
Let σ be the surface mass density of disc.
Shift 2 Physics JEE Main 2021 Paper Solutions For Feb 24
Xcom= (m1x1 – m2x2)/(m1 – m2)
Where m = σπr2
Xcom= (σ×πa2×a) – (σπa2/4) × 3a/2)/(σπa2 – σπa2/4)
Xcom= (a – 3a/8)/(1 – ¼)
Xcom= (5a/8)/(¾)
Xcom= 5a/6

Q 11: The de Broglie wavelength of a proton and α-particle are equal. The ratio of their velocities is:

(A) 4:2

(B) 4:1

(C) 1:4

(D) 4:3

Answer: (B)
From De-Broglie’s wavelength:-
λ = h/mv
Given λP = λα
v ∝ 1/m
vp/vα = mα/mp = 4mp/mp
= 4/1

Q 12: On the basis of kinetic theory of gases, the gas exerts pressure because its molecules:

(A) suffer change in momentum when impinge on the walls of container.

(B) continuously stick to the walls of container.

(C) continuously lose their energy till it reaches wall.

(D) are attracted by the walls of container.

Answer: (A)
Based on kinetic theory of gases, molecules suffer change in momentum when impinge on the walls of container. Due to this they exert a force resulting in exerting pressure on the walls of the container.

Q 13: Two electrons each are fixed at a distance ‘2d’. A third charge proton placed at the midpoint is displaced slightly by a distance x (x<<d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency:

(m = mass of charged particle)

(A) (q2/2πε0md3)1/2

(B) (πε0md3/2q2)1/2

(C) (2πε0md3/q2)1/2

(D) (2q2/πε0md3)1/2

Answer: (A)
Physics JEE Main 2021 Paper With Solutions For Shift 2
Restoring force on proton:-
Fr = 2F1 sinθ where F1 = kq2/(d2 + x2)
Fr = 2Kq2x/[d2 + x2]3/2
x <<< d
Fr = 2kq2x/d3
= q2x/2πε0d3
= kx
K = q2/2πε0d3
Angular Frequency:-
ω = √(k/m)
ω = √(q2/2πε0md3)

Q 14: An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be:

(A) 10-2 nm

(B) 10-3 nm

(C) 10-4 nm

(D) 10-1 nm

Answer: (B)

The minimum wavelength of photon will correspond to the maximum energy due to accelerating by V volts in the tube.
λmin = hc/eV
λmin = 1240nm-eV/1.24×106
λmin = 10-3 nm

Q 15: A soft ferromagnetic material is placed in an external magnetic fiel(D) The magnetic domains:

(A) decrease in size and changes orientation.

(B) may increase or decrease in size and change its orientation.

(C) increase in size but no change in orientation.

(D) have no relation with external magnetic field.

Answer: (B)
Atoms of ferromagnetic material in unmagnetized state form domains inside the ferromagnetic material. These domains have large magnetic moment of atoms. In the absence of magnetic field, these domains have magnetic moment in different directions. But when the magnetic field is applied, domains aligned in the direction of the field grow in size and those aligned in the direction opposite to the field reduce in size and also its orientation changes.

Q 16: According to Bohr atom model, in which of the following transitions will the frequency be maximum?

(A) n = 2 to n = 1

(B) n = 4 to n = 3

(C) n = 5 to n = 4

(D) n = 3 to n = 2

Answer: (A)
JEE Main 2021 Paper With Solution Physics Shift 2 Feb 24
Since, ΔE is maximum for the transition from n = 2 to n = 1
f is more for transition from n = 2 to n = 1.

Q 17: Which of the following equations represents a travelling wave?

(A) y = Aex^2 (vt + θ )

(B) y = A sin(15x – 2t)

(C) y = Aex cos(ωt – θ)

(D) y = A sin x cos ωt

Answer: (B)
Y = F(x, t)
For travelling wave y should be linear function of x and t and they must exist as (x ± vt)
Y = A sin (15x – 2t) which is a linear function in x and t.

Q 18: Zener breakdown occurs in a p-n junction having p and n both:

(A) lightly doped and have wide depletion layer.

(B) heavily doped and have narrow depletion layer.

(C) heavily doped and have wide depletion layer.

(D) lightly doped and have narrow depletion layer.

Answer: (B)
The zener breakdown occurs in the heavily doped p-n junction diode. Heavily doped p-n junction diodes have narrow depletion region. The narrow depletion layer width leads to a high electric field which causes the p-n junction breakdown.

Q 19: A particle is projected with velocity v0 along x-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. ma = -αx2. The distance at which the particle stops:

(A) (2v0/3α)1/3

(B) (3v02/2α)1/2

(C) (3v02/2α)1/3

(D) (2v02/3α)1/2

Answer: Bonus
a = vdv/dx


Given:- vi = v0
Vf = 0
Xi = 0
Xf = x
From Damping Force: a = -αx2/m

-v02/2 = (-α/m) [x3/3]
x = [3mv02/2α]1/3
Most suitable answer could be (3) as mass ‘m’ is not given in any options.

Q 20: If the source of light used in a Young’s double slit experiment is changed from red to violet:

(A) the fringes will become brighter.

(B) consecutive fringe lines will come closer.

(C) the central bright fringe will become a dark fringe.

(D) the intensity of minima will increase.

Answer: (B)
β = λD/d
As λv<λR
βv< βR
⇒ Consecutive fringe lines will come closer.
⇒ (2)

Section – B

Q 1: A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of the hexagon is ______×10-1 kg m2.

Answer: 8
Physics Solved Feb 24 Paper Shift 2 JEE Main 2021
MOI of AB about P : IABP = (M/6)(l/6)2/12
MOI of AB about O,
Physics JEE Main Feb 24 2021 Paper Solution For Shift 2
= (6/100) [(24×24/12×36) + (24×24/36)×3/4]
= 0.8 kg m2
= 8×10-1 kg m2

Q 2: Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies (K.E.)A : (K.E.)B will be A/1. So the value of A will be ________.

Answer: 2
Given that, M1/M2 = 1/2
we know that
K = p2/2M
K1/K2 = (p2/2M1 )×2M2/p2
K1/K2 = M2/M1 = 2/1
A/1 = 2/1
⇒∴ A = 2

Q 3: An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be _______ ×10-2 cm.

Answer: 667
εr = 2.25
Assuming non-magnetic material ⇒ μr = 1
Hence refractive index of the medium
n = √(μrεr )= √2.25 = 1.5
∴λvm=n
λm = C/f.n
= 3×108/3×109×1.5
= (⅔) 10-1 m
= 667×10-2 cm

Q 4: The root mean square speed of molecules of a given mass of a gas at 270C and 1 atmosphere pressure is 200 ms-1. The root mean square speed of molecules of the gas at 1270C and 2 atmosphere pressure is x/√3 ms-1. The value of x will be __________.

Answer: 400 m/s
Vrms = √(3RT1/M0)
200 = √(3R×300/M0) ….(1)
Also, x/√3 = √(3R×400/M0) …(2)
(1)÷(2)
200/(x/√3) = √(300/400) = √(3/4)
⇒x = 400 m/s

Q 5: A signal of 0.1 kW is transmitted in a cable. The attenuation of cable is -5 dB per km and cable length is 20 km. The power received at the receiver is 10-xW. The value of x is ______.

[Gain in dB = 10 log10(P0/Pi)]

Answer: 8
Power of signal transmitted: Pi = 0.1 Kw = 100w
Rate of attenuation = -5 dB/Km
Total length of path = 20 km
Total loss suffered = -5×20 = -100dB
Gain in dB = 10 log10(P0/Pi)
-100 = 10log10(P0/Pi)
log10(Pi/P0) = 10
log10(Pi/P0) = log101010
100/P0 = 1010
⇒ P0 = 1/108 = 10-8
⇒ x = 8

Q 6: A series LCR circuit is designed to resonate at an angular frequency ω0 = 105rad/s. The circuit draws 16W power from 120 V source at resonance. The value of resistance ‘R’ in the circuit is _______ Ω.

Answer: 900
P = V2/R
16 = 1202/R
⇒ R = 14400/16
⇒ R = 900 Ω

Q 7: A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force, will be ________ cm.

Answer: 2
Physics Feb 24 Shift 2 JEE Main 2021 Feb 24 Solved Paper
y = Fl/A∆l
F/A = y∆l/l
F/A = y×0.04/l …(1)
When length & diameter is doubled.
⇒ F/4A = y × ∆l/2l …(2)
(1)÷(2)
(F/A)/(F/4A) = (y×0.04/l)y×∆l/2l
4 = 0.04×2/∆l
∆l = 0.02
∆l = 2×10-2
∴ x = 2

Q 8: A cylindrical wire of radius 0.5 mm and conductivity 5×107 S/m is subjected to an electric field of 10 mV/m. The expected value of current in the wire will be x3π mA. The value of x is ____.

Answer: 5
We know that
J = σE
⇒ J = 5×107×10×10-3
⇒ J = 50×104 A/m2
Current flowing;
I = J × πR2
I = 50×104 ×π(0.5×10-3)2
I = 50×104×π×0.25×10-6
I = 125×10-3π
X = 5

Q 9: A point charge of +12 μC is at a distance 6 cm vertically above the centre of a square of side 12 cm as shown in figure. The magnitude of the electric flux through the square will be _____ ×103 Nm2/C.

Physics Feb 24 JEE Main 2021 Paper With Solution For Shift 2

Answer: 226
Using Gauss law, it is a part of cube of side 12 cm and charge at centre,
ϕ = Q/6ε0= 12μc/6ε0

12×10−6 /6×8.85×10−12

= 226×103 Nm2/C

Q 10: Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be ________ Hz. [Velocity of sound in air is 340 m/s.]

Answer: 8
Physics JEE Feb 24 Main 2021 Solved Paper Shift 2
Speed = 7.2 km/h = 2 m/s
Frequency as heard by A
f’A= fB(v + v0)/(v – vs)
f’A = 676(340 + 2)/(340 – 2)
f’A = 684Hz
∴ fBeat = f’A- fB
= 684 – 676
= 8 Hz

[/tab]

[tab title=”CHEMISTRY”]

Chemistry

SECTION A

Q 1. Given below are two statements:

(A) Both Statement I and Statement II are false

(B) Statement I is false but Statement II is true

(C) Statement I is true but Statement II is false

(D) Both Statement I and Statement II are true

Answer: (C)
For survival of aquatic life dissolved oxygen is responsible for its optimum limit 6.5 ppm and optimum limit of BOD ranges from 10-20 ppm & BOD stands for biochemical oxygen demand.

Q 2. Which one of the following carbonyl compounds cannot be prepared by addition of water on an alkyne in the presence of HgSO4 and H2SO4?

Answer: (A)
Reaction of Alkyne with HgSO4 & H2SO4 follow as
JEE Main 24th Feb Shift 2 Chemistry Paper Question 6 solution
Hence, by this process preparation of CH3CH2CHO can’t be possible.

Q 3. Which one of the following compounds is non-aromatic?

Answer: (B)
JEE Main 24th Feb Shift 2 Chemistry Paper Question 7 solution
(Not planar)
Hence, it is non-aromatic.

Q 4. The incorrect statement among the following is:

(A) VOSO4 is a reducing agent

(B) Red color of ruby is due to the presence of CO3+

(C) Cr2O3 is an amphoteric oxide

(D) RuO4 is an oxidizing agent

Answer: (B)
Red color of ruby is due to presence of CrO3 or Cr+6 not CO3+

Q 5. According to Bohr’s atomic theory:

(a) Kinetic energy of electron is ∝ Z2 / n2

(b) The product of velocity (v) of electron and principal quantum number (n). ‘vn’ ∝ z2

(c) Frequency of revolution of electron in an orbit is ∝ Z3 / n3

(d) Coulombic force of attraction on the electron is ∝ Z3 / n4

Choose the most appropriate Answer from the options given below

(A) (C) only

(B) (A) and (D) only

(C) (A) only

(D) (A), (C) and (D) only

Answer: (B)
(a) KE = –TE = 13.6 × Z2 / n2 eV
KE α Z2 / n2
(b) V = 2.188 × 106 × z / n m/s
So, Vn ∝ Z
Frequency = V / 2πr
F α Z2 / n2 [∴ r α Z2 / n2 and v α Z / n ]
(d) Force ∝ Z2 / r2
So, F ∝ Z3 / n4
So, only statement (A) is correct.

Q 6. Match List-I with List-II

List- I  List-II
(a) Valium  (iv) Tranquilizer
(b) Morphine  (iii) Analgesic
(c) Norethindrone  (i) Antifertility drug
(d) Vitamin B12  (ii) Pernicious anemia

(A) (A)-(iv), (B)-(iii), (C)-(ii), (D)-(i)

(B) (A)-(i), (B)-(iii), (C)-(iv), (D)-(ii)

(C) (A)-(ii), (B)-(iv), (C)-(iii), (D)-(i)

(D) (A)-(iv), (B)-(iii), (C)-(i), (D)-(ii)

Answer: (D)
(a) Valium (iv) Tranquilizer
(b) Morphine (iii) Analgesic
(c) Norethindrone (i) Antifertility drug
(d) Vitamin B12 (ii) Pernicious anemia

Q 7. Match List-I with List-II

List- I (Salt) List-II(Flame colour wavelength)
(a) LiCl  (i) 455.5 nm
(b) NaCl  (ii) 970.8 nm
(c) RbCl  (iii) 780.0 nm
(d) CsCl  (iv) 589.2 nm

Choose the correct Answer from the options given below:

(A) (A)-(ii), (B)-(i), (C)-(iv), (D)-(iii)

(B) (A)-(ii), (B)-(iv), (C)-(iii), (D)-(i)

(C) (A)-(iv), (B)-(ii), (C)-(iii), (D)-(i)

(D) (A)-(i), (B)-(iv), (C)-(ii), (D)-(iii)

Answer: (B)
Range of visible region: 390 nm – 760 nm
VIBGYOR
Violet – Red
LiCl Crimson Red
NaCl Golden yellow
RbCl Violet
CsCl Blue
So, LiCl which is crimson have wavelengths close to red in the spectrum of visible region which is as per given data.

Q 8. Match List-I and List-II.

List-I List-II
(A) (i) Br2 / NaOH
(B) (ii) H2 / Pd-BaSO4
(C) (iii) Zn (Hg) / Conc. HCl
(D) (iv) Cl2 / Red P, H2O

(A) (A)-(ii), (B)-(i), (C)-(iv), (D)-(iii)

(B) (A)-(iii), (B)-(iv), (C)-(i), (D)-(ii)

(C) (A)-(iii), (B)-(i), (C)-(iv), (D)-(ii)

(D) (A)-(ii), (B)-(iv), (C)-(i), (D)-(iii)

Answer: (D)

Q 9. In polymer Buna-S: ‘S’ stands for

(A) Styrene

(B) Sulphur

(C) Strength

(D) Sulphonation

Answer: (A)
Buna-S is the co-polymer of buta-1,3-diene & styrene

Q 10. Most suitable salt which can be used for efficient clotting of blood will be:

(A) Mg(HCO3)2

(B) FeSO4

(C) NaHCO3

(D) FeCl3

Answer: (D)
Blood is a negative sol, according to Hardy-Schulz’s rule, the cation with high charge has high coagulation power. Hence, FeCl3 can be used for clotting blood.

Q 11. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Hydrogen is the most abundant element in the Universe, but it is not the most abundant gas in the troposphere.

Reason R: Hydrogen is the lightest element.

In the light of the above statements, choose the correct Answer from the given below

(1) A is false but R is true

(2) Both A and R are true and R is the correct explanation of A

(3) A is true but R is false

(4) Both A and R are true but R is NOT the correct explanation of A

(A) A is false but R is true

(B) Both A and R are true and R is the correct explanation of A

(C) A is true but R is false

(D) Both A and R are true but R is NOT the correct explanation of A

Answer: (B)
Hydrogen is the most abundant element in the universe because all luminous bodies of the universe i.e. stars and nebulae are made up of hydrogen which acts as nuclear fuel and fusion reaction is responsible for their light.

Q 12. What is the correct sequence of reagents used for converting nitrobenzene into m- dibromobenzene?

JEE Main 24th Feb Shift 2 Chemistry Paper Question 15

Answer: (D)
JEE Main 24th Feb Shift 2 Chemistry Paper Question 15 solution

Q 13. The correct shape and I-I-I bond angles respectively in I3 ion are:

(A) Trigonal planar; 120o

(B) Distorted trigonal planar; 135o and 90o

(C) Linear; 180º

(D) T-shaped; 180º and 90º

Answer: (C)
I3 has sp3d hybridization (2 BP + 3 LP) and linear geometry.

Q 14. What is the correct order of the following elements with respect to their density?

(A) Cr < Fe < Co < Cu < Zn

(B) Cr < Zn < Co < Cu < Fe

(C) Zn < Cu < Co < Fe < Cr

(D) Zn < Cr < Fe < Co < Cu

Answer: (D)
Fact Based
Density depends on many factors like atomic mass. atomic radius and packing efficiency.

Q 15. The Correct set from the following in which both pairs are in correct order of melting point is

(A) LiF > LiCl ; NaCl > MgO

(B) LiF > LiCl ; MgO > NaCl

(C) LiCl > LiF ; NaCl > MgO

(D) LiCl > LiF ; MgO > NaCl

Answer: (B)
Generally,
M.P. ∝ Lattice energy = KQ1Q2 / r+ + r

∝ (packing efficiency)

Q 16. The calculated magnetic moments (spin only value) for species

[FeCl4]2–, [Co(C2O4)3]3– and MnO2–4 respectively are:

Answer: (C)

[FeCl4]2–
Fe2+ 3d6 → 4 unpaired electrons. as Cl in a weak field liquid.

Q 17. Which of the following reagent is suitable for the preparation of the product in the following reaction?

JEE Main 24th Feb Shift 2 Chemistry Paper Question 13

(A) Red P + Cl2

(B) NH2-NH2/ C2H5ONa+

(C) Ni/H2

(D) NaBH4

Answer: (B)
JEE Main 24th Feb Shift 2 Chemistry Paper Question 13 solution
It is a wolf-kishner reduction of carbonyl compounds.

Q 18. The diazonium salt of which of the following compounds will form a coloured dye on reaction with β-Naphthol in NaOH?

Answer: (C)
JEE Main 24th Feb Shift 2 Chemistry Paper Question 14 solution
Orange bright dye.

Q 19. The correct order of the following compounds showing increasing tendency towards nucleophilic substitution reaction is:

JEE Main 24th Feb Shift 2 Chemistry Paper Question 1

(A) (iv) < (i) < (iii) < (ii)

(B) (iv) < (i) < (ii) < (iii)

(C) (i) < (ii) < (iii) < (iv)

(D) (iv) < (iii) < (ii) < (i)

Answer: (C)
JEE Main 24th Feb Shift 2 Chemistry Paper Question 1 solution
Reactivity ∝ – M group present at o/p position.

Q 20. Match List-I with List-II

List- I(Metal) List-II(Ores)
(a) Aluminum  (i) Siderite
(b) Iron  (ii) Calamine
(c) Copper  (iii) Kaolinite
(d) Zinc  (iv) Malachite

(A) (A)-(iv), (B)-(iii), (C)-(ii), (D)-(i)

(B) (A)-(i), (B)-(ii), (C)-(iii), (D)-(iv)

(C) (A)-(iii), (B)-(i), (C)-(iv), (D)-(ii)

(D) (A)-(ii), (B)-(iv), (C)-(i), (D)-(iii)

Answer: (C)
Siderite FeCO3
Calamine ZnCO3
Kaolinite Si2Al2O5(OH)4 or Al2O3.2SiO2.2H2O
Malachite CuCO3.Cu(OH)2

Section B

Q 1. The formula of a gaseous hydrocarbon which requires 6 times of its own volume of O2 for complete oxidation and produces 4 times its own volume of CO2 is CxHy. The value of y is

Answer: 8
CxHy + 6O2 4CO2 + y/2 H2O
Applying POAC on ‘O’ atoms
6 × 2 = 4 × 2 + y/2 × 1
y/2 = 4 ⇒ y = 8

Q 2. The volume occupied by 4.75 g of acetylene gas at 50°C and 740 mmHg pressure is _______L. (Rounded off to the nearest integer)

(Given R = 0.0826 L atm K–1 mol–1)

Answer: 5
T = 50C = 323.15 K
P = 740 mm of Hg = 740 / 760 atm
V = ?
moles (n) = 4.75 / 26 atm
V = 4.75 / 26 × 0.0821 × 323.15 / 740 × 760
V = 4.97 5 Lit

Q 3. Sucrose hydrolysis in acid solution into glucose and fructose following first order rate law with a half-life of 3.33 h at 25ºC. After 9h, the fraction of sucrose remaining is f. The value of is _________× 10–2 (Rounded off to the nearest integer)

[Assume: ln10 = 2.303, ln2 = 0.693]

Answer: 81

Sucrose  __(Hydrolysis)→  Glucose + Fructose
t1/2 = 3.33h = 10 / 3h

Ct = C0 / {2 × T/t1/2}

Fraction of sucrose remaining = f = Ct/Co = 1/ {2 × T/t1/2}

1/f = 2^(t/t1/2)

Log(1/f) = log(2^(t/t1/2)) = t/t1/2 log(2)

9/ (10/3) × 0.3 – 8.1/10 – 0.81

= x × 10–2

x = 81

Q 4. The total number of amines among the following which can be synthesized by Gabriel synthesis is _______

JEE Main 24th Feb Shift 2 Chemistry Paper Question 6

Answer: 3
Only 1o amines can be prepared by Gabriel synthesis.

Q 5. 1.86 g of aniline completely reacts to form acetanilide. 10% of the product is lost during purification. Amount of acetanilide obtained after purification (in g) is ____× 10–2.

Answer: 243
JEE Main 24th Feb Shift 2 Chemistry Paper Question 7 solution
93 g Aniline produce 135 g acetanilide
1.86 g produce 135 × 1.86 / 93 = 2.70 g
At 10% loss, 90% product will be formed after purification.

Q 6. Among the following allotropic forms of sulphur, the number of allotropic forms, which will show paramagnetism is ______.

(a) α-sulphur (B) β-sulphur (C) S2-form

Answer: (A)
S2 is like O2 i.e. paramagnetic as per molecular orbital theory.

Q 7. C6H6 freezes at 5.5ºC. The temperature at which a solution of 10 g of C4H10 in 200 g of C6H6 freeze is ________ C. (The molal freezing point depression constant of C6H6 is 5.12C/m).

Answer: 1
ΔTf = i × Kf × m
= 1 × 5.12 × 10 / 58200 × 1000
∆Tf = 5.12 × 50 / 58 = 4.414
Tf(solution) = Tk(solvent) – ΔT = 5.5 – 4.414 = 1.086oC
≈ 1.09°C = 1 (nearest integer)

Q 8. Assuming ideal behavior, the magnitude of log K for the following reaction at 25ºC is x × 10–1. The value of x is __________. (Integer Answer)

3HC ≡ CH(g) ⇌ C6H6 (l)

[Given: ΔfG° (HC = CH) = – 2.04 × 105] mol–1

ΔfG°(C6H6) = – 1.24 × 105 J mol–1;

R = 8.314 J K–1 mol–1

Answer: 855
ΔG°r = ΔG°f [C6H6 (l)] – 3 × ΔG°f [HC = CH]

Q 9. The magnitude of the change in oxidising power of the MnO4-/ Mn2+ couple is x × 10–4 V, if the H+ concentration is decreased from 1M to 10–4 M at 25°C. (Assume concentration of MnO4- and Mn2+ to be same on change in H+ concentration). The value of x is _____. (Rounded off to the nearest integer).

[Given: 230RT / F = 0.059]

Answer: 3776
5e- + MnO4 + 8H → Mn+2 + 4H2O
JEE Main 24th Feb Shift 2 Chemistry Paper Question 1 solution
= 3776 × 10–4
So, x = 3776

Q 10. The solubility product of PbI2 is 8.0 × 10–9. The solubility of lead iodide in 0.1 molar solution of lead nitrate is x × 10–6 mol/L. The value of x is ________ (Rounded off to the nearest integer)

Given: √2 = 1.41

Answer: 141
PbI2(s) ⇌ Pb2+ (aq) + 2I (aq)
S+0.1 2s
KSP (PbI2) = 8 × 109
KSP = [Pb+2][I]2
8 × 10–9 = (S + 0.1) (2S)2 ⇒ (8 × 10–9 + 0.1) × 4S2
⇒ S2 = 2 × 10–8
S = 1.414 × 10–4 mol/Lit
= x × 10–6 mol/Lit
∴ x = 141.4 141

[/tab]

[tab title=”MATHS”]

Maths

SECTION A

Q 1: Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, c), (2, b) and (a, b) be (10/3, 7/3). If α, β are the roots of the equation ax2 + bx + 1 = 0, then the value of α2 + β2 – αβ is:

(A) 71/256

(B) -69/256

(C) 69/256

(D) -71/256

Answer: (D)
2b = a + c
(2a + 2)/3 = 10/3 and (2b + c)/3 = 7/3
⇒ a = 4
2b + c = 7, 2b – c = 4 },solving
b = 11/4 and c = 3/2
∴ Quadratic equation is 4x2+ (11/4)x + 1 = 0
∴ The value of (α + β)2 – 3αβ = (121/256) – (¾)
= -71/256

Q 2: The value of the integral, where [x] denotes the greatest integer less than or equal to x , is :

(A) –4

(B) –5

(C) -√2 – √3 – 1

(D) -√2 – √3 + 1

Answer: (C)

I =

Put x – 1 = t ; dx = dt


I = -6 + (√2 – 1) + 2√3 – 2√2 + 6 – 3√3
I = -1 – √2 – √3

Q 3: Let f: R → R be defined as

JEE Main 2021 Papers With Solutions Feb 24 Maths Shift 2

Let A = {x ∈ R ∶ f is increasing}. Then A is equal to :

(A) (-5, -4) ∪ (4,∞)

(B) (-5, ∞)

(C) (-∞, -5) ∪ (4, ∞)

(D) (-∞, -5) ∪ (-4, ∞)

Answer: (A)
f’(x) = {-55 ; x< -5 6(x2 – x – 20) ; -5 < x < 4 6(x2– x – 6) ; x > 4
⇒ f’(x) = {-55 ; x< -5 6(x – 5)(x + 4) ; –5 < x < 4 6(x – 3)(x + 2) ; x > 4
Hence, f(x) is monotonically increasing in (-5, -4) ∪ (4, ∞)

Q 4: If the curve y = ax2 + bx + c,x ∈ R passes through the point (1, 2) and the tangent line to this curve at origin is y = x, then the possible values of a, b, c are:

(A) a = 1, b = 1, c = 0

(B) a = -1, b = 1, c = 1

(C) a = 1, b = 0, c = 1

(D) a = 1/2, b = 1/2 ,c = 1

Answer: (A)
2 = a + b + c
dy/dx = 2ax + b, (dy/dx)(0,0) = 1
⇒ b = 1 and a + c = 1
Since (0, 0) lies on curve,
∴ c = 0, a = 1
TRICK: (0, 0) lies on the curve. Only option (1) has c = 0

Q 5: The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their intersection, is:

(A) 65/27

(B) 135/29

(C) 65/28

(D) 35/27

Answer: (B)
Let A and B be two subsets.
For each x∈{1,2,3,4,5} , there are four possibilities:
x ∈ A∩B, x∈ A’∩B, x ∈ A∩B’, x ∈ A’∩B’
So, the number of elements in sample space =45
Required probability
= (5C2 × 33)/45
= (10×27)/210
= 135/29

Q 6: The vector equation of the plane passing through the intersection of the planes 

and

and the point (1, 0, 2) is:

Answer: (B)
Family of planes passing through the intersection of planes is


The above curve passes through

(3 − 1) + λ(1 + 2) = 0
⇒ λ = -2/3
Hence, equation of plane is


TRICK: Only option (2) satisfies the point (1, 0, 2)

Q 7: If P is a point on the parabola y = x2 + 4 which is closest to the straight line y = 4x − 1, then the coordinates of P are :

(A) (–2, 8)

(B) (1, 5)

(C) (3, 13)

(D) (2, 8)

Answer: (D)
Tangent at P is parallel to the given line.
dy/dx|P = 4
⇒2x1 = 4
Maths Feb 24 JEE Main Paper 2021 Shift 2
⇒x1 = 2
Required point is (2, 8)

Q 8: Let A and B be 3×3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A2B2 − B2A2)X = O, where X is a 3×1 column matrix of unknown variables and O is a 3×1 null matrix, has:

(A) a unique solution

(B) exactly two solutions

(C) infinitely many solutions

(D) no solution

Answer: (C)
AT = A, BT = –B
Let A2B2 − B2A2= P
PT = (A2B2 – B2A2)T
= (A2B2)T – (B2A2)T
= (B2)T (A2)T– (A2)T (B2)T
= B2A2 – A2B
⇒ P is a skew-symmetric matrix.

∴ ay + bz = 0 …(1)
–ax + cz = 0 …(2)
–bx – cy =0 …(3)
From equation (1), (2), (3)
Δ = 0 and Δ1 = Δ2= Δ3 = 0
∴ System of equations has infinite number of solutions.

Q 9: If n ≥ 2 is a positive integer, then the sum of the series n+1C2 + 2(2C2 + 3C2 + 4C2 + …. + nC2) is

(A) n(n + 1)2 (n + 2)/12

(B) n(n – 1)(2n + 1)/6

(C) n(n + 1)(2n + 1)/6

(D) n(2n + 1)(3n + 1)/6

Answer: (C)
2C2 = 3C3
Let S = 3C3 + 3C2 + ……. + nC2 = n+1C3 (∵ nCr + nCr–1 = n+1Cr)
n+1C2 + n+1C3 + n+1C3
= n+2C2 + n+1C3
=(n + 2)!/3!(n – 1)! + (n + 1)!/3!(n – 2)!
=(n + 2)(n + 1)n/6 + (n + 1)(n)(n – 1)/6 = (n(n + 1)(2 + 1))/6
TRICK : Put n = 2 and verify the options.

Q 10: If a curve y = f(x) passes through the point (1, 2) and satisfies xdy/dx + y = bx4, then for what value of b,  

(A) 5

(B) 62/5

(C) 31/5

(D) 10

Answer: (D)
dy/dx + y/x = bx3
I.F. =

= x
∴ yx = ∫bx4 dx = bx5/5 + c
The above curve passes through (1, 2).
2 = b/5 + c
Also,

⇒ (b/25) ×32 + c ln 2 – b/25 = 62/5
⇒ c = 0 and b = 10

Q 11: The area of the region: R{(x, y): 5x2 ≤ y ≤ 2x2 + 9} is:

(A) 9√3 square units

(B) 12√3 square units

(C) 11√3 square units

(D) 6√3 square units

Answer: (B)
Solution Paper For Maths Shift 2 JEE Main Feb 24 2021
Required area

= 12√3

Q 12: Let f(x) be a differentiable function defined on [0,2] such that f’(x) =f ‘(2 – x) for all x∈(0, 2), f(0) = 1 and f(2) = e2. Then the value of is:

(A) 1 + e2

(B) 1 – e2

(C) 2(1 – e2)

(D) 2(1+e2)

Answer: (A)
f'(x) = f'(2 – x)
On integrating both sides, we get
f(x) = -f(2 – x)+c
Put x = 0
f(0) + f(2) = c
⇒ c = 1+ e2
⇒ f(x) + f(2 – x) = 1 + e2
I =

= 1+e2

Q 13: The negation of the statement ~p∧(p∨q) is∶

(A) ~p∧q

(B) p∧~q

(C) ~p∨q

(D) p∨∼q

Answer: (D)
Negation of ~p∧(p∨q) is
∼[~p∧(p∨q)]
≡ p∨ ∼(p∨q)
≡ p∨(∼p∧∼q)
≡ (p∨∼p)∧(p∨∼q)
≡ T∧(p∨∼q), where T is tautology.
≡ p∨∼q

Q 14: For the system of linear equations: x − 2y = 1, x − y + kz = −2, ky + 4z = 6,k ∈ R

Consider the following statements:

(A) The system has unique solution if k ≠ 2,k ≠ −2.

(B) The system has unique solution if k = -2.

(C) The system has unique solution if k = 2.

(D) The system has no-solution if k = 2.

(E) The system has infinite number of solutions if k ≠ -2.

Which of the following statements are correct?

(A) (B) and (E) only

(B) (C) and (D) only

(C) (A) and (D) only

(D) (A) and (E) only

Answer: (C)
x -2y + 0.z = 1
x – y + kz = -2
0.x + ky + 4z = 6
 

= 4 – k2
For unique solution, 4 – k2 ≠ 0
k ≠ ±2
For k = 2,
x – 2y + 0.z =1
x – y + 2z = -2
0.x + 2y + 4z = 6

= -8 + 2 (-20)
⇒Δx= -48 ≠ 0
For k = 2,Δx ≠ 0
So, for k = 2, the system has no solution.

Q 15: For which of the following curves, the line x + √3y = 2√3 is the tangent at the point (3√3/2, 1/2)?

(A) x2 + 9y2 = 9

(B) 2x2 – 18y2 = 9

(C) y2 = x/(6√3)

(D) x2 + y2 = 7

Answer: (A)
Tangent to x2 + 9y2 = 9 at point (3√3/2, 1/2) is x(3√3)/2 + 9y(1/2) = 9
⇒3√3 x + 9y = 18
⇒x +√3 y = 2√3
⇒ Option (A) is true.

Q 16: The angle of elevation of a jet plane from a point A on the ground is 600. After a flight of 20 seconds at the speed of 432 km/hour, the angle of elevation changes to 300. If the jet plane is flying at a constant height, then its height is:

(A) 1200√3 m

(B) 1800√3 m

(C) 3600√3 m

(D) 2400√3 m

Answer: (A)
Shift 2 Maths JEE Main 2021 Solution Feb 24
v = 432 × 1000/(60×60) m/sec
= 120 m/sec
Distance PQ = v × 20 = 2400 m
In ΔPAC
tan 600 = h/AC
⇒ AC = h/(√3)
In ΔAQD
tan 300 = h/AD
⇒AD = √3h
AD = AC + CD
⇒√3 h = h/√3 + 2400
⇒2h/√3 = 2400
⇒ h = 1200√3 m

Q 17: For the statements p and q, consider the following compound statements:

(a) (~q∧(p→q)) → ~p

(b) ((p∨q))∧~p) → q

Then which of the following statements is correct?

(A) (A) is a tautology but not (B)

(B) (A) and (B) both are not tautologies

(C) (A) and (B) both are tautologies

(D) (B) is a tautology but not (A)

Answer: (C)
Solved Paper Maths 2021 Shift 2 JEE Main 24 Feb
(A) is tautology.
Solved Paper 2021 Maths Shift 2 JEE Main 24 Feb
(B) is tautology.
∴ (A) and (B) both are tautologies.

Q 18: Let a, b∈R. If the mirror image of the point P(a, 6, 9) with respect to the line (x – 3)/7 = (y – 2)/5 = (z – 1)/(-9) is (20, b, -a, -9), then |a + b| is equal to:

(A) 86

(B) 88

(C) 84

(D) 90

Answer: (B)
P(a, 6, 9), Q (20, b, -a-9)
Midpoint of PQ=((a+20)/2, (b+6)/2, -a/2) lie on the line.

=> (a + 20 – 6)/14 = (b + 6 – 4)/10 = (-a – 2)/(-18)
=> (a + 14)/14 = (a + 2)/18
=> 18a + 252 = 14a + 28
=> 4a = -224
a = -56
(b + 2)/10 = (a + 2)/18
=> (b + 2)/10 = (-54)/18
=>(b + 2)/10 = -3
=> b = -32
|a + b| = |-56 – 32|
= 88

Q 19: Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f'(x) ≠ 0 for all x∈R. If |f(x) f'(x) f'(x) f”(x)| = 0, for all x∈R, then the value of f(1) lies in the interval:

(A) (9, 12)

(B) (6, 9)

(C) (3, 6)

(D) (0, 3)

Answer: (B)
Given f(x) f”(x) – f'(x)2 =0
Let h(x) = f(x)/f'(x)
Then h'(x) = 0
⇒ h(x) = k
⇒ f(x)/f'(x) = k
⇒ f(x) = k f’(x)
⇒ f(0) = k f'(0)
⇒ k = 1/2
Now, f(x) = ½ f'(x)
⇒∫ 2dx = ∫ f'(x)/f(x) dx
⇒ 2x = ln |f(x)| + C
As f(0) = 1 ⇒ C = 0
⇒ 2x = ln |f(x)|
⇒ f(x) = ±e2x
As f(0) = 1 ⇒ f(x) = e2x
∴ f(1) = e2 ≈ 7.38

Q 20: A possible value of tan (¼ sin-1 √63/8) is:

(A) 1/(2√2)

(B) 1/√7

(C) √7 – 1

(D) 2√2 – 1

Answer: (B)
tan (¼ sin-1 √63/8)
Let sin-1(√63/8) = θ
sin θ = √63/8
JEE 2021 Maths Solutions Paper February 24 Shift 2
cos θ = 1/8
2 cos2(θ/2) – 1 = 1/8
⇒ cos2 θ/2 = 9/16
cos θ/2 = 3/4
⇒(1- tan2 θ/4 )/(1 + tan2 θ/4) = 3/4
tan θ/4 = 1/√7

Section B

Q 1: If the area of the triangle formed by the positive x-axis, the normal and the tangent to the circle (x – 2)2+ (y – 3)2 = 25 at the point (5, 7) is A, then 24A is equal to ___.

Answer: Q is wrong
Solved Paper Shift 2 JEE 2021 Main Feb 24
Equation of normal at P is
(y – 7) = ((7 – 3)/(5 – 2))(x – 5)
⇒ 3y – 21 = 4x – 20
⇒ 4x – 3y + 1 = 0
⇒ M is (-1/4, 0)
Equation of tangent at P is
(y – 7) = (-¾) (x – 5)
⇒ 4y – 28 = -3x + 15
⇒ 3x + 4y = 43
⇒ N is (43/3, 0)
The question is wrong. The normal cuts at a point on the negative axis.

Q 2: If a + α = 1, b + β = 2 and af(x) + αf(1/x) = bx + β/2, x ≠ 0 then the value of the expression [f(x) + f(1/x) ]/(x + 1/x)

Answer: 2
af(x) + αf(1/x) = bx + β/x …(i)
Replace x by 1/x
af(1/x) + αf(x) = b/x + βx …(ii)
(i) + (ii)
(a + α)[f(x) + f(1/x) ]
= (x + 1/x)(b + β)
⇒ ( f(x) + f(1/x))/(x + 1/x)
= 2/1
= 2

Q 3: If the variance of 10 natural numbers 1,1,1,…,1,k is less than 10, then the maximum possible value of k is ________.

Answer: 11


⇒ 10(9 + k2) – (81 + k2 + 18k) < 1000
⇒ 90 + 10k2 – k2 – 18k – 81 < 1000
⇒ 9k2– 18k + 9 < 1000
⇒ (k – 1)2 < 1000/9
⇒ k – 1< (10√10)/3
⇒ k < (10√10)/3 + 1
Maximum possible integral value of k is 11.

Q 4: Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (-5, 0). If the locus of the point P is a circle of radius r, then 4r2 is equal to ___.

Answer: 56.25
Let P be (h, k), A(5, 0) and B(-5, 0)
Given PA = 3PB
⇒ PA2 = 9PB2
⇒ (h-5)2 + k2 = 9[(h + 5)2 + k2]
⇒ 8h2 + 8k2 + 100h + 200 = 0
∴ Locus of P is x2 + y2 + (25/2)x + 25 = 0
Centre = (-25/4, 0)
∴ r2 = (-25/4)2 – 25
= 625/16 – 25
= 225/16
∴4r2 = 4×225/16
= 225/4
= 56.25

Q 5: The number of the real roots of the equation (x + 1)2 + |x – 5| = 27/4 is ___.

Answer: 2
For x ≥ 5,
(x + 1)2+ (x – 5) = 27/4
⇒ x2 + 3x – 4 = 27/4
⇒ x2 + 3x – 43/4 = 0
⇒ 4x2 + 12x – 43 = 0
x = (-12 ± √(144 + 688))/8
x = (-12 ± √832)/8
= (-12 ± 28.8)/8
= (-3 ± 7.2)/2
= (-3 + 7.2)/2, (-3 – 7.2)/2 (therefore, no solution)
For x < 5,
(x + 1)2– (x – 5) = 27/4
⇒ x2 + x + 6 – 27/4=0
⇒ 4x2 + 4x – 3=0
x = (-4 ± √(16 + 48))/8
x = (-4 ± 8)/8
⇒ x = -12/8, 4/8
∴ 2 real roots.

Q 6: The students S1, S2,… S10 are to be divided into 3 groups A, B, and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is ___.

Answer: 31650
Solved Paper Maths Shift 2 JEE Main Feb 24 2021
Number of ways
= 10C1 [29 – 2] + 10C2 [28– 2] + 10C3 [27 – 2]
= 27 [10C1×4 + 10C2 ×2 + 10C3] – 20 – 90 – 240
= 128 [40 + 90 + 120 ] – 350
= (128 × 250) – 350
= 10 [3165]
= 31650

Q 7: For integers n and r, let

Shift 2 JEE Main Feb 24 2021 Solved Maths Papers

The maximum value of k for which the sum

Shift 2 2021 JEE Main Feb 24 Solved Mathematics Papers

exists, is equal to ____.

Answer: Bonus
(1+x)10 = 10C0 + 10C1x + 10C2x2 + …… + 10C10x10
(1+x)15= 15C0 + 15C1x +15C2x2 + …… + 15Ck-1xk-1 + 15Ck+1xk+1 + …15C15x15
Feb 24 JEE Main Shift 2 2021 Solved Maths Papers
Coefficient of xk+1 in (1+x)25
= 25Ck+1
25Ck + 25Ck+1 = 26Ck+1
For maximum value
as per given, k can be as large as possible.

Q 8: Let λ be an integer. If the shortest distance between the lines x – λ = 2y – 1 = -2z and x = y + 2λ = z – λ is √7/2√2, then the value of |λ| is __

Answer: 1
(x – λ)/1 = (y – 1/2)/(1/2) = z/(-1/2)
(x – λ)/2 = (y-1/2)/1 = z/(-1) …(1) Point on line = (λ, 1/2, 0)
x/1 = (y + 2λ)/1 = (z – λ)/1 …(2) Point on line = (0, -2λ, λ)
JEE Main Solution 2021 Maths Papers Feb 24 Shift 2
= |-5λ – 3/2|/√14
= √7/(2√2) (Given)
⇒ |10λ + 3| = 7
⇒ λ = -1 as λ is an integer.
⇒ |λ| = 1

Q 9: If i = √-1. If [(-1 + i√3)21/(1 – i)24 + (1 + i√3)21/(1 + i)24 ] = k, and n = [|k| ] be the greatest integral part of |k|. Then

is equal to ___

Answer: 310
JEE Main Feb 24 Shift 2 2021 Solved Maths Papers
= 29 ei(20π) +29 e
= 29 + 29 (-1)
= 0 = k
∴ n = 0
∑(j=0)5 (j + 5)2– ∑(j=0)5 (j + 5)
= [52 + 62 + 72 + 82 + 92 + 102 ] – [5 + 6 + 7 + 8 + 9 + 10]
= [(12+ 22 +… + 102) – (12 + 22+ 32+ 42) ] – [(1 + 2 + 3 + … + 10) – (1 + 2 + 3 + 4) ]
= (385 – 30) -[55 – 10]
= 355 – 45
= 310

Q 10: The sum of first four terms of a geometric progression (G.P.) is 65/12 and the sum of their respective reciprocals is 65/18. If the product of first three terms of the G.P. is 1, and the third term is α then 2α is____

Answer: 3
Let terms of GP are a, ar, ar2, ar3
a + ar + ar2 + ar3 = 65/12 …….(1)
1/a + 1/ar + 1/(ar2) + 1/ar3) = 65/18
⇒1/a (r3 + r2 + r + 1)/r3) = 65/18 …….(2)
(1)/(2), we get
a2r3 = 18/12
= 3/2
Also, a3 r3 = 1
⇒ a(3/2) = 1
⇒a = 2/3
(4/9) r3 = 3/2
⇒ r3 = 33/23
⇒ r = 3/2
α = ar2
= 2/3.(3/2)2 = 3/2
∴2α = 3

[/tab]

[/tabs]

Jee Mains 24 February 2021 Shift-I Previous Year Paper

[tabs title=”JEE MAINS EXAM Previous Year Paper” type=”centered”]

[tab title=”Physics”]

PHYSICS

SECTION A

Q 1. A current through a wire depends on time as i = α0t + βt2 where α0 = 20 A/s and β = 8 As-2. Find the charge crossed through a section of the wire in 15 s.

(A) 2100 C

(B) 260 C

(C) 2250 C

(D) 11250 C

Answer: (D) 

 

Q 2. Each side of a box made of metal sheet in cubic shape is ‘a’ at room temperature ‘T’, the coefficient of linear expansion of the metal sheet is ‘α’. The metal sheet is heated uniformly, by a small temperature ΔT, so that its new temperature is T+ΔT. Calculate the increase in the volume of the metal box:

(A) 4/3 πa3 α ΔT

(B) 4πa3 α ΔT

(C) 3a3 α ΔT

(D) 4a3 α ΔT

Answer: (C)

 

Q 3. Given below are two statements:

Statement-I: Two photons having equal linear momenta have equal wavelengths.

Statement-II: If the wavelength of a photon is decreased, then the momentum and energy of a photon will also decrease.

In the light of the above statements, choose the correct answer from the options given below.

(A) Statement-I is false but Statement-II is true

(B) Both Statement-I and Statement-II are true

(C) Both Statement-I and Statement-II are false

(D) Statement-I is true but Statement-II is false

Answer: (D) 

 

Q 4. A cube of side ‘a’ has point charges +Q located at each of its vertices except at the origin where the charge is –Q. The electric field at the centre of cube is:

JEE Main 2021 24 Feb Physics Shift 1 Question 19

Answer: (C) 

 

Q 5. If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?

Answer: (A)

 

Q 6. In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. The new amplitude of oscillation will be:

JEE Main 2021 24 Feb Physics Shift 1 Question 18

Answer: (A) 

 

Q 7. Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be

Answer: (A)

 

Q 8. In Young’s double-slit experiment, the width of one of the slits is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern.

(A) 4: 1

(B) 2: 1

(C) 3: 1

(D) 1: 4

Answer: (A) 

 

Q 9. Consider two satellites S1 and S2 with periods of revolution 1 hr and 8 hr respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S1 to the angular velocity of satellite S2 is

(A) 8: 1

(B) 1: 8

(C) 2: 1

(D) 1: 4

Answer: (A)

 

Q 10. If an emitter current is changed by 4mA, the collector current changes by 3.5 mA. The value of β will be:

(A) 7

(B) 0.875

(C) 0.5

(D) 3.5

Answer: (A)

 

Q 11. n moles of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes:

A→ B: Isothermal expansion at temperature T so that the volume is doubled from V1 to V2 and pressure changes from P1 to P2.

B → C: Isobaric compression at pressure P2 to initial volume V1.

C → A: Isochoric change leading to change of pressure from P2 to P1.

Total work done in the complete cycle ABCA is –

JEE Main 2021 24 Feb Physics Shift 1 Question 3 solution

(A) 0

(B) nRT(ln2 + 1/2)

(C) nRTln2

(D) nRT (ln2 – 1/2)

Answer: (D)

 

Q 12. The work done by a gas molecule in an isolated system is given by, , where x is the displacement, k is the Boltzmann constant and T is the temperature α and β are constants. Then the dimensions of β will be:

 

(A) [M0LT0]

(B) [M2LT2]

(C) [MLT–2]

(D) [ML2T–2]

Answer: (C)

 

Q 13. Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be

(A) 2: 1

(B) 1: 4

(C) 4: 1

(D) 1: 2

Answer: (B)

 

Q 14. Moment of inertia (M.I.) of four bodies, having same mass and radius, are reported as:

I1 = M.I. of thin circular ring about its diameter,

I2 = M.I. of circular disc about an axis perpendicular to disc and going through the centre,

I3 = M.I. of solid cylinder about its axis and

I4 = M.I. of solid sphere about its diameter.

Then:

(A) I1 = I2 = I3< I4

(B) I1 + I2 = I3 + 5/2 I4

(C) I1 + I3< I2 + I4

(D) I1 = I2 = I3> I4

Answer: (D)

 

Q 15. A cell E1 of emf 6V and internal resistance 2Ω is connected with another cell E2 of emf 4V and internal resistance 8Ω (as shown in the figure). The potential difference across points X and Y is

JEE Main 2021 24 Feb Physics Shift 1 Question 5

(A) 3.6V

(B) 10.0V

(C) 5.6V

(D) 2.0V

Answer: (C) 

 

Q 16. The focal length f is related to the radius of curvature r of the spherical convex mirror by:

(A) f = r

(B) f = – ½ r

(C) f = +½ r

(D) f = – r

Answer: (C) 

 

Q 17. If Y, K and η are the values of Young’s modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

Answer: (A) 

 

Q 18. In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B, C, D and E.

The transition A, B and C respectively represents:

(A) The series limit of Lyman series, third member of Balmer series and second member of Paschen series

(B) The first member of the Lyman series, third member of Balmer series and second member of Paschen series

(C) The ionization potential of hydrogen, second member of Balmer series and third member of Paschen series

(D) The series limit of Lyman series, second member of Balmer series and second member of Paschen series

Answer: (A)

 

Q 19. Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is

Answer: (A) 

 

Q 20. Match List-I with List-II

List – I List – II
(A)  Isothermal (i) Pressure constant
(B)  Isochoric (ii) Temperature constant
(C)  Adiabatic (iii) Volume constant
(D)  Isobaric (iv) Heat content is constant

Choose the correct answer from the options given below:

(A) (A)  – (ii), (B)  – (iv), (C)  – (iii), (D)  – (i)

(B) (A)  – (ii), (B)  – (iii), (C)  – (iv), (D)  – (i)

(C) (A)  – (i), (B)  – (iii), (C)  – (ii), (D)  – (iv)

(D) (A)  – (iii), (B)  – (ii), (C)  – (i), (D)  – (iv)

Answer: (B) 

SECTION-B

Q 1. In connection with the circuit drawn below, the value of current flowing through the 2kΩ resistor is _______ × 10–4 A.

JEE Main 2021 24 Feb Physics Shift 1 Question 10

Answer: 25
In zener diode there will be o change in current after 5V
Zener diode breakdown
⇒ i = 5 / 2 × 103
⇒ i = 2.5 × 10–3 A
⇒ i = 25 × 10–4 A

 

Q 2. An inclined plane is bent in such a way that the vertical cross-section is given by y = x2 / 4 where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with a coefficient of friction μ = 0.5, the maximum height in cm at which a stationary block will not slip downward is _____ cm.

Answer: 25
JEE Main 2021 24 Feb Physics Shift 1 Question 5
Given,
y = x2 / 4
μ = 0.5
Condition for block will not slip downward
mg sin θ = μmg cos θ
JEE Main 2021 24 Feb Physics Shift 1 Question 5 solution
⇒ tan θ = μ
And we know that
⇒ tanθ = dv / dx
⇒ dv / dx = μ ⇒ x/2 = 0.5 [y = x2 / 4 dy / dx = x / 2]
⇒ x = 1,
put x = 1 in equation y = x2/4
⇒ y = (1)2 / 4 ⇒ y = ¼ ⇒ y = 0.25
y = 25 cm

 

Q 3. An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of the light beam emerging from the analyzer is measured as 100 Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by 30° in clockwise direction, the intensity of emerging light will be________ Lumens.

 

Answer: 75
Given: I0 = 100 lumens, θ = 30o
Inet = I0 cos2θ
Inet = 100 × (√3/2)2 = 100 × 3 / 4
Inet = 75 lumens

 

Q 4. The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be ______ N.

[g = 10 ms-2]

Answer: 25
JEE Main 2021 24 Feb Physics Shift 1 Question 4 solution
Given: μs = 0.2
m = 0.5 kg
g = 10 m/s2
We know that
fs = μsN and …. (1)
To keep the block adhere to the wall
Here, N = F … (2)
fs = mg …. (3)
From equation (1), (2), and (3), we get
⇒mg = μs F
⇒ F = mg / μs ⇒ F = 0.5 × 10 / 0.2
F = 25 N (for all values of F greater than or equal to 25 N this case is possible)

 

Q 5. A hydraulic press can lift 100 kg when a mass ‘m’ is placed on the smaller piston. It can lift _______ kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass ‘m’ on the smaller piston.

Answer: 25600
JEE Main 2021 24 Feb Physics Shift 1 Question 7 solution
Atmospheric pressure P0 will be acting on both the limbs of the hydraulic lift.
Applying pascal’s law for the same liquid level
⇒ P0 + mg / A1 = Po + (100)g / A2
⇒ mg / A1 = (100)g / A2 ⇒ m / 100 = A1/ A2 …(1)
Diameter of piston on side of 100 kg is increased by 4 times so new area = 16A2
Diameter of piston on side of (m) kg is decreasing
A1 = A1 / 16
(In order to increasing weight lifting capacity, diameter of smaller piston must be reduced)
Again, mg / (A1/16) = M’g / 16A2 ⇒ 256m / M’ = A1/ A2
From equation (1) = 256m / M’ = m / 100 ⇒ M’ = 25600 kg

 

Q 6. An audio signal υm = 20sin2π(1500t) amplitude modulates a carrier υc =80 sin 2π (100,000t). The value of percent modulation is ________.

Answer: 25
We know that, modulation index = Am / Ac
From given equations, Am = 20 and Ac = 80
Percentage modulation index = Am / Ac × 100
⇒ 20 / 80 × 100 = 25%
The value of percentage modulation index is
= 25

 

Q 7. A common transistor radio set requires 12 V (D.C.) for its operation. The D.C. source is constructed by using a transformer and a rectifier circuit, which are operated at 220 V (A.C.) on standard domestic A.C. supply. The number of turns of the secondary coil are 24, then the number of turns of the primary are ______.

Answer: 440
Given,
Primary voltage, Vp = 220 V
Secondary voltage, vs = 12 V
No. of turns in secondary coil is Ns = 24
No. of turns in primary coil, Np = ?
We know that for a transformer
⇒ Np / Ns = Vp / Vs
⇒ Np = Vp × Ns / Vs = 220 × 24 / 12
⇒ Np = 440

 

Q 8. A ball with a speed of 9 m/s collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30° with the original direction. The ratio of velocities of the balls after collision is x : y, where x is _________.

Answer: 1
JEE Main 2021 24 Feb Physics Shift 1 Question 2
Momentum is conserved just before and just after the collision in both x-y direction.
In y-direction,
pi = 0
pf = mv1 sin30o – mv2 sin30o
Pf = m × ½ v1 – m × ½ v2
pi = pf, so
= mv1 / 2 – mv2 / 2 = 0
⇒ mv1 / 2 = mv2 / 2 ⇒ v1 = v2
v1 / v2 = 1

 

Q 9. An electromagnetic wave of frequency 5 GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2. Its velocity in this medium is _______ × 107 m/s.

Answer: 15
Given: f = 5 GHz
εr =2
μr = 2
Velocity of wave ⇒ v = c / n ….(1)
Where, n = √μrεr and c = speed of light = 3 × 108 m/s
n = √2 × 2 = 2
put the value of n in we get
⇒ v = 3 × 108 / 2 = 15 × 107 m/s
⇒ X × 107 = 15 × 107
X = 15

 

Q 10. A resonance circuit having inductance and resistance 2 × 10–4 H and 6.28 Ω respectively oscillates at 10 MHz frequency. The value of the quality factor of this resonator is________. [π = 3.14]

Answer: 2000
Given: R = 6.28 Ω
f = 10 MHz
L = 2 × 10-4 Henry
We know that quality factor Q is given by
⇒ Q = XL / R = ωL / R
also, ω = 2πf, so
⇒ Q = 2πfL / R
⇒ Q = 2π × 10 × 106 × 2 × 10-4 / 6.28 = 2000
Q = 2000

[/tab]

[tab title=”Chemistry”]

CHEMISTRY

SECTION-A 

Q 1. Which reagent (A) is used for the following given conversion?

JEE Main 24th Feb Shift 1 Chemistry Paper Question 10

(A) Cu / ∆ / high pressure

(B) Molybdenum Oxide

(C) Manganese Acetate

(D) Potassium Permanganate

Answer: (B)

 

Q 2. S-1: Colourless cupric metaborate is converted into cuprous metaborate in a luminous flame.

S-2: Cuprous metaborate is formed by reacting copper sulphate with boric anhydride heated in non luminous flame.

(A) S-1 is true and S-2 is false

(B) S-1 is false and S-2 is true

(C) Both are true

(D) Both are false

Answer: (D)

 

Q 3. Find A and B.

JEE Main 24th Feb Shift 1 Chemistry Paper Question 11

Answer: (B)

 

Q 4. EoM2+/ M has a positive value for which of the following elements of 3d transition series?

(A) Cu

(B) Zn

(C) Cr

(D) Co

Answer: (A)

 

Q 5. What is the reason for the formation of a meta product in the following reaction?

JEE Main 24th Feb Shift 1 Chemistry Paper Question 1

(A) Aniline is ortho/para directing

(B) Aniline is meta directing

(C) In acidic medium, aniline is converted into anilinium ion, which is ortho/para directing

(D) In acidic medium, aniline is converted into anilinium ion which is meta directing

Answer: (D) 

 

Q 6. Identify X, Y, Z in the given reaction sequence.

(A) X = Na[Al(OH)4] ; Y = CO2 ; Z = Al2O3.xH2O

(B) X = Na[Al(OH)4] ; Y = SO2 ; Z = Al2O3.xH2O

(C) X = Al(OH)3 ; Y = CO2 ; Z = Al2O3

(D) X = Al(OH)3 ; Y = SO2 ; Z = Al2O3

Answer: (A) 

 

Q 7. The missing reagent P is:

JEE Main 24th Feb Shift 1 Chemistry Paper Question 2

Answer: (A) 

Q 8. Arrange Mg, Al, Si, P and S in the correct order of their ionisation potentials.

 

Answer: P > S > Si > Mg > Al

 

Q 9. Which force is responsible for the stacking of the α-helix structure of protein? Hydrogen (1H, 2H, 3H) is ________.

(A) H-bond

(B) Ionic bond

(C) Covalent bond

(D) Van der Waals forces

Answer: (A) 

 

Q 10. The composition of gun metal is:

(A) Cu, Zn, Sn

(B) Al, Mg, Mn, Cu

(C) Cu, Ni, Fe

(D) Cu, Sn, Fe

Answer: (A)

 

Q 11. The gas evolved due to anaerobic degradation of vegetation causes:

(A) Global warming and cancer

(A) Global warming and cancer

(B) Acid rain

(C) Ozone hole

(D) Metal corrosion

Answer: (A) 

 

Q 12. The slope of the straight line given in the following diagram for adsorption is:

JEE Main 24th Feb Shift 1 Chemistry Paper Question 18

(A) 1/n (0 to 1)

(B) 1/n (0.1 to 0.5)

(C) log n

(D) log (1/n)

Answer: (A)

 

Q 13. Match the following:

(i) Caprolactam (a)  Neoprene
(ii) Acrylonitrile (b)  Buna N
(iii) 2-chlorobuta-1,3-diene (c)  Nylon – 6
(iv) 2-Methylbuta-1,3-diene (d)  Natural rubber

(A) (i) →(b) , (ii) → (c) , (iii) → (a) , (iv) → (d) 

(B) (i) → (a) , (ii) → (c) , (iii) → (b) , (iv) → (d) 

(C) (i) → (c) , (ii) → (b) , (iii) → (a) , (iv) → (d) 

(D) (i) → (c) , (ii) → (a) , (iii) → (b) , (iv) → (d) 

Answer: (C)

 

Q 14. In the given reactions,

1) I2 + H2O2 + 2OH → 2I + 2H2O + O2

2) H2O2 + HOCl → Cl + H3O+ + O2

(A) H2O2 acts as an oxidising agent in both the reactions

(B) H2O2 acts as a reducing agent in both the reactions

(C) H2O2 acts as an oxidising agent in reaction (1) and as a reducing agent in reaction (2)

(D) H2O2 acts as a reducing agent in reaction (1) and as an oxidizing agent in reaction (2)

Answer: (B) 

 

Q 15. What is the major product of the following reaction

JEE Main 24th Feb Shift 1 Chemistry Paper Question 6

Answer: (A) 

 

Q 16. Which of the following ores are concentrated by cyanide of group 1st element?

(A) Sphalerite

(B) Malachite

(C) Calamine

(D) Siderite

Answer: (A)

 

Q 17. What is the major product of the following reaction?

JEE Main 24th Feb Shift 1 Chemistry Paper Question 7

Answer: (C) 

 

Q 18. Which of the following pairs are isostructural

a) TiCl4, SiCl4

b) SO2-3, CrO2-3

c) NH3, NO3

d) ClF3, BCl3

(A) B, C

(B) A, C

(C) A, B

(D) A, D

Answer: (C)

 

Q 19. Identify the major product:

JEE Main 24th Feb Shift 1 Chemistry Paper Question 8

Answer: (B) 

Q 20. The products A and B are:

 

Answer: (A) JEE Main 24th Feb Shift 1 Chemistry Paper Question 9 solution

Section B

Q 1. Cu2+ + NH3 ⇌ [Cu(NH3)]2+ K1 = 104

[Cu(NH3)]2+ + NH3 ⇌ [Cu(NH3)]2+ K2 = 1.58 × 103
[Cu(NH3)2]2+ + NH3 ⇌ [Cu(NH3)3]2+ K3 = 5 × 102
[Cu(NH3)3]2+ + NH3 ⇌ [Cu(NH3)4]2+ K4 = 102
If the dissociation constant of [Cu(NH3)4]2+ is X × 1012

 

Determine X.
Answer: 1.26
Overall reaction constant (β):
β = K1× K2 × K3 × K4
= 104 (1.58 ×103) × 5 × 102 × 102 = 7.9 × 1011
Cu2+ + 4NH3 ⇌ [Cu(NH3)4]2+ ; β = 7.9 × 1011
So, the dissociation constant (KDisso.) will be:

1/β = 1/ 7.9 × 1011

​KDisso = 1 / β = 1.26 × 10-12
Hence, the value of X = 1.26

 

Q 2. What is the coordination number in Body Centered Cubic (BCC) arrangement of identical particles?

Answer: 8
The easiest way is to look at the atom at the body center. It lies at the center of the body diagonal and touches the eight corner atoms. So, coordination number = 8.

 

Q 3. Cl2(g)⇌ 2Cl(g)

For the given reaction at equilibrium, moles of Cl2(g) is equal to the moles of Cl(g) and the equilibrium pressure is 1atm. If Kp of this reaction is x ×10–1, find x.

Answer: 5
According to the question: Cl2 ⇌ 2Cl [Ptotal = 1 atm].
Moles of Cl2 = Moles of Cl (at equilibrium).
Given: Kp = x ×10-1
nCl2 = nCl.
Therefore, P Cl2 = P Cl
Hence, P Cl2 = P Cl = 0.5 atm
kp= (P Cl)2/ P Cl2 = 0.5 = 5 x 10-1
So, x = 5

 

Q 4. Among the following compounds, how many are amphoteric in nature?

Be(OH)2, BeO, Ba(OH)2, Sr(OH)2

Answer: 2
The oxide and hydroxide of Be are amphoteri(C) Hence BeO and Be(OH)2 is amphoteri(C) Ba(OH)2 and Sr(OH)2 are basic.

 

Q 5. S8 + bOH → cS2- + sS2O2-3 + H2O. Find the value of c.

Answer: 4
Let us look at the half reactions i.e. oxidation and reduction separately.
Oxidation:
S8 → S2O2-3
S8 + 24OH → 4S2O2-3 + 12H2O +16e- ….(1)
Reduction:
S8 → S2-
S8 + 16e- → 8S2- ….(2)
Adding both the reactions (1) and (2),
2S8 + 24OH → 4S2O2-3 + 8S2- + 12H2O
Dividing the whole equation by 2,
S8 + 12OH → 2S2O2-3 + 4S2- + 6H2O
So, c = 4

 

Q 6. 4.5 g of a solute having molar mass of 90 g/mol is dissolved in water to make a 250 mL solution. Calculate the molarity of the solution.

Answer: 0.2
WB (given weight of solute) = 4.5 g
MB (Molar mass of solute) = 90 g/mol
VS (Volume of solution) = 250 mL
= 250 / 1000 L = 1/4 L
Molarity (M) = nB / VS(L) = WB / MB.VS(L) = 4.5 / (90 ×1/4) = 0.2 molar

 

Q 7. Calculate the time taken in seconds for 40% completion of a first order reaction, if its rate constant is 3.3× 10-4 sec-1.

Answer: 1518

= 30 x 103 x 0.506 = 1518 sec

 

Q 8. 9.45g of CH2ClCOOH is dissolved in 500 mL of H2O solution and the depression in freezing point of the solution is 0.5°C. Find the percentage dissociation.

(Kf)H2O = 1.86K kg mole-1.

Answer: 34.4%
CH2Cl COOH CH2ClCOO + H+
Initial 100
Dissociated α α α
Left (1-α) α α
i = final moles / initial moles = 1 – α + α + α / 1 = 1 + α
ΔTf = i × Kf × m
0.5 = (1 + α) × 1.86 × m
Molality (m) = nB / WA (kg) = WBMB x WA (kg) = 9.45 × 1000 / 94.5 × 500 = 0.2
Here, A is for solute and B is for solvent
WA=WH2O = 500g (Density of H2O = 1g/mL)
0.5 = (1+ α) ×1.86 × 0.2
α = 0.344
Percentage of dissociation = 34.4%

 

Q 9. For a chemical reaction, Keq is 100 at 300K, the value of ΔGo is –xR Joule at 1 atm pressure. Find the value of x. (Use ln 10 = 2.3)

Answer: 1382
Given: Keq= 100 at 300K and ΔGo = –xR Joule
ΔGo = -RTln(Keq) = -2.303RTlog(Keq) = -1381.8R
Therefore, x = 1381.8 or 1382

 

Q 10. The mass of Li3+ is 8.33 times the mass of a proton. If Li3+ and proton are accelerated through the same potential difference, then the ratio of de Broglie’s wavelength of Li3+ to proton is x ×10–1. Find x

Answer: 2

m (Li3+) = 8.33 × mp+ (given)
Debroglie’s wavelength (λ) = h / p
KE = ½ mv2
Multiplying by m on both sides
m. KE = ½ mv2
2m. KE = (mv)2 = p2
P = √2m. KE
Also KE= q × V
So, P = 2mq.V
JEE Main 24th Feb Shift 1 Chemistry Paper Question 10 solution
Comparing with x × 10 -1 = 2 × 10 -1
x = 2

[/tab]

[tab title=”Maths”]

MATHS 

SECTION A

Q 1: The statement among the following that is a tautology is:

(A) A∧(A∨B)

(B) B→[A∧(A→B)]

(C) A∨(A∧B)

(D) [A∧(A→B)]→B

Answer: (D)
A∧ (~ A∨B)→B
= [(A∧~A)∨(A∧B)]→ B
= (A∧ B)→ B
= ~ (A∧B)∨B
= t

 

Q 2: Let f :R→R be defined as f(x) = 2x-1 and g:R – {1} →R be defined as g(x) = (x-½)/(x-1).

Then the composition function f(g(x)) is:

(A) Both one-one and onto

(B) onto but not one-one

(C) Neither one-one nor onto

(D) one-one but not onto

Answer: (D)
f(g(x)) = 2g(x) – 1
= 2(x – 1/2)/(x – 1) – 1
= x/(x – 1)
f(g(x)) = 1 + 1/(x – 1)

∴ one-one, into

 

Q 3: If f:R→ R is a function defined by f(x) = [x – 1] cos ((2x – 1)/2)𝜋 , where [.] denotes the greatest integer function, then f is:

(A) discontinuous only at x = 1

(B) discontinuous at all integral values of x except at x = 1

(C) continuous only at x = 1

(D) continuous for every real x

 

Answer: (D)
Doubtful points are x = n, n∈I
JEE Main 2021 Maths Papers Feb 24 Shift 1 With Solutions
f(n) = 0
Hence continuous.

 

Q 4: If the tangent to the curve y = x3 at the point P(t, t3) meets the curve again at Q, then the ordinate of the point which divides PQ internally in the ratio 1:2 is:

(A) –2t3

(B) –t3

(C) 0

(D) 2t3

Answer: (A)
Equation of tangent at P(t, t3)
(y – t3) = 3t2(x – t) ⋯(1)
Now solve the above equation with
y = x3 ⋯(2)
By (1) & (2)
x3 – t3 = 3t2 (x – t)
x2 + xt + t2 = 3t2
x2 + xt – 2t2 = 0
⇒(x – t)(x + 2t) = 0
⇒x = – 2t
⇒Q(-2t, -8t3)
Ordinate of required point = (2t3 + (-8t)3)/3
= -2t3

 

Q 5: The value of – 15C1 + 2. 15C2 – 3.15C3+ ….-15.15C1 + 14C1+ 14C3 + 14C5 + …14C11 is

(A) 214

(B) 213 – 13

(C) 216 – 1

(D) 213 – 14

Answer: (D) 


Maths Shift 1 JEE Main Feb 24 2021 Solved Papers
= (14C1+ 14C3 + 14C5 + …14C11 + 14C13) – 14C13
= 213 – 14
∴ S1 + S2 = 213 – 14

 

Q 6: An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is:

(A) 3/16

(B) 1/2

(C) 5/16

(D) 1/32

Answer: (B)
P(odd no. twice) = P(even no. thrice)
nC2 (1/2)n = nC3 (1/2)n
⇒ n = 5
Success is getting an odd number then P(odd successes) = P(1) + P(3) + P(5)
= 5C2 (1/2)5 + 5C2 (1/2)5 + 5C2 (1/2)5
= 16/25
= 1/2

 

Q 7: Let p and q be two positive number such that p + q = 2 and p4 + q4 = 272. Then p and q are roots of the equation:

(A) x2 – 2x + 2 = 0

(B) x2 – 2x + 8 = 0

(C) x2 – 2x + 136 = 0

(D) x2 – 2x + 16 = 0

Answer: (D)
(p2 + q2)2 – 2p2q2 = 272
((p + q)2 – 2pq)2 – 2p2q2 = 272
⇒16 – 16pq + 2p2q2 = 272
(pq)2 – 8pq –128 = 0
⇒pq = (8±24)/2 = 16, – 8
⇒pq = 16
Now
x2 – (p + q)x + pq = 0
x2 – 2x + 16 = 0

 

Q 8: The area (in sq.units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, is:

(A) 24π + 3√3

(B) 12π + 3√3

(C) 12π – 3√3

(D) 24π – 3√3

 

Answer: (D)
The curves intersect at point (3, ± 3√3)
Shift 1 JEE Main Feb 24 2021 Solved Maths Papers
Required area
Shift 1 2021 JEE Main Feb 24 Solved Maths Papers

 

Q 9: If ∫(cos x -sin x)/√(8-sin 2x) dx = a sin-1(sin x + cos x)/b + c where c is a constant of integration, then the ordered pair (a, b) is equal to:

(A) (1, –3)

(B) (1, 3)

(C) (–1, 3)

(D) (3, 1)

 

Answer: (B)
Put sin x + cos x = t ⇒1 + sin 2x = t2
(cos x -sin x ) dx = dt
⇒I = ∫dt/√(8-(t2-1))
= ∫dt/(9-t2)
= sin-1 (t/3) + c = sin-1(sin x + cos x)/3 + c
⇒ a = 1 and b = 3

 

Q 10: The locus of the mid-point of the line segment joining the focus of the parabola y2 = 4ax to a moving point of the parabola, is another parabola whose directrix is:

(A) x = a

(B) x = 0

(C) x = -a/2

(D) x = a/2

Answer: (B)
JEE Main 2021 Paper With Solution Maths Feb 24 Shift 1
h = (at2+a)/2, k = (2at+0)/2
⇒ t2 =(2h-a)/a and t=k/a
⇒ k2/a2 =(2h-a)/a
⇒ Locus of (h, k) is y2 = a (2x – a)
⇒ y2 = 2a(x- a/2)
Its directrix is x – a/2 = -a/2
⇒ x = 0

 

Q 11: A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is 1/4. Three stones A, B and C are placed at the points (1,1),(2,2), and (4,4) respectively. Then which of these stones is/are on the path of the man?

(A) B only

(B) A only

(C) the three

(D) C only

 

Answer: (A)
x/a + y/b = 1
h/a + k/b = 1 ⋯⋯(1)
and (1/a + 1/b)/2 = 1/4
∴1/a + 1/b = 1/2 ⋯⋯(2)
(From (1) and (2))
Line passes through fixed point B(2, 2)

 

Q 12: The function f(x) = (4×3- 3×2)/6 – 2sin x + (2x – 1)cos x:

(A) increases in [1/2, ∞)

(B) decreases (-∞, 1/2]

(C) increases in (-∞, 1/2]

(D) decreases [1/2, ∞)

Answer: (A)
f’(x) = (2x – 1) (x – sin x )
⇒ f’x ≥ 0 in x∈(-∞, 0] ⋃ [1/2, ∞)
and f’x ≤ 0 in x∈(0, ½)

 

Q 13: The distance of the point (1, 1, 9) from the point of intersection of the line (x – 3)/1 = (y – 4)/2 = (z – 5)/2 and the plane x + y + z = 17 is:

(A) 38

(B) 19√2

(C) 2√19

(D) √38

Answer: (D)
(x – 3)/1 = (y – 4)/2 = (z – 5)/2 = λ
x = λ + 3, y = 2λ+ 4, z = 2λ+5
Which lies on given plane hence
⇒ λ+3+2λ +4+2λ+5 = 17
⇒ λ = 5/5 = 1
Hence, point of intersection is Q (4, 6, 7)
∴ Required distance =PQ
= √(9+25+4)
= √38

 

Q 14:

JEE Main Solution 2021 Maths Papers Feb 24 Shift 1

(A) 2/3

(B) 0

(C) 1/15

(D) 3/2

 

Answer: (A)
JEE Main Solution Feb 24 Shift 1 2021 Maths Papers

 

Q 15: Two vertical poles are 150 m apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an observer finds the angles of elevation of their tops to be complementary, then the height of the shorter pole (in meters) is:

(A) 25

(B) 20√3

(C) 30

(D) 25√3

 

Answer: (D)
JEE Main Feb 24 Shift 1 2021 Solved Maths Papers
tan θ = h/75 = 75/3h
h2 = 752/3
h = 25√3m

 

Q 16: A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is:

(A) 560

(B) 1050

(C) 1625

(D) 575

Answer: (C)
(2I,4F)+ (3I,6F) + (4I,8F)
= 6C2 8C4 + 6C3 8C6 + 6C4 8C8

= 15 × 70 + 20 × 28 + 15 × 1
= 1050 + 560 + 15 = 1625

 

Q 17: The equation of the plane passing through the point (1,2,–3) and perpendicular to the planes 3x + y – 2z = 5 and 2x – 5y – z = 7, is:

(A) 3x – 10y – 2z + 11 = 0

(B) 6x – 5y – 2z – 2 = 0

(C) 11x + y + 17z + 38 = 0

(D) 6x – 5y + 2z + 10 = 0

Answer: (C)
JEE Main 2021 Papers With Solutions Feb 24 Maths Shift 1

 

Q 18: The population P = P(t) at time ‘t’ of a certain species follows the differential equation dP/dt = 0.5P – 450. If P(0) = 850, then the time at which population becomes zero is:

(A) ½ loge 18

(B) 2loge 18

(C) loge 9

(D) loge 18

Answer: (B)
dp/dt = (p-900)/2
Shift 1 Feb 24 JEE Main 2021 Solved Maths Papers
ln |900| – ln |50| = t/2
t/2 = ln |18|
⇒ t = 2ln 18

 

Q 19: If e^{(cos2x + cos4x + cos6x + …..∞ )loge2 satisfies the equation t2 – 9t + 8 = 0, then the value of 2sin x/(sin x + √3cos x) 0< x<π/2 is:

(A) 3/2

(B) 2√3

(C) 1/2

(D) √3

 

Answer: (C)
Maths JEE Main Shift 1 Feb 24 2021 Solved Papers
0 < x < π/2 ⇒ cot⁡x = √3
⇒(2 sin⁡x)/(sin⁡x+√3 cos⁡x )
= 2/(1+√3 cot ⁡x)
= 1/2

 

Q 20: The system of linear equations

3x – 2y – kz = 10

2x – 4y – 2z = 6

x + 2y – z = 5m

is inconsistent if :

(A) k = 3, m = 4/5

(B) k ≠ 3,m∈R

(C) k ≠ 3, m ≠ 4/5

(D) k = 3, m ≠ 4/5

 

Answer: (D)
Maths JEE Main Feb 24 Shift 1 2021 Solved Papers
⇒ 3(4 + 4) + 2(–2 + 2) -k(4 + 4) = 0
⇒ k = 3
Maths JEE Main Feb 24 Shift 1 Solved Paper 2021
⇒ 10(4 + 4) +2(-6 + 10m) -3(12 + 20m) ≠ 0
⇒ m ≠ 4/5
Solved Paper Maths Shift 1 JEE Main Feb 24 2021
⇒ 3(-6 + 10m) – 10(- 2 + 2) – 3(10m – 6) ≠ 0
⇒ 0
Solved Papers Maths Shift 1 Feb 24 2021 JEE Main
⇒3(-20m – 12) +2(10m – 6) +10(4 + 4) ≠ 0
⇒ m ≠ 4/5

Section B

Q 1:

Solution Papers Maths Shift 1 JEE Main Feb 24 2021

Solution:

Answer: 1
Solution Papers Maths Shift 1 Feb 24 2021 JEE Main
= tan 𝜋/4
= 1

Q 2: If and [x] denotes the greatest integer ≤ x, then 

is equal to

Answer: 3
Solution Papers Maths JEE Main Shift 1 Feb 24 2021

 

Q 3: If one of the diameters of the circle x2+y2 – 2x – 6y + 6 = 0 is a chord of another circle ‘C’ whose center is at (2,1), then its radius is ________

Solution:

Answer: 3
Solved Papers Maths JEE Main 2021 Feb 24 Shift 1
distance between (1,3) and (2,1) is √5
∴ (√5)2+(2)2= r2
⇒r = 3

 

Q 4: Let three vectors a b and c be such that is coplanar with a and b, a.c=7 and is perpendicular to c, where and , then the value of is _______

 

Answer: 75
Solution Papers Maths JEE Main Feb 24 Shift 1 2021

 

Q 5: The minimum value of α for which the equation 4/sin⁡x +1/(1-sin⁡x )=α has at least one solution in (0,π/2) is _______

Solution:

Answer: 9
f(x⁡) = 4/sin⁡x + 1/(1 – sin⁡x )
Let sin⁡x = t ∵x∈(0, π/2) ⇒ 0 < t < 1
f(t⁡)= 4/t + 1/(1-t)
f'(t⁡) = (-4)/t2 + 1/(1 – t⁡)2 = 0
⇒(t2-4(1-t⁡)2/t2(1-t⁡)2 = 0
⇒t = 2/3
fmin at t = 2/3
αmin = f(2/3) =4/(2/3) + 1/(1 – 2/3)
= 6 + 3
= 9

 

Q 6: Let A = {n∈N∶ n is a 3-digit number}, B = {9k + 2∶ k∈N} and C = {9k + l∶ k∈N} for some l(0 < l < 9). If the sum of all the elements of the set A∩(B∪C) is 274×400, then l is equal to ___________

Answer: 5
3 digit number of the form 9K+2 are {101,109,⋯,992}
⇒ Sum equal to (100/2)(1093) = S1= 54650
Now 274 × 400 =S1+S2
⇒274 × 400 = (100/2) [101 + 992] + S2
⇒274 × 400 = 50 × 1093 + S2
⇒S2 = 109600 – 54650
∴S2 = 54950
S2 = 54950 = (100/2) [(99+l) + (990+l)]
⇒ 2l + 1089 = 1099
⇒ l = 5

 

Q 7: Let

Solved Papers Maths JEE Main Shift 1 Feb 24 2021

where α∈R. Suppose Q = [qij ] is a matrix satisfying PQ = kI3 for some non-zero k∈R. If q23= – k/8 and |Q⁡| = k2/2, then α2 + k2 is equal to ___

 

Answer: 17
Solved Papers Maths JEE Main Feb 24 Shift 1 2021

 

Q 8: Let M be any 3×3 matrix with entries from the set {0,1,2}. The maximum number of such matrices, for which the sum of diagonal elements of MTM is seven, is __________

Answer: 540
Solution Papers Maths JEE Main 2021 Feb 24 Shift 1
⇒ a2 + b2 + c2 + d2 + e2 + f2 + g2 + h2 + i2 = 7
Case I∶ Seven (1’s) and two (0’s)
9C2 = 36
Case II∶ One (2) and three (1’s) and five (0’s)
9!/5!3! = 504
∴Total = 540

 

Q 9: If the least and the largest real values of α, for which the equation z + α|z⁡-1| + 2 i⁡ = 0 (z∈C and i =√(-1)) has a solution, are p and q respectively; then 4(p2 + q2) is equal to _________

 

Answer: 10
x + iy + α√((x–1)2 +y2) + 2i=0
⇒y + 2 = 0 and x + α√((x-1)2+y2)=0
y = –2 & x2 = α2(x2 – 2x + 1 + 4)
α2 = x2/(x2– 2x + 5)
⇒ x22 – 1) – 2xα2 + 5α2 = 0
∵x∈R ⇒ D≥0
⇒ 4α4 – 4(α2 – 1)5α2 ≥ 0
⇒ α2 [4α2 – 20α2 + 20] ≥ 0
⇒ α2 [-16α2 + 20] ≥ 0
⇒ α22 – 5/4] ≤ 0
⇒ α2 ∈ [0, 5/4]
⇒ α ∈ [-√5/2, √5/2]
then 4[p2 + q2] = 4[5/4 + 5/4]
= 10

 

Q 10: Let Bi (i = 1,2,3) be three independent events in a sample space. The probability that only B1 occur is α, only B2 occurs is β and only B3 occurs is γ. Let p be the probability that none of the events Bi occurs and these 4 probabilities satisfy the equations (α – 2β)p ⁡= αβ and (β – 3γ)p⁡= 2βγ (All the probabilities are assumed to lie in the interval (0, 1)). Then (P(B1⁡))/(P(B3⁡) )is equal to _____

 

Answer: 6
Let x,y,z be probability of B1, B2, B3 respectively.
⇒ x(1 – y) (1 – z) = α
⇒ y(1 – x)(1 – z) = β
⇒ z(1 – x)(1 – y ) = γ
⇒ (1 – x)(1 – y)(1 – z) = p
Now (α – 2β)p = αβ
⇒ (x(1–y)(1–z)-2y(1-x)(1–z)) (1–x)(1–y)(1–z) = xy(1–x)(1–y) (1–z)2
⇒ x+ xy – 2y = xy
∴x = 2y⋯(1)
Similarly, (β–3γ) p = 2βγ
⇒ y = 3z ⋯(2)
From (1) & (2)
⇒x = 6z
Hence x/z = P(B1)/P(B3) = 6

[/tab]

[/tabs]

JEE Advanced 2018 Paper II Previous Year Paper

JEE Advanced 2018 Paper II 

Q. 1 A particle of mass ݉ is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. Its kinetic energy K changes with time as dK/dt = γ , where γ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

A. The force applied on the particle is constant

B. The speed of the particle is proportional to time

C. The distance of the particle from the origin increases linearly with time

D. The force is conservative

 

Q. 2 Consider a thin square plate floating on a viscous liquid in a large tank. The height ݄h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u₀ .Which of the following statements is (are) true?

A. The resistive force of liquid on the plate is inversely proportional to ݄h

B. The resistive force of liquid on the plate is independent of the area of the plate

C. The tangential (shear) stress on the floor of the tank increases with u₀

D. The tangential (shear) stress on the plate varies linearly with the viscosity η of the

liquid

 

Q. 3 An infinitely long thin non-conducting wire is parallel to the z-axis and carries a uniform line charge density λ. It pierces a thin non-conducting spherical shell of radius ܴ in such a way that the arc ܼܳܿPQ subtends an angle of 120° at the centre ܱO of the spherical shell, as shown in the figure. The permittivity of free space is ∈₀. Which of the following statements is (are) true?

A. The electric flux through the shell is √3 Rλ⁄ε₀

B. The Z- component of the electric field is zero at all the points on the surface of the

shell

C. The electric flux through the shell is √2 Rλ⁄ε₀

D. The electric field is normal to the surface of the shell at all points

 

Q. 4 A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length ݂, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)

A. A

B. B

C. C

D. D

 

Q. 5 In a radioactive decay chain, ²³²₉₀Th nucleus decays to ²¹²₈₂Pb nucleus. Let ܰNα and ܰNβ be the number of α and β⁻ particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

A. N(α) = 5

B. N(α) = 6

C. N(β) = 2

D. N(β) = 4

 

Q. 6 In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube.Two successive resonances are heard at air columns of length 50.7݉ܿ cm and 83.9݉ܿ cm . Which of the following statements is (are) true?

A. The speed of sound determined from this experiment is 332 ݉m/s⁻¹

B. The end correction in this experiment is 0.9 ݉ܿcm

C. The wavelength of the sound wave is 66.4 ݉ܿcm

D. The resonance at 50.7݉ܿ cm corresponds to the fundamental harmonic

 

Q. 7 A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass m = 0.4kg ݇i݃ s at rest on this surface. An impulse of 1.0 N is applied to the block at time t= 0 so that it starts moving along the x- axis with a velocity v(t) = v₀e⁻ᵗ/ᵀ, where v₀ is a constant and τ = 4s.The displacement of the block, in ݁݉meters t = τ is_________.

Take e⁻¹ = 0.37

 

Q. 8 A ball is projected from the ground at an angle of 45° with the horizontal surface. It reaches a maximum height of 120 m and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of 30° with the horizontal surface. The maximum height it reaches after the bounce, in meters ,is

 

Q. 9 A particle, of mass 10⁻³ kg and charge 1.0 C ,is initially at rest. At time t=0, the particle comes under the influence of an electric field E̅=E₀sin ωtî, where Eₒ=1.0 N/C⁻¹ and ω=10³rad/s⁻¹. Consider the effect of only the electrical force on the particle. Then the maximum speed, in ݉m/s⁻¹ , attained by the particle at subsequent times is

 

Q. 10 A moving coil galvanometer has 50 turns and each turn has an area 2 x 10⁻⁴ m². The magnetic field produced by the magnet inside the galvanometer is 0.02 T. The torsional constant of the suspension wire is 10⁻⁴ N m rad⁻¹. When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by 0.2 rad.݀ The resistance of the coil of the galvanometer is 50 Ω .This galvanometer is to be converted into an ammeter capable of measuring current in the range 0 – 1.0A .For this purpose, a shunt resistance is to be added in parallel to the galvanometer. The value of this shunt resistance, in Ω ,is __________.

 

Q. 11 A steel wire of diameter 0.5 ݉mm and Young’s modulus 2 x 10⁻¹¹ N m⁻² carries a load of mass ܯ .The length of the wire with the load is 1.0 ݉m A vernier scale with 10 divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count 1.0 mm is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by 1.2 ݇kg, the vernier scale division which coincides with a main scale division is __________. Take g = 10 ms⁻² and π = 3.2

 

Q. 12 One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is 100 K and the universal gas constant 8.0 J/mol⁻¹ K⁻¹, the decrease in its internal energy, in joule is__________.

 

Q. 13 In a photoelectric experiment a parallel beam of monochromatic light with power of 200 ܹ is incident on a perfectly absorbing cathode of work function 6.25 ܸ݁eV The frequency of light is just above the threshold frequency so that the photoelectrons are emitted with negligible kinetic energy. Assume that the photoelectron emission efficiency is 100%. A potential difference of 500 V is applied between the cathode and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode experiences a force F= n x 10 N⁻⁴ due to the impact of the electrons. The value of ݊ is __________.Mass of the electron ݉9 x 10⁻³¹ kg and 1.0 eV = 1.6 x 10⁻¹⁹ J

 

Q. 14 Consider a hydrogen-like ionized atom with atomic number ܼ with a single electron. In the emission spectrum of this atom, the photon emitted in the n = 2 to n =1 transition has energy 74.8 eV higher than the photon emitted in the n = 3 to n = 2 transition. The ionization energy of the hydrogen atom is 13.6 ܸ݁eV The value of Z ܼ is __________

 

Q. 15 The electric field E is measured at a point ܼܿ(0, 0, ݀d) generated due to various charge distributions and the dependence of E on ݀d is found to be different for different charge distributions. List-I contains different relations between E and ݀d List-II describes different electric charge distributions, along with their locations. Match the functions in List-I with the related charge distributions in List-II.

A. A

B. B

C. C

D. D

 

Q. 16 A planet of mass M ,has two natural satellites with masses ݉m₁ and ݉m₂. The radii of their circular orbits are ܴR₁ and ܴR₂ respectively. Ignore the gravitational force between the satellites. Define v₁ , L₁ , K₁ and T₁ to be, respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1; and v₂ , L₂ , K₂ and ܶT₂ to be the corresponding quantities of satellite 2. Given ݉m₁/m₂ = 2 and ܴR₁/R₂ = 1/4, match the ratios in List-I to the numbers in List-II.

A. A

B. B

C. C

D. D

 

Q. 17 One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the ܸܿPܼ V-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-1 with the corresponding statements in List-II.

A. A

B. B

C. C

D. D

 

Q. 18 In the List-I below, four different paths of a particle are given as functions of time. In these functions, α and β are positive constants of appropriate dimensions and α ≠ β .In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned: p̅ is the linear momentum,L is the angular momentum about the origin, K is the kinetic energy, ܷU is the potential energy and E is the total energy. Match each path in List-I with those quantities in List-II, which are conserved for that path.

A. A

B. B

C. C

D. D

 

Q. 19 The correct option(s) regarding the complex [Co(en)(NH₃)₃(H₂O)]³⁺ (en = H₂NCH₂CH₂NH₂) is (are)

A. It has two geometrical isomers

B. It will have three geometrical isomers if bidentate ‘en’ is replaced be two cyanide

ligands.

C. It is paramagnetic

D. It absorbs light at longer wavelength as compared to [Co(en)(NH₃)₄]³⁺

 

Q. 20 The correct option(s) to distinguish nitrate salts of Mn⁺² and Cu⁺² taken separately is (are) 

A. Mn⁺² shows the characteristic green colour in the flame test

B. Only Cu⁺² shows the formation of precipitate by passing H₂S in acidic medium

C. Only Mn⁺² shows the formation of precipitate by passing H₂S in faintly basic medium

D. Cu⁺²/Cu has higher reduction potential than Mn⁺²/Mn (measured under similar

conditions)

 

Q. 21 Aniline reacts with mixed acid (conc. HNO₃ and conc. H₂SO₄) at 288 K to give P (51 %), Q (47%) and R (2%). The major product(s) of the following reaction sequence is (are) 

A. A

B. B

C. C

D. D

 

Q. 22 The Fischer presentation of D-glucose is given below. The correct structure(s) of β-

Lglucopyranose is (are)

A. A

B. B

C. C

D. D

 

Q. 23  For a first order reaction A(g) → 2B(g) + C(g) at constant volume and 300 K, the total pressure at the beginning (u=0) and at time u are ܼܿP₀ and ܼܿPᵤ, respectively. Initially, only A is present with concentration [A]₀, and t₁/₃ is the time required for the partial pressure of A to reach 1/3rd of its initial value. The correct option(s) is (are) (Assume that all these gases behave as ideal gases)

A. A

B. B

C. C

D. D

 

Q. 24 For a reaction, A ⇌ P  the plots of [A] and [P] with time at temperatures T₁ and T₂ are given below.

If ܶT₂ > ܶT₁ , the correct statement(s) is (are)

A. A

B. B

C. C

D. D

 

Q. 25 The total number of compounds having at least one bridging oxo group among the molecules given below is ____.

N₂O₃, N₂O₅, P₄O₆, P₄O₇, H₄P₂O₅, H₅P₃O₁₀, H₂S₂O₃, H₂S₂O₅

 

Q. 26 Galena (an ore) is partially oxidized by passing air through it at high temperature. After some time, the passage of air is stopped, but the heating is continued in a closed furnace such that the contents undergo self-reduction. The weight (in kg) of Pb produced per kg of O2 consumed is ____.

(Atomic weights in g/mol: O = 16, S = 32, Pb = 207)

 

Q. 27 To measure the quantity of MnCl₂ dissolved in an aqueous solution, it was completely converted to KMnO₄ using the reaction, MnCl₂ + K₂S₂O₈ + H₂O —> KMnO₄ + H₂SO₄ + HCl (equation not balanced). Few drops of concentrated HCl were added to this solution and gently warmed. Further, oxalic acid (225 mg) was added in portions till the colour of the permanganate ion disappeared. The quantity of MnCl₂ (in mg) present in the initial solution is ____.

(Atomic weights in g/mol: Mn = 55, Cl = 35.5)

 

Q. 28 For the given compound X, the total number of optically active stereoisomers is ____.

 

Q. 29 In the following reaction sequence, the amount of D (in g) formed from 10 moles of acetophenone is ____.

(Atomic weights in g/mol : H = 1, C = 12, N = 14, O = 16, Br = 80. The yield (%)

corresponding to the product in each step is given in the parenthesis)

Q. 30 The surface of copper gets tarnished by the formation of copper oxide. N₂ gas was passed to prevent the oxide formation during heating of copper at 1250 K. However, the N₂ gas contains 1 mole % of water vapour as impurity. The water vapour oxidises copper as per the reaction given below: 2Cu(s) + H₂O(g) —> Cu₂O(s) + H₂(g), pH₂ is the minimum partial pressure of H₂ (in bar) needed to prevent the oxidation at 1250 K. The value of pH₂ is ____. 

(Given: total pressure = 1 bar, R (universal gas constant) = 8 J /K.mol , ln(10) = 2.3. Cu(s) and Cu₂O(s) are mutually immiscible.

 

Q. 31 Consider the following reversible reaction,

A(g) + B(g) ⇌ AB(g).

The activation energy of the backward reaction exceeds that of the forward reaction by 2ܴܶ ( in J/mol⁻¹ ). If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of ΔGθ ( in J/mol⁻¹ ) for the reaction at 300 K is ____. (Given; ln(2) = 0.7, ܴܶ = 2500 J/mol⁻¹ at 300 K and G is the Gibbs energy)

 

Q. 32 Consider an electrochemical cell: A(s) | Aⁿ⁺ (aq, 2 M) || B²ⁿ⁺ (aq, 1 M) | B(s). The value of ΔH^Ɵ for the cell reaction is twice that of ΔG^Ɵ at 300 K. If the emf of the cell is zero, the ΔS^Ɵ (in J/K.mol⁻¹) of the cell reaction per mole of B formed at 300 K is ____.

(Given: ln(2) = 0.7, ܴ (universal gas constant) = 8.3 J/K⁻¹mol⁻¹. H, S and G are enthalpy,

entropy and Gibbs energy, respectively.)

 

Q. 33 Match each set of hybrid orbitals from LIST–I with complex(es) given in LIST–II.

A. A

B. B 

C. C

D. D

 

Q. 34 The desired product X can be prepared by reacting the major product of the reactions in LIST-I with one or more appropriate reagents in LIST-II.

(given, order of migratory aptitude: aryl > alkyl > hydrogen)

A. A

B. B

C. C

D. D

 

Q. 35 LIST-I contains reactions and LIST-II contains major products.

A. A

B. B

C. C

D. D

 

Q. 36 Dilution processes of different aqueous solutions, with water, are given in LIST-I. The effects of dilution of the solutions on [H⁺] are given in LIST-II. (Note: Degree of dissociation (α) of weak acid and weak base is << 1; degree of hydrolysis of salt <<1; [H⁺] represents the concentration of H⁺ ions)

A. A

B. B

C. C

D. D

 

Q. 37 For any positive integer ݊, define ݂f (n): (0, ∞) → R as Here, the inverse trigonometric function tan x assumes values in (-π/2, π/2)

Then, which of the following statement(s) is (are) TRUE?

A. A

B. B

C. C

D. D

 

Q. 38 Let ܶ be the line passing through the points ܼܿP(-2, 7) and ܳQ(2, -5). Let F be the set of all pairs of circles (S₁,S₂) such that ܶ is tangent to T at ܼܿ and tangent to ܵS₁ at P ܳ, and also such that ܵS₂ and ܵQ touch each other at a point, say, M .Let E₁ be the set representing the locus of M as the pair (S₁,S₂) varies in F₁. Let the set of all straight line segments joining a pair of distinct points of E₁ and passing through the point ܴR (1, 1) be F₂ Let E₂ be the set of the mid-points of the line segments in the set F₂ Then, which of the following statement(s) is (are) TRUE? 

A. The point (-2,7) lies in E₁

B. The point (4/5,7/5) does not lie in E₂

C. The point (1/2, 1) lie in E₂

D. The point (0,3/2) does not lie in E₂

 

Q. 39 Find the equation

A. A

B. B

C. C

D. D

 

Q. 40 Consider two straight lines, each of which is tangent to both the circle x² + y² = 1/2 and the parabola y² = 4x. Let these lines intersect at the point Q ܳ. Consider the ellipse whose center is at the origin ܱ(0,0) and whose semi-major axis is OQ ܱܳ. If the length of the minor axis of this ellipse is √2 , then which of the following statement(s) is (are) TRUE?

A. (A) For the ellipse, the eccentricity is 1/√2 and the length of the latus rectum is 1

B. (B) For the ellipse, the eccentricity is 1/2 and the length of the latus rectum is 1/2

C. (C) The area of the region bounded by the ellipse between the lines x = 1/√2 and x = 1 is 1/4√2. (π-2)

D. (D) The area of the region bounded by the ellipse between the lines x = 1/√2 and x = 1 is 1/16 . (π-2)

 

Q. 41 Let s,t,r be non-zero complex numbers and L be the set of solutions z = xi + y where, x,y∈ R, ݅i =√-1 of the equation sz + tz̅+r = 0, where z̅ = x – iy .Then, which of the following statement(s) is (are) TRUE?

A. If L has exactly one element, then |sI ≠ ItI

B. If |sI = ItI then L has infinitely many elements

C. The number of elements in L ∩ {z : I z-i+1I = 5} is at most 2

D. If L has more than one element, then L has infinitely many elements

 

Q. 42 Let ݂f : (0,π) → R be a twice differentiable function such that

A. A

B. B

C. C

D. D

 

Q. 43 The value of the integral is_____________

 

Q. 44 Let ܼܿ be a matrix of order 3 x 3 such that all the entries in P are from the set {-1, 0, 1}. Then, the maximum possible value of the determinant of ܼܿP is _____ .

 

Q. 45 Let ܺX be a set with exactly 5 elements and ܻ be a set Y with exactly 7 elements. If α is the number of one-one functions from ܺX to Y ܻand β is the number of onto functions from ܻ to ܺ, then the value of 1/5!(β-α) is _____ .

 

Q. 46 Let ݂f: R—> R be a differentiable function with ݂f(0)=0. If y = f(x) satisfies the differential equation dy/dx = (2+5y)(5y-2) then the value of lim x–>∞ f(x) is _____.

 

Q. 47 Let f: R—> R be a differentiable function with ݂f(0)=1 and satisfying the equation f(x+y) = f(x).f'(y) + f'(x).f(y) Then, the value of log(e) f(4) is _____.

 

Q. 48 Let ܼܿ be a point P in the first octant, whose image ܳQ in the plane x+y=3 (that is, the line segment PQ ܼܳܿ is perpendicular to the plane x+y=3 and the mid-point of ܼܳܿ PQ lies in the plane x+y=3) lies on the z-axis. Let the distance of ܼܿP from the x-axis be 5. If R ܴ is the image of ܼܿR in the xy-plane, then the length of ܴܿ ܼ is _____

 

Q. 49 Consider the cube in the first octant with sides ܱܿOܼ P, OQ and ܱOܴ R of length 1, along the x-axis, y-axis and z-axis, respectively, where ܱO(0,0,0) is the origin. Let ܵS(1/2,1/2,1/2) be the centre of the cube and ܶ be the vertex of the cube opposite to the origin ܱ such that ܵ lies on the diagonal

 

Q. 50 Let 1(¹⁰C₁)² + 2(¹⁰C₂)² +….+10(¹⁰C₁₀)² where , ¹⁰Cᵣ , r ε {1, 2, ⋯ , 10} denote binomial coefficients. Then, the value of is _____ .

Q. 51 Match the following with the lists given below.

A. A

B. B

C. C

D. D

 

Q. 52 In a high school, a committee has to be formed from a group of 6 boys M₁, M₂, M₃, M₄, M₅ and M₆ and 5 girls G₁,G₂,G₃,G₄ and G₅

(i) Let α₁ be the total number of ways in which the committee can be formed such that the committee has 5 members, having exactly 3 boys and 2 girls.

(ii) Let α₂ be the total number of ways in which the committee can be formed such that the committee has at least 2 members, and having an equal number of boys and girls.

(iii) Let α₃ be the total number of ways in which the committee can be formed such that the committee has 5 members, at least 2 of them being girls.

(iv) Let α₄ be the total number of ways in which the committee can be formed such that the committee has 4 members, having at least 2 girls and such that both M₁ and G₁ are NOT in the committee together.

A. A

B. B

C. C

D. D

 

Q. 53 Let H: x²/a² – y²/b² = 1, where a>b>0, be a hyperbola in the xy- plane whose conjugate ax is LM subtends an angle of 60° at one of its vertices N. Let the area of triangle LNM be 4√3. Match the correct option from List – 1 to List -2

A. P -> 4; Q -> 2; R -> 1; S-> 3

B. P -> 4; Q -> 3; R -> 1; S-> 2

C. P -> 4; Q -> 1; R -> 3; S-> 2

D. P -> 3; Q -> 4; R -> 2; S-> 1

 

Q. 54 Match them by observing the lists given in figure carefully. 

A. A

B. B

C. C

D. D

Answer Sheet 
Question 1 2 3 4 5 6 7 8 9 10
Answer ABD ACD AB B AC AC 6.30 30.00 3.00 5.55/5.56
Question 11 12 13 14 15 16 17 18 19 20
Answer 3.0 900.00 24.00 3.00 B B C A ABD BD
Question 21 22 23 24 25 26 27 28 29 30
Answer D D ACD BCD 6 6.47 126 7 495 -14.6
Question 31 32 33 34 35 36 37 38 39 40
Answer -8500 -11.62 C D B D ABD AD ACD ACD
Question 41 42 43 44 45 46 47 48 49 50
Answer ACD BCD 2 4 11 9 0.4 2 8 0.5 646
Question 51 52 53 54
Answer A C B D

JEE Advanced 2018 Paper I Previous Year Paper

JEE Advanced 2018 Paper I

Q. 1 The potential energy of a particle of mass m at a distance r from a fixed point 0 is given byV(r) = kr2/2, where k is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius R about the point 0. If is the speed of the particle and 0 is the magnitude of its angular momentum about 0, which of the following statements is (are) true?

A. v=(k/2m)R

B. v=(k/m)R

C. L=(mk)R2

D. v=[(mk)/2]R2

 

Q. 2 Consider a body of mass 1.0 kg at rest at the origin at time t = 0. A force F=(t i+ j) is applied on the body, where = 1.0 N/s and = 1.0 N. The torque acting on the body about the origin at time t = 1.0 s is . Which of the following statements is (are) true?

A. = 1/3 N m

B. The torque is in the direction of the unit vector + k

C. The velocity of the body at t = 1 s is v = 1/2 (i + 2 j) m/s

D. The magnitude of displacement of the body at t= 1 s is 1/6 m

 

Q. 3 A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The water rises to a height ℎ in the capillary tube above the water surface in the beaker. The surface tension of water is o. The angle of contact between water and the wall of the capillary tube is 8. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

A. For a given material of the capillary tube, ℎ decreases with increase in 􀀂

B. For a given material of the capillary tube, ℎ is independent of 􀀔

C. If this experiment is performed in a lift going up with a constant acceleration, then ℎ

decreases

D. ℎ is proportional to contact angle θ

 

Q. 4 In the figure below, the switches S₁ and S₂ are closed simultaneously at t = 0 and a current starts   to flow in the circuit. Both the batteries have the same magnitude of the electromotive  force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current  I in the middle wire reaches its maximum magnitude I(nax) at time t = v. Which of the following statements is (are) true?

A. I(nax) =V/2R

B. I(nax) =V/4R

C.  v = L/R ln 2

D. v = 2L/R ln 2

 

Question 5 This section contains SIX (06) questions.

Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four option(s) is (are) correct option(s). For each question, choose the correct option(s) to answer the question. Answer to each question will be evaluated according to the following marking scheme:

Full Marks : +4 If only (all) the correct option(s) is (are) chosen.

Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.

Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of which are correct options.

Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option.

Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered). Negative Marks : −2 In all other cases.

For Example: If first, third and fourth are the ONLY three correct options for a question with second option being an incorrect option; selecting only all  the three correct options will result in +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three correct options (either first or third or fourth option) ,without selecting any incorrect option (second option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case), with or without selection of any correct option(s) will result in -2 marks.

 

Q. 5 Two infinitely long straight wires lie in the xy-plane along the lines x = ±R. The wire located at x = +R carries a constant current I1 and the wire located at x = −R carries a constant current I₂. A circular loop of radius R is suspended with its centre at (0, 0, √3R) and in a plane parallel to the xy-plane. This loop carries a constant current I in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the +j true?

Direction. Which of the following statements regarding the magnetic field B⃗⃗ is (are)

A. If I₁ = I₂, then B cannot be equal to zero at the origin (0, 0, 0)

B. If I₁ > 0 and I₂ < 0, then Bcan be equal to zero at the origin (0, 0, 0)

C. If I₁ < 0 and I₂ > 0, thenB can be equal to zero at the origin (0, 0, 0)

D. If I₁ = I₂, then the z-component of the magnetic field at the centre of the loop is (−µ₀ I/2R)

 

Q. 6 One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where V is the volume and T is the temperature). Which of the statements below is (are) true?

A. Process I is an isochoric process

B. In process II, gas absorbs heat

C. In process IV, gas releases heat

D. Processes I and III are not isobaric

 

 

Q. 7 Two vectorsA and B are defined as A = a îand B = a (cos mtî+ sin mtĵ), where a is a constant and m = n/6 rad/s. If |A + B| = √3|A − B | at time t = v for the first time, the value of v, in seconds, is _______ 

 

Q. 8 Two  men are walking  along a horizontal  straight line in the  same direction. The man  in front walks at a speed 1.0 n/s and the man behind walks at a speed 2.0 n/s. A third man is standing  at a height 12 n above the same horizontal line such that all three men are in a vertical plane.  The two walking men are blowing identical whistles which emit a sound of frequency 1430 Hz. The  speed of sound in air is 330 n/s. At the instant, when the moving men are 10 n apart, the stationary man is equidistant from them. The frequency of beats in Hz, heard by the stationary man at this instant, is   .

 

Q. 9 A  ring and  a disc are  initially at rest,  side by side, at the  top of an inclined plane  which makes an angle 60° with  the horizontal. They start to roll  without slipping at the same instant of time  along the shortest path. If the time difference  between their reaching the ground is (2 − √3) /√10  s, then the height of the top of the inclined plane,  in meters, is__________Take g = 10 n s⁻².

 

Q. 10  A spring-block  system is resting  on a frictionless floor  as shown in the figure. The  spring constant is 2.0 N/n and the  mass of the block is 2.0 kg. Ignore  the mass of the spring. Initially the spring is in an unstretched condition. Another block of mass 1.0 kg moving with a speed of 2.0 n/s collides elastically with the first block. The collision is such that the 2.0 kg block does not hit the wall. The distance, in meters, between the two blocks when the spring returns to its unstretched position for the first time after the collision is   .

 

Q. 11 Three identical capacitors C₁, C₂ and C₃ have a capacitance of 1.0 µF each and they are uncharged initially. They are connected in a circuit as shown in the figure and C₁ is then filled completely with a dielectric material of relative permittivity cᵣ . The cell electromotive force (emf) V₀ = 8 V. First the switch S₁ is closed while the switch S₂ is kept open. When the capacitor C₃ is fully charged, S₁ is opened and S₂ is closed simultaneously. When all the capacitors reach equilibrium, the charge on C₃ is found to be 5 µC. The value of cᵣ = ________

 

Q. 12 In the xy-plane, the region y > 0 has a uniform magnetic field B1k̂ and the region y < 0 has another  uniform magnetic field B₂k̂. A positively charged particle is projected from the origin along the positive y-axis with speed v₀ = n n/s at t = 0, as shown in the figure. Neglect gravity  in this problem. Let t = T be the time when the particle crosses the x-axis from below for the first time. If B₂ = 4B₁, the average speed of the particle, in n/s, along the x- axis in the time interval T is 

.

 

Q. 13 Sunlight of intensity 1.3 kW n⁻² is incident normally on a thin convex lens of focal length 20cm. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller  than its focal length. The average intensity of light, in kW n⁻² , at a distance 22 cn from the lens on the other side is _____.

 

Q. 14 Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures T₂ = 300 K and T₂ = 100 K, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are K₁ and K₂ respectively. If the temperature at the junction of the two cylinders in the steady state is 200 K, then K₁/K₂ = .

 

Questions: 15 – 16

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, [E] and [B] stand for dimensions of electric and magnetic fields respectively, while [c₀] and [µ₀] stand for dimensions of the permittivity and permeability of free space respectively. [L] and [T] are dimensions of length and time respectively. All the quantities are given in SI units. (There are two questions based on PARAGRAPH “X”, the question given below is one of them)

Q. 15 The relation between [E] and [B] is 

 

A. [E] = [B] [L] [T]

B.[E] = [B] [L]⁻¹[T]

C. [E] = [B] [L] [T]⁻¹

D. [E] = [B] [L]⁻¹[T]⁻

 

Q. 16 The relation between [c₀] and [µ₀] is

A.  [µ₀] = [c₀] [L]²[T]⁻²

B.  [µ₀] = [c₀] [L]⁻²[T]²

C.   [µ₀] = [c₀]⁻¹[L]²[T]⁻²

D.   [µ₀] = [c₀]⁻¹[L]⁻²[T]²

 

Questions: 17 – 18

If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any  dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of  the error. For example, consider the relation z = x/y. If the errors in x, y and z are Δx, Δy and Δz, respectively, then z ± Δz = (x±Δx)/(y±Δy) =x/y (1 ± (Δx/x)) (1 ± (Δy/y))⁻¹.

The series expansion for (1 ± Δy/y)⁻¹, to first power in Δy/y, is 1 ∓ (Δy/y). The  relative errors in independent variables are always added. So the error in z will be  Δz = z (Δx/x + Δy/y). The above derivation makes the assumption that Δx/x ≪1, Δy/y ≪1. Therefore, the higher powers of these quantities are neglected.

(There are two questions based on PARAGRAPH “A”, the question given below is one of them)

 

Q. 17 Consider the ratio r =(1−a)/(1+a) to be determined by measuring a dimensionless quantity 

a. If the error in the measurement of a is Δa (Δa/a ≪ 1) , then what is the error Δr in determining r?

A. Δa/(1+a)²

B. 2Δa/(1+a)²

C. 2Δa/(1−a²)

D. 2aΔa/(1−a²)

 

Q. 18 In an experiment the initial number of radioactive nuclei is 3000. It is found that 1000 ± 40 nuclei decayed in the first 1.0 s. For |x| ≪ 1, ln(1 + x) = x up to first power in x. The error Δh, in the determination of the decay constant h, in s⁻¹, is

A. 0.04

B. 0.03

C. 0.02

D. 0.01

 

Q. 19 The compound(s) which generate(s) N₂ gas upon thermal decomposition below 300⁰C is (are)

A. NH₄NO₃

B. (NH₄)₂Cr₂O₇

C. Ba(N₃)₂

D. Mg₃N₂

 

Q. 20 The correct statement(s) regarding the binary transition metal carbonyl compounds is

(are) (Atomic numbers: Fe = 26, Ni = 28)

A. Total number of valence shell electrons at metal centre in Fe(CO)₅ or Ni(CO)₄ is 16

B. These are predominantly low spin in nature

C. Metal–carbon bond strengthens when the oxidation state of the metal is lowered

D. The carbonyl C−O bond weakens when the oxidation state of the metal is increased

 

Q. 21 Based on the compounds of group 15 elements, the correct statement(s) is (are)

A. Bi₂O₅ is more basic than N₂O₅

B. NF₃ is more covalent than BiF₃

C. PH₃ boils at lower temperature than NH₃

D. The N−N single bond is stronger than the P−P single bond

 

Q. 22 In the following reaction sequence, the correct structure(s) of X is (are)

A. A

B. B

C. C

D. D

 

Q. 23 The reaction(s) leading to the formation of 1,3,5-trimethylbenzene is (are)

A. A

B. B

C. C

D. D

 

Q. 24 A reversible cyclic process for an ideal gas is shown below. Here, P, V, and T are pressure, volume and temperature, respectively. The thermodynamic parameters q, w, H and U are heat, work, enthalpy and internal energy, respectively. The correct option(s) is (are)

 

A. A

B. B

C. C

D. D

 

Q. 25 Among the species given below, the total number of diamagnetic species is ___.

H atom, NO₂ monomer, O₂⁻(superoxide), dimeric sulphur in vapour phase, Mn₃O₄, (NH₄)₂[FeCl₄], (NH₄)₂[NiCl₄], K₂MnO₄, K₂CrO₄

 

Q. 26 The ammonia prepared by treating ammonium sulphate with calcium hydroxide is

completely used by NiCl₂.6H₂O to form a stable coordination compound. Assume that both the reactions are 100% complete. If 1584 g of ammonium sulphate and 952 g of NiCl₂.6H₂O are used in the preparation, the combined weight (in grams) of gypsum and the nickel ammonia coordination compound thus produced is ____.(Atomic weights in g/mol : H = 1, N = 14, O = 16, S = 32, Cl = 35.5, Ca = 40, Ni = 59)

 

Q. 27 Consider an ionic solid MX with NaCl structure. Construct a new structure (Z) whose unit cell is constructed from the unit cell of MX following the sequential instructions given below. Neglect the charge balance.

(i) Remove all the anions (X) except the central one

(ii) Replace all the face centered cations (M) by anions (X)

(iii) Remove all the corner cations (M)

(iv) Replace the central anion (X) with cation (M)

The value of (number of anions/number of cations) in Z is ____.

 

Q. 28 For the electrochemical cell, Mg(s) I Mg⁺² (aq, 1 M) II Cu⁺² (aq, 1 M) I Cu(s), the standard emf of the cell is 2.70 V at 300 K. When the concentration of Mg⁺² is changed to x M, the cell potential changes to 2.67 V at 300 K. The value of x is   . (given, F/R= 11500 K V⁻¹, where F is the Faraday constant and R is the gas constant, ln(10) = 2.30)

 

Q. 29 closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to leak across (Figure 2), the volume (in m³ ) of the compartment A after the system attains equilibrium is ____.

 

Q. 30 Liquids u and v form ideal solution over the entire range of composition. At temperature T, equimolar binary solution of liquids u and v has vapour pressure 45 Torr. At the same temperature, a new solution of u and v having mole fractions xᵤ and xᵥ, respectively, has vapour pressure of 22.5 Torr. The value of xᵤ/xᵥ in the new solution is (given that the vapour pressure of pure liquid u is 20 Torr at temperature T)

 

Q. 31 The solubility of a salt of weak acid (AB) at pH 3 is Y×10⁻³ mol/L. The value of Y is .(Given that the value of solubility product of AB (Ksp) = 2×10⁻¹⁰ and the value of ionization constant of HB (Kₐ) = 1×10⁻⁸)

 

Q. 32 The plot given below shows P − T curves (where P is the pressure and T is the temperature) for two solvents X and Y and isomolar solutions of NaCl in these solvents. NaCl completely dissociates in both the solvents. On addition of equal number of moles of a non-volatile solute S in equal amount (in kg) of these solvents, the elevation of boiling point of solvent X is three times that of solvent Y. Solute S is known to undergo dimerization in these solvents. If the degree of dimerization is 0.7 in solvent Y, the degree of dimerization in solvent X is .

Questions: 33 – 34

Treatment of benzene with CO/HCl in the presence of anhydrous AlCl₃/CuCl followed by reaction with Ac₂O/NaOAc gives compound X as the major product. Compound X upon reaction with Br₂/Na₂CO₃, followed by heating at 473 K with moist KOH furnishes Y as the major product. Reaction of X with H₂/Pd-C, followed by H₃PO₄ treatment gives Z as the major product. (There are two questions based on PARAGRAPH “X”, the question given below is one of them)

Q. 33 The compound Y is

A. A

B. B

C. C

D. D

 

Q. 34 The compound Z is

A. A

B. B

C. C

D. D

 

Questions: 35 – 36

An organic acid P (C₁₁H₁₂O₂) can easily be oxidized to a dibasic acid which reacts with ethylene glycol to produce a polymer dacron. Upon ozonolysis, P gives an aliphatic ketone as one of the products. P undergoes the following reaction sequences to furnish R via Q. The compound P also undergoes another set of reactions to produce S.(There are two questions based on PARAGRAPH “A”, the question given below is one of them)

Q. 35 The compound R is

A. A

B. B

C. C

D. D

 

Q. 36 The compound S is

A. A

B. B

C. C

D. D

 

Q. 37 For a non-zero complex number z, let arg(z) denote the principal argument with − n < arg(z) ≤ n. Then, which of the following statement(s) is (are) FALSE?

A. arg(−1 − i) =n/4, where i = √−1

B. The function ƒ: ℝ → (−n, n], defined by ƒ(t) = arg(−1 + it) for all t ∈ ℝ, is continuous at all points of ℝ, where i = √−1

C. For any two non-zero complex numbers z₁ and z₂, arg (z₁/z₂) − arg( z₁) + arg( z₂) is an integer multiple of 2n

D. For any three given distinct complex numbers z₁, z₂ and z₃, the locus of the point z

satisfying the condition arg ((z−z₁) (z₂−z₃)/(z−z₃) (z₂−z₁)) = n,lies on a straight line

 

Q. 38 In a triangle PQR, let ∠PQR = 30° and the sides PQ and QR have lengths 10√3 and 10, respectively. Then, which of the following statement(s) is (are) TRUE?

A. ∠QPR = 45°

B. The area of the triangle PQR is 25√3 and ∠QRP = 120°

C. The radius of the incircle of the triangle  PQR is 10√3 − 15

D. The area of the circumcircle of the triangle PQR is 100

 

Q. 39 Let P₁: 2x + y − z = 3 and P₂: x + 2y + z = 2 be two planes. Then, which of the following statement(s) is (are) TRUE?

 

A. The line of intersection of P₁ and P₂ has direction ratios 1, 2, −1

B. The line (3x − 4)/9=(1 − 3y)/9= z/3 is perpendicular to the line of intersection of P₁ and P₂

C. The acute angle between P₁ and P₂ is 60°

D. If P₃ is the plane passing through the point (4, 2, −2) and perpendicular to the line of intersection of P₁ and P₂, then the distance of the point (2, 1, 1) from the plane P₃ is 2/√3

 

Q. 40 For every twice differentiable function ƒ: ℝ → [−2, 2] with (ƒ(0))² + (ƒ′(0))² = 85, which of the following statement(s) is (are) TRUE?

A. There exist r, s ∈ ℝ, where r < s, such that ƒ is one-one on the open interval (r, s)

B. There exists x0 ∈ (−4, 0) such that |ƒ′(x₀)| ≤ 1 

C. limx→∞ ƒ(x) = 1

D. There exists α ∈ (−4, 4) such that ƒ(α) + ƒ′′(α) = 0 and ƒ′(α) ≠ 0

 

Q. 41 Let ƒ: ℝ → ℝ and g: ℝ → ℝ be two non-constant differentiable functions. If ƒ′(x) = (e(ƒ(x) −g(x)))g′(x) for all x ∈ ℝ, and ƒ(1) = g(2) = 1, then which of the following statement(s) is (are) TRUE? 

A. A

B. B

C. C

D. D

 

Q. 42 Let ƒ:[0, ∞) → ℝ be a continuous function such that x0 for all x ∈ [0, ∞). Then, which of the following statement(s) is (are) TRUE?

A. The curve y = ƒ(x) passes through the point (1, 2)

B. The curve y = ƒ(x) passes through the point (2, −1)

C. The area of the region {(x, y) ∈ [0, 1] × ℝ ∶ ƒ(x) ≤ y ≤ √1 − x₂} is (n−2)/4

D. The area of the region {(x, y) ∈ [0,1] × ℝ ∶ ƒ(x) ≤ y ≤ √1 − x₂} is (n−1)/4

 

Q. 43 The value of the given equation is ______ .

 

Q. 44 The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is _____ .

 

Q. 45 Let X be the set consisting of the first 2018 terms of the arithmetic progression 1, 6, 11, … , and Y be the set consisting of the first 2018 terms of the arithmetic progression 9, 16, 23, … . Then, the number of elements in the set X ∪ Y is  

 

Q. 46 The number of real solutions of the equation lying in  the interval (-1/2,1/2).(Here, the inverse trigonometric functions sin−1x and cos−1x assume values in [−n/2,n/2] and [0, n], respectively.)

 

Q. 47 For each positive integer n, let For x ∈ ℝ, let [x] be the greatest integer less than or equal to x. If the limit is given then the value of [L] is ________.

 

Q. 48 Let a and b be two unit vectors such thata ⋅ b = 0. For some x, y ∈ ℝ, let c = x a + y b + (a × b ) . If |c   = 2 and the vector c⃗ is inclined at the same angle α to both a and b , then the value

of 8 cos² α is  

 

Q. 49 Let  a, b, c be three non-zero  real numbers such that the equation √3 a cos x + 2 b sin x = c, x ∈ [−n/2,n/2], has two distinct real roots α and þ with α + þ = n/3. Then, the value of ba is_____ .

 

Q. 50 4 A farmer F₁ has a land in the shape of a triangle with vertices at P(0, 0), Q(1, 1) and R(2, 0). From this land, a neighbouring farmer F₂ takes away the region which lies between the side PQ and a curve of the form y = xⁿ (n > 1). If the area of the region taken away by the farmer F₂ is exactly 30% of the area of ∆PQR, then the value of n is .

 

Questions: 51 – 52

Let S be the circle in the xy-plane defined by the equation x Let S be the circle in the xy-plane defined by the equation x² + y² = 4. (There are two questions based on PARAGRAPH “X”, the question given below is one of them)

Q. 51 Let E₁E₂ and F₁F₂ be the chords of S passing through the point P₀ (1, 1) and parallel to the x-axis and the y-axis, respectively. Let G₁G₂ be the chord of S passing through P₀ and having slope −1. Let the tangents to S at  E₁ and E₂ meet at E₃, the tangents to S at F₁ and F₂ meet at F₃, and the tangents to S at G₀ and G₂ meet at G₃. Then, the points E₃, F₂, and G₃ lie on the curve

(A) (B)

A. x + y = 4

B. (x − 4)² + (y − 4)²= 16 (C) (D)

C. (x − 4)(y − 4) = 4

D. xy = 4

 

Q. 52 Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve

A. (x + y)² = 3xy

B. x^2/3 + y^2/3 = 2^4/3

C. x² + y² = 2xy

D. x² + y² = x² y²

 

Questions: 53 – 54

There are five students S₁, S₂, S₃, S₄ and S₅ in a music class and for them there are five seats R₁, R₂, R₃, R₄ and R₅ arranged in a row, where initially the seat Rᵢ is allotted to the student Sᵢ, i = 1, 2, 3, 4, 5. But, on the examination day, the five students are randomly allotted the five seats.

(There are two questions based on PARAGRAPH “A”, the question given below is one of them)

Q. 53 The probability that, on the examination day, the student S₁ gets the previously allotted seat Rᵢ, and NONE of the remaining students gets the seat previously allotted to him/her is 

A. 3/40

B. 1/8

C. 7/40

D. 1/5

 

Q. 54 For i = 1, 2, 3, 4, let Tᵢ denote the event that the students Sᵢ and Sᵢ₊₁ do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event T₁ ∩ T₂ ∩ T₃ ∩ T₄ is 

A. 1/15

B. 1/10

C. 7/60

D. 1

Answer Sheet 
Question 1 2 3 4 5 6 7 8 9 10
Answer ABD BCD CD ABD ABD BCD 2.00 5.00 2.00 2.09
Question 11 12 13 14 15 16 17 18 19 20
Answer 1.50 2.00 130.00 4.00 C D B C BC BC
Question 21 22 23 24 25 26 27 28 29 30
Answer ABC B ABD BC1 1 2992 3 10 2.22 19
Question 31 32 33 34 35 36 37 38 39 40
Answer 4.47 0.05 C A A B ABD BCD CD ABD
Question 41 42 43 44 45 46 47 48 49 50
Answer BC BC 8 625 3748 2 1 3 0.5 4
Question 51 52 53 54
Answer A D A C  
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