Category: Engineering Entrance Exam

JEE Advanced 2017 paper II  

Q. 1 Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density ρ remains uniform throughout the volume. The rate of fractional change in density (dρ/ρdt) is constant. The velocity v of any point on the surface of the expanding sphere is proportional to

A. R

B. R³

C. 1/R

D. R²/³

 

Q. 2 Consider regular polygons with number of sides n = 3, 4, 5…… as shown in the figure. The center of mass of all the polygons is at height ℎ from the ground. They roll on a horizontal surface about the leading vertex without slipping and sliding as depicted. The maximum increase in height of the locus of the center of mass for each polygon is Δ. Then Δ depends on n and ℎ as

A. Δ=h sin²(Π/n)

B. Δ=h ((1/cos(Π/n)-1)

C. Δ=h sin(2Π/n)

D. Δ=h tan²(Π/2n)

 

Q. 3 A photoelectric material having work-function φ∘ is illuminated with light of wavelength λ(λ < hc/φ∘)The fastest photoelectron has a de Broglie wavelength λd A change in wavelength of the incident light by λd results in a change Δλd in λd. Then the ratio Δλd/Δλ is proportional to

A. λd/λ

B. (λd)²/λ²

C. (λd)³/λ

D. (λd)³/λ²

 

Q. 4 A symmetric star shaped conducting wire loop is carrying a steady state current I as shown in the figure. The distance between the diametrically opposite vertices of the star is 4a. The magnitude of the magnetic field at the center of the loop is

A. A

B. B

C. C

D. D

 

Q. 5 Three vectors P̅, Q̅ and R̅ are shown in the figure. Let S be any point on the vector R̅. The distance between the points P and S is b|R̅|. The general relation among vectors P̅, Q̅ and R̅ is

A. A

B. B

C. C

D. D

 

Q. 6 A rocket is launched normal to the surface of the Earth, away from the Sun, along the line joining the Sun and the Earth. The Sun is 3×10⁵ times heavier than the Earth and is at a distance 2.5×10⁴ times larger than the radius of the Earth. The escape velocity from Earth’s gravitational field is vₑ = 11.2 km/s⁻¹. The minimum initial velocity (vₛ) required for the rocket to be able to leave the Sun-Earth system is closest to (Ignore the rotation and revolution of the Earth and the presence of any other planet)

A. vs=22 km/s⁻¹

B. vs=42 km/s⁻¹

C. vs=62 km/s⁻¹

D. vs=72 km/s⁻¹

 

Q. 7 A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is δT=0.01 seconds and he measures the depth of the well to be L= 20 meters. Take the acceleration due to gravity g= 10 m/s² and the velocity of sound is 300 m/s⁻¹. Then the fractional error in the measurement, δL/L is closest to

A. 0.2%

B. 1%

C. 3%

D. 5%

 

Q. 8 A uniform magnetic field B exists in the region between x = 0 and x =3R/2(region 2 in the figure) pointing normally into the plane of the paper. A particle with charge +Q and momentum p directed along x-axis enters region 2 from region 1 at point P₁(y = −R). Which of the following option(s) is/are correct?

A. For B > 2p/3QR , the particle will re-enter region 1

B. For B=8p/13QR, the particle will enter region 3 through the point P₂ on x-axis

C. When the particle re-enters region 1 through the longest possible path in region 2,

the magnitude of the change in its linear momentum between point P₁ and the

farthest point from y-axis is p/√2

D. For a fixed B, particles of same charge Q and same velocity v, the distance between

the point P1 and the point of re-entry into region 1 is inversely proportional to the

mass of the particle

 

Q. 9 The instantaneous voltages at three terminals marked X, Y and Z are given by

Vₓ = V∘sin ωt, 

Vᵧ = V∘sin (ωt+2Π/3) and

V􀀁 = V∘sin (ωt+4Π/3)

An ideal voltmeter is configured to read rms value of the potential difference between its terminals. It is connected between points X and Y and then between Y and Z. The reading(s) of the voltmeter will be

A. A

B. B

C. C

D. D

 

Q. 10 A point charge +Q is placed just outside an imaginary hemispherical surface of radius R as shown in the figure. Which of the following statements is/are correct?

A. The electric flux passing through the curved surface of the hemisphere is -Q/2ε∘(1-1/ √2)

B. Total flux through the curved and the flat surfaces is Q/ε∘

C. The component of the electric field normal to the flat surface is constant over the

surface

D. The circumference of the flat surface is an equipotential

 

Q. 11 Two coherent monochromatic point sources S₁ and S₂ of wavelength λ = 600 nm are placed symmetrically on either side of the centre of the circle as shown. The sources are separated by a distance d = 1.8 mm. This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is Δθ. Which of the following options is/are correct?

A. A dark spot will be formed at the point P₂

B. At P₂ the order of the fringe will be maximum

C. The total number of fringes produced between P₁ and P₂ in the first quadrant is close to 3000

D. The angular separation between two consecutive bright spots decreases as we move

from P₁ to P₂ along the first quadrant

 

Q. 12 A source of constant voltage V is connected to a resistance R and two ideal inductors L₁ and L₂ through a switch S as shown. There is no mutual inductance between the two inductors. The switch S is initially open. At t = 0, the switch is closed and current begins to flow. Which of the following options is/are correct?

A. After a long time, the current through L₁ will be VL₂/R(L₁+L₂)

B. After a long time, the current through L₂ will be VL₁/R(L₁+L₂)

C. The ratio of the currents through L₁ and L₂ is fixed at all times (t > 0)

D. At t = 0, the current through the resistance R is V/R

 

Q. 13 A rigid uniform bar AB of length L is slipping from its vertical position on a frictionless floor (as shown in the figure). At some instant of time, the angle made by the bar with the vertical is θ. Which of the following statements about its motion is/are correct?

A. The midpoint of the bar will fall vertically downward

B. The trajectory of the point A is a parabola

C. Instantaneous torque about the point in contact with the floor is proportional to sinθ

D. When the bar makes an angle θ with the vertical, the displacement of its midpoint

from the initial position is proportional to (1 − cosθ)

 

Q. 14 A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque τ about an axis normal to the plane of the paper passing through the point Q. Which of the following options is/are correct?

A. If the force is applied at point P tangentially then τ decreases continuously as the

wheel climbs

B. If the force is applied normal to the circumference at point X then τ is constant

C. If the force is applied normal to the circumference at point P then τ is zero

D. If the force is applied tangentially at point S then τ≠ 0 but the wheel never climbs the step

 

Questions: 15 – 16

Consider a simple RC circuit as shown in Figure 1.

Process 1: In the circuit the switch S is closed at t = 0 and the capacitor is fully charged to voltage V₀(i.e., charging continues for time T >> RC). In the process some dissipation (Ed) occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is Ec. Process 2: In a different process the voltage isfirst set to V₀/3 and maintained for a charging time T >> RC. Then the voltage is raised to 2V₀/3 without discharging the capacitor and again maintained for a time T>> RC. The process is repeated one more time by raising the voltage to V₀ and the capacitor is charged to the same final voltage V₀ as in Process 1. These two processes are depicted in Figure 2.

Q. 15 In Process 1, the energy stored in the capacitor Ec and heat dissipated across resistance ED are related by:

A. Ec=ED

B. Ec=ED ln 2

C. Ec=1/2ED

D. Ec=2ED

 

Q. 16 In Process 2, total energy dissipated across the resistance ED is:

A. ED=1/2 CV₀²

B. Ed=3(1/2 CV₀²)

C. ED=1/3(1/2CV₀²)

D. ED=3 CV₀²

 

Questions: 17 – 18

One twirls a circular ring (of mass M and radius R) near the tip of one’s finger as shown in Figure 1. In the process the finger never loses contact with the inner rim of the ring. The finger traces out the surface of a cone, shown by the dotted line. The radius of the path traced out by the point where the ring and the finger is in contact is r. The finger rotates with an angular velocity ω₀. The rotating ring rolls without slipping on the outside of a smaller circle described by the point where the ring and the finger is in contact (Figure 2). The coefficient of friction between the ring and the finger is μ and the acceleration due to gravity is g.

Q. 17 The total kinetic energy of the ring is

A. Mω₀²R²

B. 1/2Mω₀²(R-r)²

C. Mω₀²(R-r)²

D. 3/2Mω₀²(R-r)²

 

Q. 18 The minimum value of ω₀ below which the ring will drop down is

A. √(g/μ(R-r))

B. √(2g/μ(R-r))

C. √(3g/2μ(R-r))

D. √(g/2μ(R-r))

 

Q. 19 Pure water freezes at 273 K and 1 bar. The addition of 34.5 g of ethanol to 500 g of water changes the freezing point of the solution. Use the freezing point depression constant of water as 2 K kg/mol⁻¹. The figures shown below represent plots of vapour pressure (V.P.) versus temperature (T). [molecular weight of ethanol is 46 g/mol⁻¹ ] Among the following, the option representing change in the freezing point is

A. A

B. B

C. C

D. D

 

Q. 20 For the following cell in the figure, when the concentration of Zn²⁺ is 10 times the concentration of Cu²⁺ , the expression for ΔG (in J/mol⁻¹ ) is

[F is Faraday constant; R is gas constant; T is temperature; E° (cell) =1.1V ]

A. 1.1F

B. 2.303RT − 2.2F

C. 2.303RT + 1.1F

D. −2.2F

 

Q. 21 The standard state Gibbs free energies of formation of C(graphite) and C(diamond) at T = 298 K are in figure.The standard state means that the pressure should be 1 bar, and substance should be pure at a given temperature. The conversion of graphite [C(graphite)] to diamond [C(diamond)] reduces its volume by 2 x 10⁻⁶ m³ /mol⁻¹. If C(graphite) is converted to C(diamond) isothermally at T = 298 K, the pressure at which C(graphite) is in equilibrium with C(diamond), is [Useful information: 1 J = 1 kg m²s⁻² ; 1 Pa = 1 kg m⁻¹s⁻²; 1 bar = 10⁵ Pa]

A. 14501 bar

B. 58001 bar

C. 1450 bar

D. 29001 bar

 

Q. 22 Which of the following combination will produce H₂ gas?

A. Fe metal and conc. HNO₃

B. Cu metal and conc.HNO₃

C. Zn metal and NaOH(aq)

D. Au metal and NaCN(aq) in the presence of air

 

Q. 23 The order of the oxidation state of the phosphorus atom in H₃PO₂, H₃PO₄, H₃PO₃, and H₄P₂O₆ is

A. H₃PO₃ > H₃PO₂ > H₃PO₄ > H₄P₂O₆

B. H₃PO₄ > H₃PO₂ > H₃PO₃ > H₄P₂O₆

C. H₃PO₄ > H₄P₂O₆ >H₃PO₃ > H₃PO₂

D. H₃PO₂ > H₃PO₃ > H₄P₂O₆ >H₃PO₄

 

Q. 24 The major product of the following reaction is

A. A

B. B

C. C

D. D

 

Q. 25 The order of basicity among the following compounds is

A. II > I > IV > III

B. IV > II > III > I

C. IV > I > II > III

D. I > IV > III > II

 

Q. 26 The correct statement(s) about surface properties is(are)

A. Adsorption is accompanied by decrease in enthalpy and decrease in entropy of the

system

B. The critical temperatures of ethane and nitrogen are 563 K and 126 K, respectively.

The adsorption of ethane will be more than that of nitrogen on same amount of activated charcoal at a given temperature

C. Cloud is an emulsion type of colloid in which liquid is dispersed phase and gas is

dispersion medium

D. Brownian motion of colloidal particles does not depend on the size of the particles

but depends on viscosity of the solution

 

Q. 27 For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant K in terms of change in entropy is described by 

A. With increase in temperature, the value of K for exothermic reaction decreases

because the entropy change of the system is positive

B. With increase in temperature, the value of K for endothermic reaction increases

because unfavourable change in entropy of the surroundings decreases

C. With increase in temperature, the value of K for endothermic reaction increases

because the entropy change of the system is negative

D. With increase in temperature, the value of K for exothermic reaction decreases

because favourable change in entropy of the surroundings decreases

 

Q. 28 In a bimolecular reaction, the steric factor P was experimentally determined to be 4.5. The correct option(s) among the following is(are)

A. The activation energy of the reaction is unaffected by the value of the steric factor

B. Experimentally determined value of frequency factor is higher than that predicted by Arrhenius equation

C. Since P = 4.5, the reaction will not proceed unless an effective catalyst is used

D. The value of frequency factor predicted by Arrhenius equation is higher than that

determined experimentally

 

Q. 29 For the following compounds, the correct statement(s) with respect to nucleophilic substitution reactions is(are)

A. I and III follow SN₁ mechanism

B. I and II follow SN₂ mechanism

C. Compound IV undergoes inversion of configuration

D. The order of reactivity for I, III and IV is: IV > I > III

 

Q. 30 Among the following, the correct statement(s) is(are)

A. Al(CH₃)₃ has the three-centre two-electron bonds in its dimeric structure

B. BH₃ has the three-centre two-electron bonds in its dimeric structure

C. AlCl₃ has the three-centre two-electron bonds in its dimeric structure

D. The Lewis acidity of BCl₃ is greater than that of AlCl₃

 

Q. 31 The option(s) with only amphoteric oxides is(are)

A. Cr₂O₃, BeO, SnO, SnO₂

B. Cr₂O₃, CrO, SnO, PbO

C. NO, B₂O₃, PbO, SnO₂

D. ZnO, Al₂O₃, PbO, PbO₂

 

Q. 32 Compounds P and R upon ozonolysis produce Q and S, respectively. The molecular formula of Q and S is C₈H₈O. Q undergoes Cannizzaro reaction but not haloform reaction, whereas S undergoes haloform reaction but not Cannizzaro reaction. The option(s) with suitable combination of P and R, respectively, is(are)

A. A

B. B

C. C

D. D

 

Questions: 33 – 34

Upon heating KClO3 in the presence of catalytic amount of MnO2, a gas W is formed. Excess amount of W reacts with white phosphorus to give X. The reaction of X with pure HNO3 gives Y and Z. 

Q. 33 W and X are, respectively

A. O₃ and P₄O₆

B. O₂ and P₄O₆

C. O₂ and P₄O₁₀

D. O₃ and P₄O₁₀

 

Q. 34 Y and Z are, respectively

A. N₂O₃ and H₃PO₄

B. N₂O₅ and HPO₃

C. N₂O₄ and HPO₃

D. N₂O₄ and H₃PO₃

 

Questions: 35 – 36

 

Q. 35 The reaction of compound P with CH₃MgBr (excess) in (C₂H₅)₂O followed by addition of H₂O gives Q. The compound Q on treatment with H₂SO₄ at 0°C gives R. The reaction of R with CH₃COCl in the presence of anhydrous AlCl₃ in CH₂Cl₂ followed by treatment with H₂O roduces compound S. [Et in compound P is ethyl group]

A. A

B. B

C. C

D. D

 

Q. 36 The reactions, Q to R and R to S, are

A. Dehydration and Friedel-Crafts acylation

B. Aromatic sulfonation and Friedel-Crafts acylation

C. Friedel-Crafts alkylation, dehydration and Friedel-Crafts acylation

D. Friedel-Crafts alkylation and Friedel-Crafts acylation

 

Q. 37 The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y-2z=5 and 3x – 6y – 2z=7 is

A. 14x + 2y – 15z = 1

B. 14x – 2y + 15z = 27

C. 14x + 2y + 15z = 31

D. -14x + 2y + 15z = 3

 

Q. 38 Let O be the origin and let PQR be an arbitrary triangle. The point S is such that(in figure) Then the triangle PQR has S as its

A. centroid

B. circumcentre

C. incentre

D. orthocenter

 

Q. 39 If y=y(x) satisfies the differential equation(in figure) and y(0) =√7, then y(256)=

A. 3

B. 9

C. 16

D. 80

 

Q. 40 If f: ℝ → ℝ is a twice differentiable function such that f″(x)>0 for all x ∈ ℝ, and f(1/2)=1/2, f(1)=1, then

A. f′(1)≤0

B. 0<f′(1)<1/2

C. 1/2<f′(1)≤1

D. f′(1)>1

 

Q. 41 How many 3×3 matrices M with entries from {0, 1, 2} are there, for which the sum of the diagonal entries of MᵀM is 5?

A. 126

B. 198

C. 162

D. 135

 

Q. 42 Let S = {1, 2, 3, … , 9} . For k = 1, 2, … ,5, let Nₖ be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N₁+N₂+N₃+N₄+N₅=

A. 210

B. 252

C. 125

D. 126

 

Q. 43 Three randomly chosen nonnegative integers x,y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even, is

A. 36/55

B. 6/11

C. 1/2

D. 5/11

 

Q. 44 choose the correct answer from options:

A. g′(Π/2)=-2Π

B. g′(-Π/2)=2Π

C. g′(Π/2)=2Π

D. g′(-Π/2)=-2Π

 

Q. 45 Let α and β be nonzero real numbers such that 2 cosβ − cosα)+ cos α cos β = 1. Then which of the following is/are true?

A. A

B. B

C. C

D. D

 

Q. 46 If f: ℝ → ℝ is a differentiable function such that f′(x) > 2f(x) for all x ∈ ℝ, and f(0) = 1, then

A. f(x) is increasing in (0, ∞)

B. f(x) is decreasing in (0, ∞)

C. f(x) > e²ˣ in (0, ∞)

D. f(x) < e²ˣ in (0, ∞)

 

Q. 47 choose the correct option:

A. A

B. B

C. C

D. D

 

Q. 48 choose the correct option:

A. f′(x) = 0 at exactly three points in (-Π,Π)

B. f′(x) = 0 at more than three points in (-Π,Π)

C. f(x) attains its maximum at x = 0

D. f(x) attains its minimum at x = 0

 

Q. 49 If the line x=α divides the area of region R = { (x,y)∈R²: x³≤y≤x,0≤x ≤ 1} into two equal parts, then

A. 0 < α ≤ 1/2

B. 1/2 < α < 1

C. 2a⁴ – 4α² + 1=0

D. a⁴ + 4α² – 1=0

 

Q. 50 choose the correct option:

A. I > logₑ 99

B. I < logₑ 99

C. I < 49/50

D. I > 49/50

 

Questions: 51 – 52

Let O be the origin, and OX, OY, OZ be three unit vectors in the directions of the sides QR, RP, PQ, respectively, of a triangle PQR 

Q. 51 |OX x OY|=

A. sin(P+Q)

B. sin2R

C. sin(P+R)

D. sin(Q+R)

 

Q. 52 If the triangle PQR varies, then the minimum value of cos (P+Q) +cos (Q+R) +cos(R+P) is 

A. -5/3

B. -3/2

C. 3/2

D. 5/3

 

Questions: 53 – 54

Let p,q be integers and let α, β be the roots of the equation, x²- x − 1 = 0, where α≠β. For n = 0, 1, 2, … , let aₙ = pαⁿ+qβⁿ (FACT: If a and b are rational numbers and a+b√5 = 0, then a = 0 = b). 

 

Q. 53 value of a₁₂ is:

A. a₁₁ – a₁₀

B. a₁₁ + a₁₀

C. 2a₁₁ – a₁₀

D. a₁₁ – 2a₁₀

 

Q. 54 If a₄ = 28, then p+ 2q = 

A. 21

B. 14

C. 7

D. 12

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	A	B	D	A	A	B	B	AB	AD	AD
Question	11	12	13	14	15	16	17	18	19	20
Answer	BC	ABC	ACD	CD	A	C	D	A	C	B
Question	21	22	23	24	25	26	27	28	29	30
Answer	A	C	C	C	C	AB	BD	AB	ABCD	ABD
Question	31	32	33	34	35	36	37	38	39	40
Answer	AD	AB	C	B	A	D	C	D	A	D
Question	41	42	43	44	45	46	47	48	49	50
Answer	B	D	B	ABCD	ABCD	AC	AD	BC	BC	BD
Question	51	52	53	54
Answer	A	B	B	D

JEE Advanced 2017 Paper I

Q. 1 A flat plate is moving normal to its plane through a gas under the action of a constant force F. The gas is kept at a very low pressure. The speed of the plate v is much less than the average speed u of the gas molecules. Which of the following options is/are true? one or more than 1 correct answer.

A. The pressure difference between the leading and trailing faces of the plate is

proportional to uv

B. The pressure difference between the leading and trailing faces of the plate is

proportional to uv

C. The plate will continue to move with constant non-zero acceleration, at all times

D. At a later time the external force F balances the resistive force

 

Q. 2 A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at x = 0, in a coordinate system fixed to the table. A point mass m is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block, its position is x and the velocity is v. At that instant, which of the following options is/are correct?

A. A

B. B

C. C

D. D

 

Q. 3 A block M hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at O. A transverse wave pulse (Pulse 1) of wavelength λ0 is produced at point O on the rope. The pulse takes time TOA to reach point A. If the wave pulse of wavelength λ0 is produced at point A (Pulse 2) without disturbing the position of M it takes time TAO to reach point O. Which of the following options is/are correct?

A. The time Tₐₒ = Tₒₐ

B. The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the midpoint of rope

C. The wavelength of Pulse 1 becomes longer when it reaches point A

D. The velocity of any pulse along the rope is independent of its frequency and

wavelength

 

Q. 4 A human body has a surface area of approximately 1 m². The normal body temperature is 10 K above the surrounding room temperature T₀. Take the room temperature to be T₀= 300 K. For T₀ = 300 K, the value of σT₀⁴ = 460 Wm⁻² (where σ is the Stefan Boltzmann constant). Which of the following options is/are correct?

A. The amount of energy radiated by the body in 1 second is close to 60 Joule

B. If the surrounding temperature reduces by a small amount ΔT₀ ≪ T₀, then to

maintain the same body temperature the same (living) human being needs to radiate

ΔW = 4σT₀³ΔT₀ more energy per unit time

C. Reducing the exposed surface area of the body (e.g. by curling up) allows humans to maintain the same body temperature while reducing the energy lost by radiation

D. If the body temperature rises significantly then the peak in the spectrum of

electromagnetic radiation emitted by the body would shift to longer wavelengths

 

Q. 5 A circular insulated copper wire loop is twisted to form two loops of area A and 2A as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field B points into the plane of the paper. At t= 0, the loop starts rotating about the common diameter as axis with a constant angular velocity ω in the magnetic field. Which of the following options is/are correct?

A. The emf induced in the loop is proportional to the sum of the areas of the two loops

B. The amplitude of the maximum net emf induced due to both the loops is equal to the amplitude of maximum emf induced in the smaller loop alone

C. The net emf induced due to both the loops is proportional to cos ωt

D. The rate of change of the flux is maximum when the plane of the loops is

perpendicular to plane of the paper

 

Q. 6 In the circuit shown, L= 1 μH , C= 1 μF and R = 1kΩ. They are connected in series with an a.c. source V = V₀ sin wt as shown. Which of the following options is/are correct?

A. The current will be in phase with the voltage if ω = 10⁴ rad. s⁻¹

B. The frequency at which the current will be in phase with the voltage is independent of R

C. At ω~0 the current flowing through the circuit becomes nearly zero

D. At ω≫ 10⁶ rad. s⁻¹, the circuit behaves like a capacitor

 

Q. 7 For an isosceles prism of angle A and refractive index μ, it is found that the angle of minimum deviation δm=A. Which of the following options is/are correct?

A. A

B. B

C. C

D. D

 

Q. 8 A drop of liquid of radius R = 10⁻² m having surface tension S = 0.1/4π Nm-1 divides itself into K identical drops. In this process the total change in the surface energy ΔU = 10⁻³ J.If K = 10ᵃ then the value of α is

 

Q. 9 An electron in a hydrogen atom undergoes a transition from an orbit with a quantum number into another with quantum number nf. Vᵢ and Vf are respectively the initial and final potential energies of the electron. If Vᵢ/Vf = 6.25, then the smallest possible nf is

 

Q. 10 A monochromatic light is travelling in a medium of refractive index n = 1.6. It enters a stack of glass layers from the bottom side at an angle θ = 30°. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as nm = n – mΔn, where nm is the refractive index of the mth slab and Δn = 0.1 (see the figure). The ray is refracted out parallel to the interface between the (m – 1)th and mth slabs from the right side of the stack. What is the value of m?

 

Q. 11 A stationary source emits sound of frequency f₀ = 492 Hz. The sound is reflected by a large car approaching the source with a speed of 2 ms⁻¹. The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz? (Given that the speed of sound in air is 330 ms!! and the car reflects the sound at the frequency it has received)

 

Q. 12 131I is an isotope of Iodine that β decays to an isotope of Xenon with a half-life of 8 days.A small amount of a serum labelled with 131I is injected into the blood of a person. The activity of the amount of 131I injected was 2.4 ×10! Becquerel (Bq). It is known that the injected serum will get distributed uniformly in the bloodstream in less than half an hour. After 11.5 hours, 2.5 ml of blood is drawn from the person’s body, and gives an activity of 115 Bq. The total volume of blood in the person’s body, in liters is approximately (you may use e^x ≈ 1 + x for |x| ≪ 1 and ln 2 ≈ 0.7).

 

Questions: 13 – 15

Answer Q.13, Q.14 and Q.15 by appropriately matching the information given in

the three columns of the following table. 

 

Q. 13 In which case will the particle move in a straight line with constant velocity?

A. (III) (ii) (R)

B. (III) (ii) (R)

C. (III) (iii) (P)

D. (II) (iii) (S)

 

Q. 14 In which case will the particle describe a helical path with axis along the positive z direction? 

A. (IV) (i) (S)

B. (II) (ii) (R)

C. (III) (iii) (P)

D. (IV) (ii) (R)

 

Q. 15 In which case would the particle move in a straight line along the negative direction of yaxis (i.e., move along – ŷ)?

A. (II) (iii) (Q)

B. (III) (ii) (R)

C. (IV) (ii) (S)

D. (III) (ii) (P)

Questions: 16 – 18

 

Answer Q.16, Q.17 and Q.18 by appropriately matching the information given in

the three columns of the following table.

 

Q. 16 Which of the following options is the only correct representation of a process in which ΔU = ΔQ – PΔV ?

A. (II) (iv) (R)

B. (III) (iii) (P)

C. (II) (iii) (S)

D. (II) (iii) (P)

 

Q. 17 Which one of the following options is the correct combination?

A. (IV) (ii) (S)

B. (III) (ii) (S)

C. (II) (iv) (P)

D. (II) (iv) (R)

 

Q. 18 Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?

A. (I) (ii) (Q)

B. (IV) (ii) (R)

C. (III) (iv) (R)

D. (I) (iv) (Q)

 

Q. 19 An ideal gas is expanded from (p₁, V₁, T₁) to (p₂, V₂, T₂) under different conditions. The correct statement(s) among the following is(are)

A. The work done on the gas is maximum when it is compressed irreversibly from (p2, V2) to (p1, V1) against constant pressure p1

B. If the expansion is carried out freely, it is simultaneously both isothermal as well as

adiabatic

C. The work done by the gas is less when it is expanded reversibly from V₁ to V₂ under

D. The change in internal energy of the gas is (i) zero, if it is expanded reversibly with T₁ = T₂, and (ii) positive, if it is expanded reversibly under adiabatic conditions with T₁ ≠ T₂

 

Q. 20 For a solution formed by mixing liquids L and M, the vapour pressure of L plotted against the mole fraction of M in solution is shown in the following figure. Here xL and xM represent mole fractions of L and M, respectively, in the solution. The correct statement(s) applicable to this system is(are)

A. The point Z represents vapour pressure of pure liquid M and Raoult’s law is obeyed from xL = 0 to xL = 1

B. The point Z represents vapour pressure of pure liquid L and Raoult’s law is obeyed

when xL → 1 C. The point Z represents vapour pressure of pure liquid M and Raoult’s law is obeyed when xL→ 0

D. Attractive intermolecular interactions between L-L in pure liquid L and M-M in pure liquid M are stronger than those between L-M when mixed in solution

 

Q. 21 The correct statement(s) about the oxoacids, HClO₄ and HClO, is(are)

A. The central atom in both HClO₄ and HClO is sp³ hybridized

B. HClO₃ is more acidic than HClO because of the resonance stabilization of its anion

C. HClO₄ is formed in the reaction between Cl₂ and H₂O

D. The conjugate base of HClO₄ is weaker base than H₂O

 

Q. 22 The colour of the X₂ molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to

A. the physical state of X₂ at room temperature changes from gas to solid down the

group

B. decrease in ionization energy down the group

C. decrease in π*-σ* gap down the group

D. decrease in HOMO-LUMO gap down the group

 

Q. 23 Addition of excess aqueous ammonia to a pink coloured aqueous solution of MCl₂·6H₂O (X) and NH₄Cl gives an octahedral complex Y in the presence of air. In aqueous solution, complex Y behaves as 1:3 electrolyte. The reaction of X with excess HCl at room temperature results in the formation of a blue coloured complex Z. The calculated spin only magnetic moment of X and Z is 3.87 B.M., whereas it is zero for complex Y. Among the following options, which statement(s) is(are) correct?

A. Addition of silver nitrate to Y gives only two equivalents of silver chloride

B. The hybridization of the central metal ion in Y is d²sp³

C. Z is a tetrahedral complex

D. When X and Z are in equilibrium at 0°C, the colour of the solution is pink

 

Q. 24 The IUPAC name(s) of the following compound is(are)

A. 1-chloro-4-methylbenzene

B. ] 4-chlorotoluene

C. 4-methylchlorobenzene

D. 1-methyl-4-chlorobenzene

 

Q. 25 The correct statement(s) for the following addition reactions is(are)

A. O and P are identical molecules

B. (M and O) and (N and P) are two pairs of diastereomers

C. (M and O) and (N and P) are two pairs of enantiomers

D. Bromination proceeds through trans-addition in both the reactions

 

Q. 26 A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is 8 g cm⁻³, then the number of atoms present in 256 g of the crystal is N * 10²⁴ . The value of N is

 

Q. 27 The conductance of a 0.0015 M aqueous solution of a weak monobasic acid was determined by using a conductivity cell consisting of platinized Pt electrodes. The distance between the electrodes is 120 cm with an area of cross section of 1 cm². The conductance of this solution was found to be 5 * 10⁻⁷ S. The pH of the solution is 4. The value of limiting molar conductivity (Λ°m) of this weak monobasic acid in aqueous solution is Z * 10² S cm⁻¹ mol⁻¹. The value of Z is

 

Q. 28 The sum of the number of lone pairs of electrons on each central atom in the following species is [TeBr₆]²⁻, [BrF₂]⁺, SNF₃, and [XeF₃]⁻ (Atomic numbers: N = 7, F = 9, S = 16, Br = 35, Te = 52, Xe = 54)

 

Q. 29 Among H₂, He₂⁺, Li₂, Be₂, B₂, C₂, N₂, O₂⁻, and F₂, the number of diamagnetic species is (Atomic numbers: H = 1, He = 2, Li = 3, Be = 4, B = 5, C = 6, N = 7, O = 8, F = 9) 

 

Q. 30 Among the following, the number of aromatic compound(s) is

Questions: 31 – 33

Answer Q.31, Q.32 and Q.33 by appropriately matching the information given in

the three columns of the following table.

Q. 31  For the given orbital in Column 1, the only CORRECT combination for any hydrogen-like species is

A. (I) (ii) (S)

B. (IV) (iv) (R)

C. (II) (ii) (P)

D. (III) (iii) (P)

 

Q. 32 For hydrogen atom, the only CORRECT combination is

A. (I) (i) (S)

B. (II) (i) (Q)

C. (I) (i) (P)

D. (I) (iv) (R)

 

Q. 33 For He+ ion, the only INCORRECT combination is

A. (I) (i) (R)

B. (II) (ii) (Q)

C. (I) (iii) (R)

D. (I) (i) (S)

 

Q. 34 For the synthesis of benzoic acid, the only CORRECT combination is

A. (II) (i) (S)

B. (IV) (ii) (P)

C. (I) (iv) (Q)

D. (III) (iv) (R)

 

Q. 35 The only CORRECT combination that gives two different carboxylic acids is

A. (II) (iv) (R)

B. (IV) (iii) (Q)

C. (III) (iii) (P)

D. (I) (i) (S)

 

Q. 36 The only CORRECT combination in which the reaction proceeds through radical mechanism is

A. (III) (ii) (P)

B. (IV) (i) (Q)

C. (II) (iii) (R)

D. (I) (ii) (R)

 

Q. 37 If 2x − y + 1 = 0 is a tangent to the hyperbola , then which of the following CANNOT be sides of a right angled triangle?

A. a, 4, 1

B. a, 4, 2

C. 2a, 8, 1

D. 2a, 4, 1

 

Q. 38 If a chord, which is not a tangent, of the parabola y² = 16x has the equation 2x + y = p, and midpoint (ℎ, k), then which of the following is(are) possible value(s) of p, ℎ and k 

A. p = -2 , h =2 ,k = -4

B. p = -1 , h =1 , k = -3

C. p=2, h=3 ,k = -4

D. p=5 , h=4 , k=-3

 

Q. 39 Let [x] be the greatest integer less than or equals to x. Then, at which of the following point(s) the function f(x)= x cos(π(x + [x])) is discontinuous?

A. x = −1

B. x = 0

C. x = 1

D. x = 2

 

Q. 40 Let f: ℝ → (0, 1) be a continuous function. Then, which of the following function(s) has(have) the value zero at some point in the interval (0, 1)?

A. A

B. B

C. C

D. D

 

Q. 41 Which of the following is(are) NOT the square of a 3×3 matrix with real entries?

A. A

B. B

C. C

D. D

 

Q. 42 then which of the following is(are) possible value(s) of x?

A. A

B. B

C. C

D. D

 

Q. 43 Let X and Y be two events such that P(X) = 1/3 , P(X|Y) = 1/2 and P(Y|X) = 2/5. Then

A. P(Y)= 4/15

B. P(X′|Y) = 1/2

C. P(X∩Y)= 1/5

D. P(XUY)= 2/5

 

Q. 44 For how many values of p, the circle x² + y² +2x + 4y – p = 0 and the coordinate axes have exactly three common points?

Q. 45 Choose the correct option

 

Q. 46 For a real number α, if the system of linear equations, has infinitely many solutions, then 1 + α + α² =

 

Q. 47 Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let x be the number of such words where no letter is repeated; and let y be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then, y/9x= 

 

Q. 48 The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?

Questions: 49 – 51

Answer Q.49, Q.50 and Q.51 by appropriately matching the information given in the three columns of the following table.

 

Q. 49 For a = √2, if a tangent is drawn to a suitable conic (Column 1) at the point of contact (−1, 1), then which of the following options is the only CORRECT combination for obtaining its equation?

A. (I) (i) (P)

B. (I) (ii) (Q)

C. (II) (ii) (Q)

D. (III) (i) (P)

 

Q. 50 If a tangent to a suitable conic (Column 1) is found to be y = x + 8 and its point of contact is (8, 16), then which of the following options is the only CORRECT combination? 

A. (I) (ii) (Q)

B. (II) (iv) (R)

C. (III) (i) (P)

D. (III) (ii) (Q)

 

Q. 51 The tangent to a suitable conic (Column 1) at ( √3, 1/2) is found to be √3x + 2u = 4, then which of the following options is the only CORRECT combination?

A. (IV) (iii) (S)

B. (IV) (iv) (S)

C. (II) (iii) (R)

D. (II) (iv) (R)

 

Questions: 52 – 54

Answer Q.52, Q.53 and Q.54 by appropriately matching the information given in the three columns of the following table.

 

Q. 52 Which of the following options is the only CORRECT combination?

A. (I) (i) (P)

B. (II) (ii) (Q)

C. (III) (iii) (R)

D. (IV) (iv) (S)

 

Q. 53 Which of the following options is the only CORRECT combination?

A. (I) (ii) (R)

B. (II) (iii) (S)

C. (III) (iv) (P)

D. (IV) (i) (S)

 

Q. 54 Which of the following options is the only INCORRECT combination?

A. (I) (iii) (P)

B. (II) (iv) (Q) 

C. (III) (i) (R)

D. (II) (iii) (P)

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	ABD	BC	AD	C	BD	BC	ACD	6	5	8
Question	11	12	13	14	15	16	17	18	19	20
Answer	6	5	D	A	B	D	B	D	ABC	BD
Question	21	22	23	24	25	26	27	28	29	30
Answer	ABD	CD	BCD	AB	BD	2	6	6	6	5
Question	31	32	33	34	35	36	37	38	39	40
Answer	C	A	C	A	C	D	ABC	C	ABCD	AB
Question	41	42	43	44	45	46	47	48	49	50
Answer	BD	AB	AB	2	2	1	5	6	B	C
Question	51	52	53	54
Answer	D	B	B	C

JEE Advanced 2016 Paper 2

Q. 1 The electrostatic energy of Z protons uniformly distributed uniformly throughout a spherical nucleus of radius R is given in the picture. Thea measured masses of the neutron, ¹H₁, ¹⁵N₇ and ¹⁵O₈ are 1.008665 u, 1.0077825 u, 15.000109 u and 15.003065 u, respectively. Given that the radii of both the ¹⁵N₇ and ¹⁵O₈ are same, 1 u = 931.5 MeV/c² (c is the speed of light) and e²/(4Πε0) = 1.44 MeV fm. Assuming that the difference between the binding energies of ¹⁵N₇ ¹⁵O₈ is purely due to the electrostatic energy, the radius of either of the nuclei is (1 fm = 10⁻¹⁵ m)

E=35Z (Z-1) e24 0R

A. 2.85 fm

B. 3.03 fm

C. 3.42 fm

D. 3.80 fm

 

Q. 2 An accident in a nuclear laboratory resulted in deposition of a certain amount of

radioactive material of half – life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the maximum number of days after which the laboratory can be considered safe for use?

A. 64

B. 90

C. 108

D. 120

 

Q. 3 A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure Pᵢ = 10⁵ Pa and volume Vⁱ = 10⁻³ m³ changes to a final state at P􀀁 = (1/32) x 10⁵ Pa and V􀀁 = 8 x 10⁻³ m³ in an adiabatic quasi-static process, such that P³.V⁵ = constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at Pᵢ followed by an isochoric (isovolumetric) process at volume V􀀁. The amount of heat supplied to the system in the two-step process is approximately

A. 112 J

B. 294 J

C. 588 J

D. 813 J

Q. 4 The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a lenght of 1 m at 10 ⁰C. Now the end P is maintained at 10 ⁰C, while the end S is heated and maintained at 400 ⁰C. The system is thermally insulated from its surroundings. If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is 1.2 x 10⁻⁵K⁻¹, the change in lenght of the wire PQ is

A. 0.78 mm

B. 0.90 mm

C. 1.56 mm

D. 2.34 mm

 

Q. 5 A small object is placed 50 cm to the left of a thin convex lens of focal lenght 30 cm. A convex spherical mirror of radius of curvature 100 cm is placed to the right of the lens at a distance of 50 cm. The mirror is tilted such that the axis of the mirror is at an angle of θ = 30⁰ to the axis of the lens, as shown in the figure.

If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates (in cm) of the point (x,y) at which the image is formed are 

A. (0, 0)

B. (50 – 25√3, 25)

C. (25, 25√3)

D. (125/3, 25/√3)

 

Q. 6 There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale. The Vernier scale of one of the calipers (C₁) has 10 equal divisions that correspond to 9 main scale divisions. The Vernier scale of the other caliper (C₂) has 10 equal divisions that correspond to 11 main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in cm) by calipers C₁ and C₂, respectively, are

A. 2.85 and 2.82

B. 2.87 and 2.83

C. 2.87 and 2.86

D. 2.87 and 2.87

 

Q. 7 Two thin circular discs of mass m and 4m, having radii of a and 2a, respectively, are rigidly fixed by a massless, rigid rod of lenght l = √24a through their centres. This assembly is laid on a firm and flat surface, and set rolling without slipping on the surface so that the angular speed about the axis of the rod is ω . The angular momentum of the entire assembly about the point ‘O’ is L (see the figure). Which of the following statements(s) is (are) true?

A. The center of mass of the assembly rotates about the z – axis with an angular speed of ω/5

B. The magnitude of an angular momentum of center of mass of the assembly about the point O is 81ma²ω

C. The magnitude of angular momentum of the assembly about its center of mass is

17ma²ω/2

D. The magnitude of the z – component of L is 55 ma²ω

 

Q. 8 Light of wavelenght λₚₕ falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is Φ and the anode is a wire mesh of conducting material kept at a distance d from the cathode. A potential difference V is maintained between the electrodes. If the minimum de Broglie wavelenght of the electrons passing through the anode is λₑ, which of the following statements(s) is (are) true? 

A. λₑ, decreases with increase in Φ and λₚₕ

B. λₑ is approximately halved, if d is doubled

C. For large potential difference (V≪ Φ/e), λₑ is approximately halved if V is made four times

D. λₑ increases at the same rate as λₚₕ for λₚₕ <he/Φ

 

Q. 9 In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a period motion is T = (2π) √7(R – r)/ 5g. The values of R and r are measured to be (60 ± 1) mm and (10 ± 1) mm, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s, 0.54 s and 0.59 s . The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement(s) is (are) true?

A. The error in the measurement of r is 10%

B. The error in the measurement of T is 3.57%

C. The error in the measurement of T is 2%

D. The error in the determined value of g is 11%

 

Q. 10 Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers Rc < R/2, which of the following statement(s) about any one of the galvanometers is (are) true?

A. The maximum voltage range is obtained when all the components are connected in

Series 

B. The maximum voltage range is obtained when the two resistors and one galvanometer are connected in series, and the second galvanometer is connected in parallel to the first galvanometer.

C. The maximum current range is obtained when all the components in parallel

D. The maximum current range is obtained when the two galvanometers are connected in series and the combination is connected in parallel with both the resistors.

 

Q. 11 In the circuit shown below, the key is pressed at time t = 0. Which of the following statement(s) is(are) true?

A. The volunteer displays -5 V as soon as the key is pressed, and displays +5 V after a

long time.

B. The voltmeter will display 0 V at time t = In 2 seconds

C. The current in the ammeter becomes 1/e of the initial value after 1 second

D. The current in the ammeter becomes zero after a long time

 

Q. 12 A block with mass M is connected by a massless spring with stiffness constant ƙ to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x₀. Consider two cases : (i) when the block is at x₀ ; and (ii) when then block is at x = x₀ + A. In both the cases, a particle with mass m ( 

A. The amplitude of oscillation in the first case changes by a factor of √[(M/(m+M)],

whereas in the second case it remains unchanged

B. The final time period of oscillation in both the cases is same

C. The total energy decreases in both the cases

D. The instantaneous speed at x₀ of the combined masses decreases in both the cases

 

Q. 13  While conducting the Young’s double slit experiment, a student replaced the two slits with a large opaque plate in the x- y plane containing two small holes that act as two coherent point sources (S₁,S₂) emitting light of wavelength 600 nm. The student mistakenly placed the screen parallel to the x-z plane (for z > 0) at a distance D = 3 m from the mid -point of S₁S₂ , as shown schematically in the figure. The distance between the sources d = 0.6003 mm. The origin O is at the intersection of the screen and the line joining S₁S₂. Which of the following is(are) true of the intensity pattern on the screen?

A. Straight bright and dark bands parallel to the x – axis

B. The region very close to the point O will be dark

C. Hyberbolic bright and dark bands with foci symmetrically placed about O in the x –

direction

D. Semi circular bright and dark bands centered at point 0

 

Q. 14  A rigid wire loop of square shape having side of length L and resistance R is moving along the x-axis with a constant velocity v₀ in the plane of the paper. At t = 0, the right edge of the loop enters a region of length 3L where there is a uniform magnetic field B₀ into the plane of the paper, as shown in the question figure. For sufficiently large v₀, the loop eventually crosses the region. Let x be the location of the right edge of the loop. Let v(x), I(x) and F(x) represent the velocity of the loop, current in the loop, and force on the loop, respectively as a function of x. Counter-clockwise current is taken as positive. Which of the given schematic plot(s) is/are correct? (Ignore gravity)

A. A

B. B

C. C

D. D

 

Questions: 15 – 16

 

Q. 15 The distance r of the block at time t is

A. (R/4) [ eʷᵗ+ e⁻ʷᵗ ]

B. (R/2) cos ωt

C. (R/4) [ e²ʷᵗ + e⁻²ʷᵗ ]

D. (R/2) cos 2ωt

 

Q. 16 The net reaction of the disc on the block is

A. (1/2) mω²R ( e²ʷᵗ – e⁻²ʷᵗ ) ĵ + mgk̂

B. (1/2) mω²R ( eʷᵗ – e²ʷᵗ ) ĵ + mgk̂

C. -mω²R cos ωt ĵ – mgk̂

D. mω²R sin ωt ĵ – mgk̂

 

Questions: 17 – 18

Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a lightweight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius r ≪ h. Now a high voltage source (HV) is connected across the conducting plates such that the bottom plate is at +V₀ and the top plate is at -V₀. Due to their conducting surface, the balls will get charged, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)

Q. 17 Which one of the following statements is correct?

A. The balls will stick to the top plate and remain there

B. The balls will bounce back to the bottom plate carrying the same charge they went up with

C. The balls will bounce back to the bottom plate carrying the opposite charge they went up with

D. The balls will execute simple harmonic motion between the two plates

 

Q. 18 The average current in the steady state registered by the ammeter in the circuit will be

A. zero

B. proportional to the potential V₀

C. proportional to V

D. proportional to V

 

Q. 19 For the following electrochemical cell at 298 K ,

Pt (s) | H₂ (g,1 bar) | H⁺ (aq, 1 M) || M⁴⁺ (aq), M²⁺ (aq) | Pt (s)

E_cell = 0.092 V when [M²⁺ (aq)] / [M⁴⁺ (aq)] = 10ˣ

Given: E⁰ [M⁴⁺ / M²⁺)] = 0.151 V; 2.303 (RT/V) = 0.059 V.

The value of x is

A. -2

B. -1

C. 1

D. 2

 

Q. 20 The given qualitative sketches I, II and III shows the variation of surface tension with a molar concentration of three different aqueous solutions of KC₁, CH₃OH and CH₃(CH₂)₁₁OSO₃⁻Na⁺ at room temperature. The correct assignment of the sketches is 

A. A

B. B

C. C

D. D

 

Q. 21 In the given reaction sequence in aqueous solution, the species X Y and Z, respectively, are 

A. A

B. B

C. C

D. D

 

Q. 22 The geometries of the ammonia complexes of Ni²⁺ , Pt²⁺ and Zn²⁺, respectively, are 

A. octahedral, square planar and tetrahedral

B. square planar, octahedral and tetrahedral

C. tetrahedral, square planar and octahedral

D. octahedral, tetrahedral and square planar

 

Q. 23 The correct order of acidity for the given compounds is

A. I > II >I II > IV

B. III > I > II >I V

C. III > IV > II > I

D. I >I II > IV > II

 

Q. 24 The major product of the given reaction sequence is

A. A

B. B

C. C

D. D

 

Q. 25 According to Molecular Orbital Theory,

A. C₂²⁻ is expected to be diamagnetic

B. O₂²⁺ is expected to have a longer bond length than O₂

C. N₂⁺ and N₂⁻ have the same bond order

D. He₂⁺ has the same energy as two isolated He atoms

 

Q. 26 Mixture(s) showing positive deviation from Raoult’s law at 35 ᵒC is (are)

A. carbon tetrachloride + methanol

B. carbon disulphide + acetone

C. benzene + toluene

D. phenol + aniline

 

Question 27  ONE OR MORE THAN ONE of the four given options is (are) correct. 

Q. 27 The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is(are) 

A. The number of the nearest neighbours of an atom present in the topmost layer is 12

B. The efficiency of atom packing is 74%

C. The number of octahedral and tetrahedral voids per atom are 1 and 2, respectively

D. The unit cell edge length is 2√2 times the radius of the atom

 

Q. 28 Extraction of copper from copper pyrite (CuFeS₂) involves

A. crushing followed by concentration of the ore by froth-flotation

B. removal of iron as slag

C. self-reduction step to produce ‘blister copper’ following evolution of SO₂

D. refining of ‘blister copper’ by carbon reduction

 

Q. 29 The nitrogen containing compound produced in the reaction of HNO₃ with P₄O₁₀ 

A. can also be prepared by reaction of P₄ and HNO₃

B. is diamagnetic

C. contains one N-N bond

D. reacts with Na metal producing a brown gas

 

Q. 30 For “invert sugar”, the correct statement(s) is(are)

(Given : specific rotations of (+) -sucrose, (+)-maltose, L-(-)glucose and L-(+)-fructose in aqueous solution are +66⁰ , +140⁰ , -52⁰ and +92⁰ , respectively)

A. ‘ínvert sugar’ is prepared by acid catalyzed hydrolysis of maltose

B. ‘ínvert sugar’ is an equimolar mixture of D-(+)- glucose and D-(-)- fructose

C. specific rotation of ‘invert sugar’ is -20⁰

D. on reaction with Br₂ water, ‘invert sugar’ forms saccharic acids as one of the products

 

Q. 31 Reagent(s) which can be used to bring about the given transformation is (are)

A. LiAlH₄ in (C₂H₅)₂O

B. BH₃ in THF

C. NaBH₄ in C₂H₅OH

D. Raney Ni/H₂ in THF

 

Q. 32 Among the given, reaction(s) which give(s) tert-butyl benzene as the major product is(are)

A. A

B. B

C. C

D. D

 

Questions: 33 – 34

•Read the paragraph and answer the following questions

•Each question has ONE correct option

Thermal decomposition of gaseous X₂ to gaseous X at 298K takes place according to the following equation:

X₂ (g) ⇄ 2X (g)

The standard reaction Gibbs energy, ΔᵣG°, of this reaction is positive. At the start of the reaction, there is one mole of X₂ and no X. As the reaction proceeds the number of moles of X formed is given by β. Thus, β(equilibrium) is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gasses to behave ideally. (Given: R = 0.083L bar K⁻¹mol⁻¹)

Q. 33 The equilibrium constant K_ρ for this reaction at 298 K, in terms of β_equilibrium, is 

A. 8(β_equilibrium)² / (2 – β_equilibrium)

B. 8(β_equilibrium)² / (4 – β_equilibrium)

C. 4(β_equilibrium)² / (2 – β_equilibrium)

D. 4(β_equilibrium)² / (4 – β_equilibrium)

 

Q. 34 The INCORRECT statement among the following, for this reaction, is

A. Decrease in the total pressure will result in formation of more moles of gaseous X

B. At the start of the reaction , dissociation of gaseous X₂ takes place spontaneusly

C. β_equilibrium = 0.7

D. K_C < 1

 

Question 35

Treatment of compound O with KMnO₄/H+ gave P, which on heating with ammonia gave P. The compound Q on treatment with Br₂/NaOH produced R. On strong heating, Q gave S, which on further treatment with ethyl 2- bromopropanoate in the presence of KOH followed by acidification gave a compound T.

 

Q. 35 The compound R is

A. A

B. B

C. C

D. D

 

Question 36

Treatment of compound O with KMnO₄/H+ gave P, which on heating with ammonia gave P. The compound Q on treatment with Br₂/NaOH produced R. On strong heating, Q gave S, which on further treatment with ethyl 2- bromopropanoate in the presence of KOH followed by acidification gave a compound T.

Q. 36 The compound T is

A. glycine

B. alanine

C. valine

D. serine

 

Q. 37 Let P be the given lower triangular matrix and I be the identity matrix of order 3. If Q = [qᵥ ] is a matrix such that P⁵⁰ – Q = I, then (q₃₁ + q₃₂) / q₂₁ equals

A. 52

B. 103

C. 201

D. 205

 

Q. 38 Let bᵢ > 1 for i = 1, 2, …, 101. Suppose loge b₁, loge b₂, …, loge b₁₀₁ are in Arithmetic Progression (A. P.) with the common difference logₑ2. Suppose a₁, a₂, …, a₁₀₁ are in A. P. such that a₁ = b₁ and a₅₁ = b₅₁. If t = b₁ + b₂ + … + b₅₁ and s = a₁ + a₂ + … + a₅₁, then

A. s > t and a₁₀₁ > b₁₀₁

B. s > t and a₁₀₁ < b₁₀₁

C. s < t and a₁₀₁ > b₁₀₁

D. s < t and a₁₀₁ < b₁₀₁

 

Q. 39 The value of the given summation is equal to

K=1121sin 4+(k – 1) 6 sin 4 + k6

A. 3 – √3

B. 2(3 – √3)

C. 2(√3 – 1)

D. 2(2 + √3)

 

Q. 40 The value of the given integral is

A. Π²/4 – 2

B. Π²/4 + 2

C. Π² – e^(Π/2)

D. Π² + e^(Π/2)

 

Q. 41 Area of the region { (x, y) ∈ R² : y ≥ √ (|x + 3|), 5y ≤ x + 9 ≤ 15 } is equal to

A. 1/6

B. 4/3

C. 3/2

D. 5/3

 

Q. 42 Let P be the image of the point (3, 1, 7) with respect to the plane x – y + z = 3. The the equation of the plane passing through P and containing the straight line x/1 = y/2 = z/1 is

A. x + y – 3z = 0

B. 3x + z = 0

C. x – 4y + 7z = 0

D. 2x – y = 0

 

Q. 43 Let the given equality be true for all x > 0. Then

 

A. f(1/2) ≥ f(1)

B. f(1/3) ≤ f(2/3)

C. f'(2) ≤ 0

D. f'(3)/f(3) ≥ f'(2)/f(2)

 

Q. 44 Let a, b ∈ R and f : R → R be defined by f(x) = a cos (|x³ – x|) + b sin (|x³ + x|). Then f is 

A. differentiable at x = 0 if a = 0 and b = 1

B. differentiable at x = 1 if a = 1 and b = 0

C. NOT differentiable at x = 0 if a = 1 and b = 0

D. NOT differentiable at x = 1 if a = 1 and b = 1

 

Q. 45 Let f : R → (0, ∞) and g : R → R be twice differentiable functions such that f” and g” are continuous functions on R. Suppose f'(2) = g(2) = 0, f”(2) ≠ 0 and g'(2) ≠ 0.

If limit_(x → 2) [f(x) g(x)] / [f'(x) g'(x)] = 1, then

A. f has a local minimum at x = 2

B. f has a local maximum at x = 2

C. f”(2) > f(2)

D. f(x) – f”(x) = 0 for at least one x ∈ R

 

Q. 46 Let f : [-1/2, 2] → R and g : [-1/2, 2] → R be functions defined by f(x) = [x² – 3] and g(x) = |x| f(x) + |4x – 7| f(x), where [y] denotes the greatest integer less than or equal to y for y ∈ R. Then 

A. f is discontinuous exactly at three points in [-1/2, 2]

B. f is discontinuous exactly at four points in [-1/2, 2]

C. g is NOT differentiable exactly at four points in (-1/2, 2)

D. g is NOT differentiable exactly at five points in (-1/2, 2)

 

Q. 47 Let a, b ∈ R and a² + b² ≠ 0. Suppose S = { z ∈ C : z = 1/(a + ibt), t ∈ R, t ≠ 0 }, where i = √-1. If z = x + iy and z ∈ S, then (x, y) lies on

A. the circle with radius 1/2a and centre (1/2a, 0) for a > 0, b ≠ 0

B. the circle with radius -1/2a and centre (-1/2a, 0) for a < 0, b ≠ 0

C. the x-axis for a ≠ 0, b = 0

D. the y-axis for a = 0, b ≠ 0

 

Q. 48 Let P be the point on the parabola y² = 4x which is at the shortest distance from the center S of the circle x² + y² – 4x – 16y + 64 = 0. Let Q be the point on the circle dividing the line segment SP internally. Then

A. SP = 2√5

B. SQ : QP = (√5 + 1) : 2

C. the x-intercept of the normal to the parabola at P is 6

D. the slope of the tangent to the circle at Q is 1/2

 

Q. 49 Let a, λ, μ ∈ R. Consider the system of liner equations

ax + 2y = λ

3x – 2y = μ

Which of the following statement(s) is(are) correct?

A. If a = -3, then the system has infinitely many solutions for all values of λ and μ

B. If a ≠ -3, then the system has a unique solution for all values of λ and μ

C. If λ + μ = 0, then the system has infinitely many solutions for a = -3

D. If λ + μ ≠ 0, then the system has no solution for a = -3

 

Q. 50 Let û = u_1 î + u_2 ĵ + u_3 k̂ be a unit vector in R³ and ŵ = (1/√6)(î + ĵ + 2k̂). Given that there exists a vector v in R³ such that |û x v̂| = 1 and ŵ . (û x v̂) = 1. Which of the following statement(s) is(are correct?

A. There is exactly one choice for such vector v

B. There are indefinitely many choices for such vector v

C. If û lies in the xy-plane then |u_1| = |u_2|

D. If û lies in the xz-plane then 2 |u_1| = |u_3|

 

Questions: 51 – 52

Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are 1/2, 1/6 and 1/3, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2, respectively, after two games.

Q. 51 P(X > Y) is

A. 1/4

B. 5/12

C. 1/2

D. 7/12

 

Q. 52 P(X = Y) is

A. 11/36

B. 1/3

C. 13/36

D. 1/2

 

Questions: 53 – 54

Let F₁(x₁, 0) and F₂(x₂, 0), for x₁ < 0 and x₂ > 0, be the foci of the ellipse x²/9 + y²/8 = 1. Suppose a parabola having vertex at the origin and focus at F₂ intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant. 

Q. 53 The orthocentre of the triangle F₁MN is

A. (-9/10, 0)

B. (2/3, 0)

C. (9/10, 0)

D. (2/3, √6)

 

Q. 54 If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of area of the triangle MQR to area of the quadrilateral MF₁NF₂ is

A. 3 : 4

B. 4 : 5

C. 5 : 8

D. 2 : 3

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	C	C	C	A	C	B	AC	C	ABD	BC
Question	11	12	13	14	15	16	17	18	19	20
Answer	ABCD	ABD	BD	AB	A	B	C	D	D	D
Question	21	22	23	24	25	26	27	28	29	30
Answer	A	A	A	A	AC	AB	BCD	ABC	BD	BC
Question	31	32	33	34	35	36	37	38	39	40
Answer	CD	BCD	B	C	A	B	B	B	C	A
Question	41	42	43	44	45	46	47	48	49	50
Answer	C	C	BC	AB	AD	BC	ACD	ACD	BCD	BC
Question	51	52	53	54
Answer	B	C	A	C

JEE Advanced 2016 Paper 1

Q. 1 In a historical experiment to determine Planck’s constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength (λ) of incident light and the corresponding stopping potential (V₀) are given in the image below. Given that c=3×10⁸ m s⁻¹ and e=1.6×10⁻¹⁹C, Planck’s constant (in units of J s) found from such an experiment is

A. 6.0×10⁻³⁴

B. 6.4×10⁻³⁴

C. 6.6×10⁻³⁴

D. 6.8×10⁻³⁴

 

Q. 2 A uniform wooden stick of mass 1.6 kg and length l rests in an inclined manner on a smooth, vertical wall of height h(

A. h/l = √3/16, f = (16√3/3)N

B. h/l = 3/16, f = (16√3/3)N

C. h/l = 3√3/16, f = (8√3/3)N

D. h/l = 3√3/16, f = (16√3/3)N

 

Q. 3 A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly at 3 kW of heat (thermal load). The temperature of water fed into the device cannot exceed 30° C and the entire stored 120 litres of water is initially cooled to 10° C. The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is – (Specific heat of water is 4.2 kJ kg⁻¹ K⁻¹ and the density of water is 1000 kg m⁻³)

A. 1600

B. 2067

C. 2533

D. 3933

 

Q. 4 A parallel beam of light is incident from air at an angle α on the side PQ of a right angled triangular prism of refractive index n=√2. Light undergoes total internal reflection in the prism at the face PR when α has a minimum value of 45°. The angle θ of the prism is 

A. 15°

B. 22.5°

C. 30°

D. 45°

 

Q. 5 An infinite line charge of uniform electric density λ lies along the axis of an electrically conducting infinite cylindrical shell of radius R. At time = 0, the space inside the cylinder is filled with a material of permittivity ε and electrical conductivity σ. The electrical conduction in the material follows Ohm’s law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density j(t) at any point in the material?

A. I

B. II

C. III

D. IV

 

Q. 6 Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principal quantum number n, where n>>1. Which of the following statement(s) is(are) true?

A. Relative change in the radii of two consecutive orbitals does not depend on Z

B. Relative change in the radii of two consecutive orbitals varies as 1/n

C. Relative changes in the energy of two consecutive orbitals varies as 1/n³

D. Relative change in the angular momenta of two consecutive orbitals varies as 1/n

 

Q. 7 Two loudspeakers M and N are located 20 m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car is initially at a point P, 1800 m away from the midpoint Q of the line MN and moves towards Q constantly at 60 km/hr along the perpendicular bisector of MN. It crosses Q and eventually reaches a point R, 1800 m away from Q. Let v(t) represent the beat frequency measured by a person sitting in the car at time t. Let Vₚ, Vᵩ and Vᵣ be the beat frequencies measured at locations P, Q and R respectively. The speed of sound in air is 330 m s⁻¹. Which of the following statement(s) is(are) true regarding the sound heard by the person?

A. Vₚ + Vᵣ = 2Vᵩ

B. The rate of change in beat frequency is maximum when the car passes through Q

C. The plot in image I. represents schematically the variation of beat frequency with time

D. The plot in image II. represents schematically the variation of beat frequency with time

 

Q. 8 An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is(are) true? 

A. The temperature distribution over the filament is uniform

B. The resistance over small sections of the filament decreases with time

C. The filament emits more light at higher band of frequencies before it breaks up

D. The filament consumes less electrical power towards the end of the life of the bulb

 

Q. 9 A piano-convex lens is made of a material of refractive index n. When a small object is placed 30 cm away in front of the curved surface of the lens, an image of double size of the object is produced. Due to reflection from the convex surface of the lens, another faint image is observed at a distance of 10 cm away from the lens. Which of the following statement(s) is(are) true?

A. The refractive index of the lens is 2.5 cm

B. The radius of the convex surface is 45 cm

C. The faint image is erect and real

D. The focal length of the lens is 20 cm

 

Q. 10 A length-scale (l) depends on the permittivity (ε) of a dielectric material. Boltzmann constant (kB), the absolute temperature (T). The number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression(s) for l is(are) dimensionally correct?

A. I

B. II

C. III

D. IV

 

Q. 11 A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that 90° vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at a constant rate of 10 A s⁻¹. Which of the following statement(s) is(are) true?

A. The magnitude of induced emf in the wire is (μ₀/π) volt

B. If the loop is rotated at a constant angular speed about the wire, an additional emf of

(μ₀/π) volt is induced in the wire

C. The induced current in the wire is in opposite direction to the current along the

hypotenuse

D. There is a repulsive force between the wire and the loop

 

Q. 12 The position vector r ⃗ of a particle of mass m is given by the following equation

r ⃗(t)-at³iˆ+βt²jˆ, where a=10/3 m s⁻³, β=5 m s⁻² and m=0.1 kg. At t=1 s, which of the following statement(s) is(are) true about the particle?

A. The velocity v ⃗ is given by v ⃗ =(10iˆ+10jˆ)m s⁻¹

B. The angular momentum L ⃗ with respect to the origin is given by L ⃗ =-(5/3)kˆ N m s

C. The force F ⃗ is given by F ⃗ =(iˆ+2jˆ)N

D. The torque r ⃗ with respect to the origin is given by r ⃗ = -(20/3)kˆ N m

 

Q. 13 A transparent slab of thickness d hhas a refractive index n(z) that increases with z. Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n₁ and n₂ (>n₁), as shown in the figure. A ray of light is incident with angle θ₁ from medium 1 and emerges in medium 2 with refraction angle θf with a lateral displacement l. Which of the following statement(s) is(are) true? 

A. n₁sinθ₁= n₂sinθ

B. n₁sinθ₁=(n₂-n₁)sinθf

C. l is independent of n₂

D. l is independent on n(z)

 

Q. 14 A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P) by the metal. The sensor has a scale that displays log₂(P/P₀), where P₀ is a constant. When the metal surface is at a temperature of 487° C, the sensor shows a value 1. Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to 2767 °C? 

 

Q. 15 The isotope ¹²₅B having a mass 12.014 u undergoes β-decay to ¹²₆C, ¹²₆C has an excited state of the nucleus (¹²₆C*) at 4.041 MeV above its ground state. If ¹²₅B decays to ¹²₆C*, the maximum kinetic energy of the β-particle in units of MeV is –

(1 u = 931.5 MeV/c², where c is the speed of light in vaccum)

 

Q. 16 A hydrogen atom in its ground state is irradiated by light of wavelength 970. Taking hc l e = 1.237 x 10⁻⁶ eV m and the ground state energy of hydrogen atom as -13.6 eV, the number of lines present in the emission spectrum is?

 

Q. 17 Consider two solid spheres P and Q each of density 8 gm cm⁻³ and diameter 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density 0.8 gm cm⁻³ and viscosity n=3 poiseulles. Sphere Q is dropped into a liquid of density 1.6 gm cm⁻³ and viscosity n=2 poiseulles. The ratio of the terminal velocities of P and Q is?

 

Q. 18 Two inductors L₁ (inductance 1 mH, internal resistance 3Ω) and L₂ (inductance 2 mH, internal resistance 4Ω), and a resistor R (resistance 12Ω) are all connected in parallel across a 5 V battery. The circuit is switched on at time t=0. The ratio of the maximum to the minimum current (I₁/I₂) drawn from the battery is?

(I₁ = maximum, I₂ = minimum)

 

Q. 19 P is the probability of finding the 1s electron of hydrogen atom in a spherical shell of infinitesimal thickness, dr, at a distance r from the nucleus. The volume of this shell is 4πr²dr. The qualitative sketch of the dependence of P on r is –

A. I

B. II

C. III

D. IV

 

Q. 20 One mole of an ideal gas at 300 K in thermal contact with surroundings expands isothermally from 1.0 L to 2.0 L against a constant pressure of 3.0 atm. In this process, the change in entropy of surroundings (ΔS) in JK⁻¹ is (1 L atm = 101.3 J)

A. 5.763

B. 1.013

C. -1.013

D. -5.763

 

Q. 21 The increasing order of atomic radii of the following group 13 element is

A. Al<Ga<In<Tl

B. Ga<Al<In<Tl

C. Al<In<Ga<Tl

D. Al<Ga<Tl<In

 

Q. 22 Among [Ni(co₄)], [NiCl₄]²⁻, [Co(NH₃)₄Cl₂]Cl, Na₃[CoF₆], Na₂O₂ and CsO₂, the total number if paramagnetic compound is

A. 2

B. 3

C. 4

D. 5

 

Q. 23 On complete hydrogenation, natural rubber produces

A. Ethylene-propylene copolymer

B. Vulcanised rubber

C. Polypropylene

D. Polybutylene

 

Q. 24 Choose the correct option(s)

According to the Arrhenius equation,

A. A high activation energy usually implies a fast reaction

B. Rate constant increases with increase in temperature. This is due to a greater

number of collisions whose energy exceeds the activation energy

C. Higher the magnitude of activation energy, stronger is the temperature dependence

of the rate constant

D. The pre-exponential factor is a measure of the rate at which collisions occur,

irrespective of their energy

 

Q. 25 A plot of the number of neutrons (N) against the number of protons (P) of stable nuclei exhibits upward deviation from linearity for atomic number Z>20. For an unstable nucleus having N/P ratio less than 1, the possible mode(s) of decay is(are)

A. β – decay (β emission)

B. orbital or K-electron capture

C. neutron emission

D. β – decay (positron emission)

 

Q. 26 The crystalline form of borax has

A. Tetranuclear [B₄O₅(OH₄)²⁻] unit

B. All boron atoms in the same place

C. Equal number of sp² and sp³ hybridised boron atoms

D. One terminal hydroxide per boron atom

 

Q. 27 The compound(s) with TWO lone pairs of electrons on the central atom is(are)

A. BrF₅

B. CIF₃

C. XeF₄

D. SF₄

 

Q. 28 The reagent(s) that can selectively precipitate S²⁻ from a mixture of S²⁻ and SO₄²⁻ in aqueous solution is(are)

A. CuCl₂

B. BaCl₂

C. Pb(OOCCH₃)₂

D. Na₂[Fe(CN)₅ NO]

 

Q. 29 Positive Tollen’s test is observed for

A. I

B. II

C. III

D. IV

 

Q. 30 The product(s) of the following reaction is(are)

A. I

B. II

C. III

D. IV

 

Q. 31 The correct statement(s) about the filtering reaction sequence is(are)

A. R is steam volatile

B. Q gives dark bullet coloration with 1% aqueous FeCl₃ solution

C. S gives yellow precipitate with 2, 4-dinitrophenylhydrazine

D. S gives dark violet coloration with 1% aqueous FeCl₃ solution

 

Q. 32 The mole fraction of a solute in a solution is 0.1. At 298 K, molarity of this solution is the same as its molality. Density of this solution at 298 K is 2.0 g cm⁻³. The ratio of the molecular weights of the solute and solvent, (MW₁/MW₂), is – (MW₁= solute, MW₂=solvent)

 

Q. 33 The diffusion coefficient of an ideal gas is proportional to its mean free path and means speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion of this gas increases x times. The value of x is – 

 

Q. 34 In neutral or fairly alkaline solution, 8 moles of permanganate anion quantitatively oxidise thiosulphate anions to produce X moles of a sulphur containing product. The magnitude of X is –

 

Q. 35 The number of geometric isomers possible for the complex [CoL₂Cl₂]⁻ (L=H₂NCH₂CH₂O⁻) is –

 

Q. 36 In the following monobromination reaction, the number of possible chiral products is 

 

Q. 37 Let –π/6 < θ<-π/12. Suppose α₁ and β₁ are the roots of the equation x² – 2xsecθ + 1=0 and α₂ and β₂ are the roots of the equation x² + 2xtanθ – 1 =0. If α₁ > β₁ and α₂ > β₂, then α₁+ β₂ equals

A. 2(secθ-tanθ)

B. 2secθ

C. -2tanθ

D. 0

 

Q. 38 A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of days of selecting the team is 

A. 380

B. 320

C. 260

D. 95

 

Q. 39 Let S={xϵ(-π,π):x≠0, ±π/2}. The sum of all distinct solutions of the equation

√3secx+cosecx+2(tanx-cotx)=0 in the set S is equal to

A. -7π/9

B. -2π/9

C. 0

D. 5π/9

 

Q. 40 A computer producing factory has only two plants T₁ and T₂. Plant T₁ produces 20% and plant T₂ produces 80% of the total computers produced. 7% of computers are produced in the factory turn out to be defective. It is known that p(computer turns out to be defective given that it is produced in plant T₁) = 10P (computer turns out to be defective given that it is produced in plant T₂), where P(E) denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T₂ is

A. 36/73

B. 47/79

C. 78/93

D. 75/83

 

Q. 41 The least value of a ϵ R for which 4ax²+1/x≥1, for all x>0 is

A. 1/64

B. 1/32

C. 1/27

D. 1/25

 

Q. 42 Consider a pyramid OPQRS located in the first octant (x≥0, y≥0, z≥0) with O as origin, and OP and OR along the x-axis and the y-axis respectively. The base of OPQR of the pyramid is a square with OP – 3. The point S is directly above the midpoint T of diagonal OQ such that TS=3. Then

A. The acute angle between OQ and OS is π/3

B. The equation of the plane containing the triangle OQS is x-y =0

C. The length of the perpendicular from P to the plane containing the triangle OQS is 3/ √2

D. The perpendicular distance from O to the straight line containing RS is √15/2

 

Q. 43 Let f:(0,∞) → R be a differentiable functions such that f’(x) =2-f(x)/2 for all x ϵ (0,∞) and f(1)≠1. Then

A. I

B. II

C. III

D. IV

 

Q. 44 P is a matrix where a ϵ R. Suppose Q=[qᵢ] is a matrix such that PQ =kI, where k ϵ R and k≠0 and I is the identity matrix of order 3. If q₂₃=-k/8 and det(Q) =k²/2, then

A. a=0, k=8

B. 4a-k+8=0

C. det(P adj(Q)) =2⁹

D. det(Q adj(P))=2¹³

 

Q. 45 In a triangle XYZ, let x, y, z be the lengths of sides opposite to the angles X, Y, Z, respectively, and 2s=x+y+z. If (s-x/4) = (s-y/3) = (s-z/2) and area of incircle of the triangle XYZ is 8π/3, then 

A. Area of the triangle is 6√6

B. The radius of the circumference of the triangle XYZ is (35/6)√6

C. (sinX/2)(sinY/2)(sinZ/2)= 4/35

D. sin²(X+Y/2)= 35

 

Q. 46 A solution curve of the differentials equation (x²+xy+4x+2y+4)dy/dx-y²=0, x>0, passes through the point (1,3). Then the solution curve

A. Intersects y=x+2 exactly at one point

B. Intersects y=x+2 exactly at two points

C. Intersects y=(x+2)²

D. Does NOT intersect y=(x+3)²

 

Q. 47 Let f:R→R, g:R→R and h:R→R be differentiable functions such that f(x) =x³+3x+2, g(f(x)) =x and h(g(g(x))) =x for all x ϵ R. Then

A. g’(2)=1/15

B. h’(1)=666

C. h(0)=16

D. h(g(3)) =36

 

Q. 48 The circle C₁:x²+y²=3, with centre at O, intersects the parabola x²=2y at the point P in the first quadrant. Let the tangent to the circle C₁ at P touches other two circles C₂ and C₃ at R₂ and R₃, respectively. Suppose C₂ and C₃ have equal radii 2√3 and centres Q₂ and Q₃, respectively. If Q₂ and Q₃ lie on the y-axis, then

A. Q₂Q₃=12

B. R₂R₃=4√6

C. area of the triangle OR₂R₃ is 6√2

D. Area of the triangle PQ₂Q₃ is 4√2

 

Q. 49 Let RS be the diameter of the circle x²+y²=1, where S is the point (1,0). Let P be a variable point (other than R and S) on the circle and tangents to the circle at S and P meet at point Q. The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. Then the locus of E passes through the point(s) 

A. (1/3,1/√3)

B. (1/4,1/2)

C. (1/3,-1/√3)

D. (1/4,-1/2)

 

Q. 50 The total number of distinct x ϵ R for the following matrix is 

 

Q. 51 Let m be the smallest positive integer such that the coefficient of x² in the expansion of (1+x)² +(1+x)³+….+(1+x)⁴⁹+(1+mx)⁵⁰ is (3n+1)⁵¹C₃ for some positive integer n. Then the value of n is

 

Q. 52 The total number of distinct x ϵ [0,1] for which the following is

 

Q. 53 Let α, β ϵ R be such that (refer image). Then 6(α+β) equals

 

Q. 54 Let z=-1+√3i/2, where i=√-1, and r, s ϵ {1,2,3}. Let P(refer image) and I be the identity matrix of order 2. Then the total number of ordered pairs (r, s) for which P² = -I is

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	B	D	B	A	C	ABD	ABC	CD	AC	BD
Question	11	12	13	14	15	16	17	18	19	20
Answer	AD	ABD	ACD	9	8 OR 9	6	3	8	D	C
Question	21	22	23	24	25	26	27	28	29	30
Answer	B	B	A	BCD	BD	ACD	BC	AC	ABC	B
Question	31	32	33	34	35	36	37	38	39	40
Answer	BC	9	4	6	5	5	C	A	C	C
Question	41	42	43	44	45	46	47	48	49	50
Answer	C	BCD	A	BC	ACD	AD	BC	ABC	AC	2
Question	51	52	53	54
Answer	5	1	7	1

JEE Advanced 2015 Paper 2 

Q. 1 A large spherical mass M is fixed at one position and two identical point masses m are kept on a line passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of length l and this assembly is free to move along the line connecting them. All three masses interact only through their mutual gravitational interaction. When the point mass nearer to M is at a distance r = 3l from M, the tension in the rod is zero for m = k(M/288). The value of k is

 

Q. 2 The energy of a system as a function of time t is given as E(t) = A²exp(-at), where a = 0.2 s⁻¹. The measurement of A has an error of 1.25%. If the error in the measurement of time is 1.50%, the percentage error in the value of E(t) at t=5 s is

 

Q. 3 The densities of two solid spheres A and B of the same radii R vary with radial distance r as Pₐ(r) = k(r/R) and Pᵦ(r) = k(r/R)⁵, respectively, where k is a constant. The moments of inertia of the individual spheres about axes passing through their centres are Iₐ and Iᵦ, respectively. If Iᵦ/Iₐ = n/10, the value of n is

 

Q. 4 Four harmonic waves of equal frequencies and equal intensities I₀ have phase angles 0, π/3, 2π/3 and π. When they are superposed, the intensity of the resulting wave is nI₀. The value of n is

 

Q. 5 For a radioactive material, its activity A and rate of change of its activity R are defined as A = -dN/dt and R = -dA/dt, where N(t) is the number of nuclei at time t. Two radioactive sources P (mean life l) and Q (mean life 2l) have the same activity at t = 0. Their rates of change of activities at t = 2l are Rₚ and Rᵩ, respectively. If Rₚ/Rᵩ = n/e, then the value of n is 

 

Q. 6 A monochromatic beam of light is incident at 60⁰ on one face of an equilateral prism of refractive index n and emerges from the opposite face making an angle θ(n) with the normal (see the figure). For n = √3 the value of θ is 60⁰ and dθ/dn = m. The value of m is 

 

Q. 7 In the following circuit, the current through the resistor R (= 2 Ω) is I Amperes. The value of I is

 

Q. 8 An electron in an excited state of Li²⁺ion has angular momentum 3h/2π. The de Broglie wavelength of the electron in this state is pπa₀ (where a₀ is the Bohr radius). The value of p is

 

Q. 9 Two spheres P and Q of equal radii have densities p₁ and p₂, respectively. The spheres are connected by a massless string and placed in liquids L₁ and L₂ of densities d₁ and d₂ and viscosities n₁ and n₂, respectively. They float in equilibrium with the sphere P in L₁ and sphere Q in L₂ and the string being taut (see figure). If sphere P alone in L₂ has terminal velocity V of P and Q alone in L has terminal velocity V of Q, then

A. |V of P|/|V of Q| = n₁/n₂

B. |V of P|/|V of Q| = n₂/n₁

C. V of P. V of Q > 0

D. V of P. V of Q < 0

 

Q. 10 In terms of potential difference V, electric current I, permittivity E₀, permeability u₀ and speed of light c, the dimensionally correct equation(s) is (are)

A. μ₀I² = ε₀V²

B. cI = μ₀V

C. I =ε₀cV

D. μ₀cI = ε₀V

 

Q. 11 Consider a uniform spherical charge distribution of radius R₁ centred at the origin O. In this distribution, a spherical cavity of radius R₂, centred at P with distance OP = a = R₁ – R₂ (see figure) is made. If the electric field inside the cavity at position r is E(r), then the correct statement(s) is (are)

A. E is uniform, its magnitude is independent of R2 but its direction depends on r

B. E is uniform, its magnitude depends of R2 but its direction depends on r

C. E is uniform, its magnitude is independent of a but its direction depends on a

D. E is uniform and both its magnitude and direction depend on a

 

Q. 12 In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in the figure. Then the correct statement(s) is(are)

A. P has more tensile strength than Q

B. P is more ductile than Q

C. P is more brittle than Q

D. The Young’s modulus of P is more than that of Q

 

Q. 13 A spherical body f radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r) is the pressure at s(r < R), then the correct option(s) is(are) 

A. P(r = 0) = 0

B. P(r = 3R/4) / P(r = 2R/3) = 63/80

C. P(r = 3R/5) / P(r = 2R/5) = 16/21

D. P(r = R/2) / P(r = R/3) = 20/27

 

Q. 14 A parallel plate capacitor having plates of area S and plate separation d, has capacitance C₁ in air. When two dielectrics of different relative permittivities (E₁ = 2 and E₂ = 4) ar introduced between the two plates as shown in the figure, the capacitance becomes C₂. The ratio C₂/C₁ is

A. 6/5

B. 5/3

C. 7/5

D. 7/3

 

Q. 15 An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature T₁, pressure P₁ and volume V₁ and the spring is in its relaxed state. The gas is then heated very slowly to temperature T₂, pressure P₂ and volume V₂. During this process the piston moves out by a distance x. Ignoring the friction between the piston and the cylinder, the correct statement(s) is(are) 

A. If V₂ = 2V₁ and T₂ = 3T₁, then the energy stored in the spring is 1/4 P₁V₁

B. If V₂ = 2V₁ and T₂ = 3T₁, then the change in internal energy is 3 P₁V₁

C. If V₂ = 3V₁ and T₂ = 4T₁, then the work done by the gas is 7/3 P₁V₁

D. If V₂ = 3V₁ and T₂ = 4T₁, then the heat supplied to the gas is 17/6 P₁V₁

 

Q. 16  A fission reaction is given, where x and y are two particles. Considering U to be at rest, the kinetic energies of the products are denoted by Kₓₑ, Kₛᵣ, Kₓ(2MeV) and Kᵧ(2MeV), respectively. Le the binding energies per nucleon of U, Xe and Sr be 7.5 MeV, 8.5 MeV and 8.5 MeV, respectively. Considering different conservation laws, the correct option(s) is(are) 

A. x = n, y = n, Kₛᵣ = 129 MeV, Kₓₑ = 86 MeV

B. x = p, y = e⁻, Kₛᵣ = 129 MeV, Kₓₑ = 86 MeV

C. x = p, y = n, Kₛᵣ = 129 MeV, Kₓₑ = 86 MeV

D. x = n, y = n, Kₛᵣ = 86 MeV, Kₓₑ = 129 MeV

 

Questions: 17 – 18 

In a thin rectangular metallic strip a constant current I flows along the positive xdirection, as shown in the figure. The length, width and thickness of the strip are

I, w and d, respectively.

A uniform magnetic field B is applied on the strip along the positive y-direction. Due to this, the charge carriers experience a net deflection along the z-direction. This results in accumulation of charge carriers on the surface PQRS and appearance of equal and opposite charges on the face opposite to PQRS. A potential difference along the z-direction is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.

Q. 17 Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are w₁ and w₂ and thicknesses are d₁ and d₂ respectively. Two points K and M are symmetrically located on the opposite faces parallel to the x-y plane (see figure). V₁ and V₂ are the potential differences between K and M in strips 1 and 2, respectively. Then, for a given current I flowing through them in a given magnetic field strength B, the correct statement(s) is(are)

A. If w₁ = w₂ and d₁= 2d₂ , then V₂ = 2V₁

B. If w₁ = w₂ and d₁= 2d₂ , then V₂ =V₁

C. If w₁ = 2w₂ and d₁= d₂ , then V₂ = 2V₁

D. If w₁ = 2w₂ and d₁ =d₂ , then V₂ = V₁

 

Q. 18 Consider two different metallic strips (1 and 2) of same dimensions (length l, width w and thickness d) with carrier densities n₁ and n₂, respectively. Strip 1 is placed in magnetic field B₁ and strip 2 is placed in magnetic field B₂, both along positive y-directions. Then V₁ and V₂ are the potential differences developed between K and M in strips 1 and 2, respectively. Assuming that the current I is the same for both the strips, the correct option(s) is(are)

A. If B₁ = B₂ and n₁ = 2n₂ , then V₂ = 2V₁

B. If B₁ = B₂ and n₁ = 2n₂ , then V₂ =V₁

C. If B₁ = 2B₂ and n₁ = n₂ , then V₂ = 0.5V₁

D. If B₁ = 2B₂ and n₁ =n₂ , then V₂ = V₁

 

Questions: 19 – 20

Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n₁ surrounded by a medium of lower refractive index n₂. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n₁ and n₂ as shown in the figure. All rays with the angle of incidence i less than a particular value iₘ are confined in the medium of refractive index n₁. The numerical aperture (NA) of the structure is defined as sin iₘ. 

Q. 19 For two structures namely S₁ with n₁ = √45/4 and n₂ = 3/2, and S₂ with n₁ = 8/5 and n₂ = 7/5 and taking the refractive index of water to be 4.3 and that of air to be I, the correct option(s) is (are)

A. NA of S₁ immersed in water is the same as that of S₂ immersed in a liquid of refractive index 16/3√15

B. NA of S₁ immersed in liquid of refractive index 6/√15 is the same as that of S₂ immersed in water

C. NA of S₁ placed in air is the same as that of S₂ immersed in liquid of refractive index 4/ √15

D. NA of S₁ placed in air is the same as that of S₂ placed in water

 

Q. 20 If two structures of same cross-sectional area, but different numerical apertures NA₁ and NA₂ (NA₂ < NA₁) are joined longitudinally, the numerical aperture of the combined structure is

A. NA₁NA₂/NA₁+NA₂

B. NA₁ + NA₂

C. NA₁

D. NA₂

 

Q. 21 The number of hydroxyl group(s) in Q is

 

Q. 22 Among the following the number of reaction(s) that produce(s) benzaldehyde is

 

Q. 23 In the complex acetylbromidodicarbonylbis(triethylphosphine)iron(II), the number of Fe-C bond(s) is

 

Q. 24 Among the complex ions, [Co(NH₂-CH₂-CH₂-CH₂-NH₂)₂Cl₂]⁺, [CrCl₂(C₂O₄)₂]³⁻,

[Fe(H₂O)₄(OH)₂]⁺, [Fe(NH₃)₂(CN)₄]⁻, [Co(NH₂-CH₂-CH₂-NH₂)₂(NH₃)Cl]²⁺ and [Co(NH₃)₄(H₂O)Cl]²⁺, the number of complex ion(s) that show(s) cis-trans isomerism is 

 

Q. 25 Three moles of B₂H₆ are completely reacted with methanol. Th number of moles of boroncontaining product formed is

 

Q. 26 The molar conductivity of a solution of a weak acid HX (0.01 M) is 10 times smaller than the molar conductivity of a solution of weal acid HY (0.10 M). If the given condition is satisfied, the difference in pKa values, ₚKₐ(HX) – ₚKₐ(HY), is (consider the degree of ionization of both acids to be <<1)

 

Q. 27 The closed vessel with rigid walls contains 1 mol of U and 1 mol of air at 298 K. Considering complete decay of U to Pb, the ratio of the final pressure to the initial pressure of the system of 298 K is

 

Q. 28 In dilute aqueous H₂SO₄, the complec diaquodioxalatoferrate(II) is oxidized by MnO₄⁻. For this reaction, the ratio of the rate of change of H⁺ to the rate of change of [MnO₄⁻] is

Q. 29 In the following reactions, the product S is

A. (A)

B. (B)

C. (C)

D. (D)

 

Q. 30 The major product U in the following reactions is

A. (A)

B. (B)

C. (C)

D. (D)

 

Q. 31 In the following reactions, the major product W is

A. (A)

B. (B)

C. (C)

D. (D)

 

Q. 32 The correct statement(s) regarding, (i) HClO, (ii) HClO₂, (iii) HClO₃ and (iv) HClO₄, is (are) 

A. The number of Cl=O bonds in (ii) and (iii) together is two

B. The number of lone pairs of electrons on Cl in (ii) and (iii) together is three

C. The hybridization of Cl in (iv) is sp³

D. Amongst (i) to (iv), the strongest acid is (i)

 

Q. 33 The pair(s) of ions where BOTH the ions are precipitated upon passing H₂S gas in presence of dilute HCl, is (are)

A. Ba²⁺, Zn²⁺

B. Bi³⁺, Fe³⁺

C. Cu²⁺, Pb²⁺

D. Hg²⁺, Bi³⁺

 

Q. 34 Under hydrolytic conditions, the compounds used for preparation of linear polymer and for chain termination, respectively, are

A. CH₃SiCl₃ and Si(CH₃)₄

B. (CH₃)₂SiCl₂ and (CH₃)₃SiCl

C. (CH₃)₂SiCl₂ and CH₃SiCl₃

D. SiCl₄ and (CH₃)₃SiCl

 

Q. 35 When O₂ is adsorbed on a metallic surface, electron transfer occurs from the metal to O₂. The TRUE statement(s) regarding this adsorption is(are)

A. O₂ is physisorbed

B. heat is released

C. occupancy of pi2p of O₂ is increased

D. bond length of π₂ₚ of O₂ is increased

 

Q. 36 One mole of a monoatomic real gas satisfies the equation p(V – b) = RT where b is a constant. The relationship of interatomic potential V(r) and interatomic distance r for the gas is given by

A. (A)

B. (B)

C. (C)

D. (D)

 

Question 37

In the given reactions

 

Q. 37 In the given reactions Compound X is

1 

  2

  3

  4

A. (A)

B. (B)

C. (C)

D. (D)

 

Q. 38 The major compound Y is

A. (A)

B. (B)

C. (C)

D. (D)

 

Questions: 39 – 40

When 100 mL of 1.0 M HCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a temperature increase of 5.7 degrees C was measured for the beaker and its contents (Expt. 1). Because the enthalpy of neutralization of a strong acid with a strong base is a constant (-57.9 kJ mol⁻¹), this experiment could be used to measure the calorimeter constant. In a second experiment (Expt. 2), 100 mL of 2.0 M acetic acid (Ka = 2.0 x 10⁻⁵) was mixed with 100 mL of 1.0 mL MaOH (under identical conditions to Expt. 1) where a temperature rise of 5.6 degrees C was measured. (Consider heat capacity of all solutions as 4.2 J g⁻¹ K⁻¹ and density of all solutions as 1.0 g mL⁻¹)

Q. 39 Enthalpy of dissociation (in kJ mol⁻¹) of acetic acid obtained from the Expt. 2 is

A. 1.0

B. 10.0

C. 24.5

D. 51.4

 

Q. 40 The pH of the solution after Expt. 2 is

A. 2.8

B. 4.7

C. 5.0

D. 7.0

 

Q. 41 For any integer k, let aₖ = cos(kπ/7) + i sin(kπ/7), where i = √-1. The value of the given expression is

 

Q. 42 Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the firs eleven terms is 6:11 and the seventh term lies in between 130 and 140, then the common difference of this A.P. is

 

Q. 43 The coefficient of x⁹ in the (1+x)(1+x³)…(1+x¹⁰⁰) is

 

Q. 44 Suppose that the foci of the ellipse x²/9 + y²/5 = 1 are (f₁, 0) and (f₂, 0) where f₁>0 and f₂<0. Let P₁ and P₂ be two parabolas with a common vertex at (0, 0) and with foci at (f₁, 0) and (2f₂, 0), respectively. Let T₁ be a tangent to P₁ which passes through (2f₂, 0) and (T₂ be a tangent to P₂ which passes through (f₁, 0). If m1 is the slope of T₁ and m₂ is the slope of T₂, then the value of (1/m₁² + m₂²) is

 

Q. 45 Let m and n be two positive integers greater than 1, then the value of m/n is

 

Q. 46 Find the value:

If

=01(e9x+3tan-1x)12 + 9×21 + x2dx

where tan-1x takes only principal values, then the value of loge1 + -34is

 

Q. 47 Let R —> R be a continuous odd function, which vanishes exactly at one point and f(1) = 1/2. F(x) is given for all x is element of [-1, 2] and G(x) is given for all x is element of [-1,2]. Find the value of f(1/2) from the given data.

 

Q. 48 Suppose that p, q and r are three non-coplanar vectors in R³. Let the components of a vector s along p, q and r be 4, 3 and 5, respectively. If the components of this vector s along (-p+q+r), (p-q+r) and (-p-q+r) are x, y and z, respectively, then the value of 2x+y+z is

 

Q. 49 Let S be the set of all non-zero real numbers a such that the quadratic equation ax² – x + a = 0 has two distinct real roots x₁ and x₂ satisfying the inequality |x₁ – x₂| < 1. Which of the following intervals is (are) a subset(s) of S?

A. (-1/2, -1/√5)

B. (-1/√5, 0)

C. (0, 1/√5)

D. (1/√5 , 1/2)

 

Q. 50 If a = 3sin⁻¹(6/11) and b = 3cos⁻¹ (4/9), where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are)

A. cosβ > 0

B. sinβ < 0

C. cos(α +β) > 0

D. cosα < 0

 

Q. 51 Let E₁ and E₂ be two ellipses whose centres are at the origin. The major axes of E₁ and E₂ lie along the x-axis and the y-axis, respectively. Let S be the circle x² + (y-1)² = 2. The straight line x + y = 3 touches the curves S, E₁ and E₂ at P, Q and R, respectively. Suppose that PQ = PR = 2√2/3. If e₁ and e₂ are the eccentricities of E₁ and E₂, respectively, then the correct expression(s) is(are)

A. e₁² + e₂² = 43/40

B. e₁e₂ = √7/2√10

C. |e₁² – e₂²| = 5/8

D. e₁e₂ = √3/4

 

Q. 52 Consider the hyperbola H : x² – y² = 1 and a circle S with center N(x₂, 0). Suppose that H and S touch each other at a point P(x₁, y₁) with x₁>1 and y₁>0. The common tangent to H and S at P intersects the x-axis at point M. If (l, m) is the centroid of the triangle PMN, then the correct expression(s) is(are)

A. dl/d₁ = 1 – 1/3x₁² for x₁ > 1

B. dm/dx₁ = x₁/3√(x²-1) for x₁ > 1

C. dl/dx₁ = 1 + 1/3x₁² for x₁ > 1

D. dm/dy₁ = 1/3 for y₁ > 0

 

Q. 53 The option(s) with the values of a and L that satisfy the given equation is (are)

A. a = 2, L = [(e^4pi) – 1]/[(e^pi) – 1]

B. a = 2, L = [(e^4pi) + 1]/[(e^pi) + 1]

C. a = 4, L = [(e^4pi) – 1]/[(e^pi) – 1]

D. a = 4, L = [(e^4pi) + 1]/[(e^pi) + 1]

 

Q. 54 Let f, g : [-1, 2] —-> R be continuous functions which are twice differentiable on the interval (-1, 2). Let the values of f and g at the points -1, 0 and 2 be as given in the table. In each of the intervals (-1, 0) and (0, 2) the function (f – 3g)” never vanishes. Then the correct statement(s) is(are)

 

x=-1	x= 0	x=2
f(x)	3	6	0
g(x)	0	1	-1

 

A. f'(x) – 3g'(x) = 0 has exactly three solutions in (-1, 0)U(0, 2)

B. f'(x) – 3g'(x) = 0 has exactly one solution in (-1, 0)

C. f'(x) – 3g'(x) = 0 has exactly one solution in (0, 2)

D. f'(x) – 3g'(x) = 0 has exactly two solutions in (-1, 0) and exactly two solutions in (0,2)

 

Q. 55 Let f(x) = 7tan⁸x + 7tan⁶x – 3tan⁴x – 3tan²x for all x is element of (-π/2, π/2). Then the correct expression(s) is(are)

A. (A)

B. (B)

C. (C)

D. (D)

 

Q. 56 Let f'(x) = 192x³/2+sin⁴πx for all x is a real number with f(1/2) = 0. If the given condition is satisfied, then the possible values of m and M are 

m1/21f(x) dx M

A. m = 13, M = 24

B. m = 1/4, M = 1/2

C. m = -11, M = 0

D. m = 1, M = 12

 

Questions: 57 – 58

Let n₁ and n₂ be the number of red and black balls, respectively, in box I. Let n₃ and n₄ be the number of red and black balls, respectively, in box II. 

Q. 57 One of the two boxes, box I and box II, was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probability that this red ball was drawn from box II is 1/3, then the correct option(s) with the possible values of n₁, n₂, n₃ and n₄ is (are)

A. n₁ = 3, n₂ = 3, n₃ = 5, n₄ = 15

B. n₁ = 3, n₂ = 6, n₃ = 10, n₄ = 50

C. n₁ = 8, n₂ = 6, n₃ = 5, n₄ = 20

D. n₁ = 6, n₂ = 12, n₃ = 5, n₄ = 20

 

Q. 58 A ball is drawn at random from box I and transferred to box II. If the probability of drawing a red ball from box I, after this transfer is 1/3, then the correct option(s) with the possible values of n₁ and n₂ is (are)

A. n₁ = 4 and n₂ = 6

B. n₁ = 2 and n₂ = 3

C. n₁ = 10 and n₂ = 20

D. n₁ = 3 and n₂ = 6

 

Q. 59 Let F: R —> R be a thrice differentiable function. Suppose that F(1) = 0, F(3) = -4 and F'(x) < 0 for all x is element of (1/2, 3). Let f(x) = xF(x) for all x is element of R. The correct statement(s) is(are)

A. f'(1) < 0

B. f(2) < 0

C. f'(x) is not equal to 0 for any x is element of (1, 3)

D. f'(x) = 0 for some x is element of (1, 3)

 

Q. 60 Let F: R —> R be a thrice differentiable function. Suppose that F(1) = 0, F(3) = -4 and F'(x) < 0 for all x is element of (1/2, 3). Let f(x) = xF(x) for all x is element of R. Using the given data, the correct expression(s) is (are)

A. 9f'(3) + f'(1) – 32 = 0

B. (B)

C. 9f'(3) – f'(1) + 32 = 0

D. (D)

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	7	4	6	3	2	2	1	2	AD	AC
Question	11	12	13	14	15	16	17	18	19	20
Answer	D	AB	BC	D	ABC	A	D	C	C	D
Question	21	22	23	24	25	26	27	28	29	30
Answer	4	4	3	6	6	3	9	8	A	B
Question	31	32	33	34	35	36	37	38	39	40
Answer	A	BC	CD	B	BCD	C	C	D	A	B
Question	41	42	43	44	45	46	47	48	49	50
Answer	4	9	8	4	2	9	7	9	AD	BCD
Question	51	52	53	54	55	56	57	58	59	60
Answer	AB	ABD	AC	BC	AB	D	B	D	ABC	CD

JEE Advanced 2015 Paper 1

Q. 1 An infinitely long uniform line charge distribution of charge per unit length x lies parallel to the y-axis in the y-z plane at z = (root of 3/2)a (see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is xL/nE0 (E0 = permittivity of free space), then the value of n is

Q. 2 Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength 90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value on n is (hc = 1242 eV nm)

 

Q. 3 A bullet is fired vertically upwards with velocity v from the surface of a spherical planet. When it reaches its maximum height, its acceleration due to the planet’s gravity is 1/4th of its value at the surface of the planet. If the escape velocity from the planet is vesc = v(root of N), then the value of N is (ignore energy loss due to atmosphere)

 

Q. 4 Two identical uniform discs roll without slipping on two different surfaces AB and CD (see figure) starting at A and C with linear speeds v₁ and v₂, respectively, and always remain in contact with the surfaces. If they reach B and D with the same linear speed and v₁ = 3 m/s, then v₂ in m/s is (g = 10 m/s²)

 

Q. 5 Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits 10⁴ times the power emitted from B. The ratio (xA/xB) of their wavelengths xA and xB at which the peaks occur in their respective radiation curves is

 

Q. 6 A nuclear power plant supplying electrical power to a village uses a radioactive material of half life T years as the fuel. The amount of fuel at the beginning is such that the total power requirement of the village is 12.5% of the electrical power available from the plant at that time. If the plant is able to meet the total power needs of the village for a maximum period of nT years, then the value of n is

 

Q. 7 A Young’s double slit interference arrangement with slits S₁ and S₂ is immersed in water (refractive index = 4/3) as shown in the figure. The positions of maxima on the surface of water are given by x² = p²m²λ² – d², where λ is the wavelength of light in air (refractive index = 1), 2d is the separation between the slits and m is an integer. The value of p is

 

Q. 8 Consider a concave mirror and a convex lens (refractive index = 1.5) of focal length 10 cm each, separated by a distance of 50 cm in air (refractive index = 1) as shown in the figure. An object is placed at a distance of 15 cm from the mirror. Its erect image formed by this combination has magnification M₁. When the set-up is kept in a medium of refractive index 7/6, the magnification becomes M₂. The magnitude |M₂/M₁| is

 

Q. 9 Consider a Vernier callipers in which each 1 cm on the main scale is divided into 8 equal divisions and a screw gauge with 100 divisions on its circular scale. In the Vernier callipers, 5 divisions of the Vernier scale coincide with 4 divisions on the main scale and in the screw gauge, one compete rotation of the circular scale moves it by two divisions on the linear scale. Then:

A. If the pitch of the screw gauge is twice the least count of the Vernier callipers, the

least count of the screw gauge is 0.01 mm.

B. If the pitch of the screw gauge is twice the least count of the screw gauge is 0.005 mm.

C. If the least count of the linear scale of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge is 0.01 mm.

D. If the least count of the linear scale of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge isi 0.005 mm.

 

Q. 10 Planck’s constant h, speed of light c and gravitational constant G are used to form a unit of length L and a unit of mass M. Then the correct option(s) is (are)

A. M ∝ √c

B. M ∝ √G

C. L ∝ √h

D. L ∝ √G

 

Q. 11 Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies w₁ and w₂ and have total energies E₁ and E₂, respectively. The variations of their momenta p with positions x are shown in the figures. If a/b = n² and a/R = n, then the correct equation(s) is(are)

A. E₁w₁ = E₂w₂

B. w₂/w₁ = n²

C. w₁w₂ = n²

D. E₁/w₁ = E₂/w₂

 

Q. 12 A ring of mass M and radius R is rotating with angular speed w about a fixed vertical axis passing through its centre O with two point masses each of mass M/8 at rest at O. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. At some instant the angular speed of the system is 8w/9 and one of the masses is at a distance of 3R/5 from O. At this instant the distance of the other mass from O is

A. ⅔R

B. R/3

C. ⅗R

D. ⅘R

 

Q. 13 The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density are kept parallel to each other. In their resulting electric field, point charges q and -q are kept in equilibrium between them. The point charges are confined to move in the x direction only. If they are given a small displacement about their equilibrium then the correct statement(s) is(are)

A. Both charges execute simple harmonic motion.

B. Both charges will continue moving in the direction of their displacement.

C. Charge +q executes simple harmonic motion while charge -q continues moving in the direction of its displacement.

D. Charge -q executes simple harmonic motion while charge +q continues moving in the direction of its displacement.

 

Q. 14 Two identical glass rods S₁ and S₂ (refractive index = 1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light P is placed inside rod S₁ on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside S₂. The distance d is

A. 60 cm

B. 70 cm

C. 80 cm

D. 90 cm

 

Q. 15 A conductor (shown in the figure) carrying constant current I is kept in the x-y plane in a uniform magnetic field B. If F is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is(are)

A. If B is along z, F ∝ (L + R)

B. If B is along x, F = 0

C. If B is along y, F ∝ (L + R)

D. If B is along z, F = 0

 

Q. 16 A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature T. Assuming the gases are ideal, the correct statement(s) is (are)

A. The average energy per mole of the gas mixture is 2RT.

B. The ratio of speed of sound in the gas mixture to that in helium gas is root of 6/5

C. The ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/2

D. The ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/√2

 

Q. 17 In an aluminium (Al) bar of square cross section, a square hole is drilled and is filled with iron (Fe) as shown in the figure The electrical resistivities of Al and Fe are 2.7 x 10⁻⁸ ohm m and 1.0 x 10⁷ ohm m, respectively. The electrical resistance between the two faces P and Q of the composite bar is

A. 2475/64

B. 1875/64

C. 1875/49

D. 2475/132

 

Q. 18 For photo-electric effect with incident photon wavelength lambda, the stopping potential is V₀. Identify the correct variation(s) of V₀ with λ and 1/λ.

A. (A)

B. (B)

C. (C)

D. (D)

 

Q. 19 Match the nuclear processes given in column I with the appropriate option(s) in column II. 

A. A – R,T ; B – P,S ; C – Q,T ; D – R

B. A – P,Q ; B – R,S ; C – T ; D – P

C. A – S ; B – P,T ; C – Q ; D – R

D. A – P ; B – R ; C – S,T ; D – P,Q

 

Q. 20 A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in column I (a and U₀ are constants). Match the potential energies in column I to the corresponding statement(s) in column II.

A. A – Q,S ; B – P,R ; C – P,T ; D – P

B. A – P,T ; B – R,S ; C – Q ; D – Q,R

C. A – P,Q,R,T ; B – Q,S ; C – P,Q,R,S ; D – P,R,T

D. A – P,T ; B – P,R ; C – S,Q ; D – T

 

Q. 21 The total number of sterioisomers that can exist for M is

Q. 22 The number of resonance structures for N is

 

Q. 23 The total number of lone pairs of electrons in N₂O₃ is

 

Q. 24 For the octahedral complexes of Fe³+ in SCN (thiocyanato-S) and in CN⁻ ligand environments, the difference between the spin-only magnetic moments in Bohr magnetons (when approximated to the nearest integer) is

[Atomic number of Fe = 26]

 

Q. 25 Among the triatomic molecules/ions, BeCl₂, N₃⁻, N₂O, NO₂⁺, O₃, SCl₂, ICl₂⁻, I₃⁻ and XeF₂, the total number of linear molecule(s)/ion(s) where the hybridization of the central atom does not have contribution from the d-orbital(s) is

[Atomic number: S = 16, Cl = 17, I = 53 and Xe = 54]

 

Q. 26 Not considering the electronic spin, the degeneracy of the second excited state (n = 3) of H atom is 9, while the degeneracy of the second excited state of H⁻ is

 

Q. 27 All the energy released from the reaction X —-> Y, delta, G⁰ = -193 kJ mol⁻¹ is used for oxidizing M⁺ as M⁺ —-> M³⁺ + 2e⁻, E⁰ = -0.25 V. Under standard conditions, the number of moles of M⁺ oxidized when one mole of X is converted to Y is [F = 96500 C mol⁻²]

 

Q. 28 If the freezing point of a 0.01 molal aqueous solution of a cobalt (III) chloride-ammonia complex (which behaves as a strong electrolyte) is -0.0558 degrees C, the number of chloride(s) in the coordination sphere of the complex is

[Kf of water = 1.86 K kg mol⁻¹] 

 

Q. 29 Compound(s) that on hydrogenation produce(s) optically inactive compound(s) is(are) 

A. (A)

B. (B)

C. (C)

D. (D)

 

Q. 30 The major product of the following reaction is

A. (A)

B. (B)

C. (C)

D. (D)

 

Q. 31 In the following reaction the major product is

A. (A)

B. (B)

C. (C)

D. (D)

 

Q. 32 The structure of D-(+)-glucose is given. The stricture of L-(-)-glucose is

A. (A)

B. (B)

C. (C)

D. (D)

 

Q. 33 The major product of the reaction is

A. (A)

B. (B)

C. (C)

D. (D)

 

Q. 34 The correct statement(s) about Cr²+ and Mn³+ is(are) [Atomic numbers of Cr = 24 and Mn = 25

A. Cr²+ is a reducing agent

B. Mn³⁺ is an oxidizing agent

C. Both Cr²+ and Mn³+ exhibit d⁴ electronic configuration

D. When Cr²+ is used as a reducing agent, the thromium ion attains d⁵ electronic

configuration

 

Q. 35 Copper is purified by electrolytic refining of blister copper. The correct statement(s) about this process is(are) 

A. Impure Cu strip is used as cathode

B. Acidified aqueous CuSO₄ is used as electrolyte

C. Pure Cu deposits at cathode

D. Impurities settle as anode-mud

 

Q. 36 Fe³⁺ is reduced to Fe²⁺ by using

A. H₂O₂ in presence of NaOH

B. Na₂O₂ in water

C. H₂O₂ in presence of H₂SO₄

D. Na₂O₂ in presence of H₂SO₄

 

Q. 37 The % yield of ammonia as a function of time in the reaction at (P, T₁) is given. If this reaction is conducted at (P, T₂) with T₂>T₁, the % yield of ammonia as a function of time is represented by

A. (A)

B. (B)

C. (C)

D. (D)

 

Q. 38 If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms wih m fraction of octahedral holes occupied by aluminium ions and n fraction of tetrahedral holes occupied by magnesium ions, m and n, respectively, are

A. 1/2, 1/8

B. 1, 1/4

C. 1/2, 1/2

D. 1/4, 1/8

 

Q. 39 Match the anionic species given in Column I that are present in the ore(s) given in Column II.

Column – I Column – II 

(A) Carbonate (P) Siderite 

(B) Sulphide (Q) Malachite 

(C) Hydroxide (R) Bauxite 

(D) Oxide (S) Calamine (T) Argentite

A. A – P,T ; B – R ; C- T,S ; D – Q

B. A – P,Q,S ; B – T ; C – Q,R ; D – R

C. A – P,Q,S ; B – T ; C – P,R ; D – R

D. A – P,Q,S ; B – P,R ; C – S ; D – T,R

 

Q. 40 Match the thermodynamic processes given under column I with the expressions given under column II.

A. A – P,T ; B – Q,S ; C – S,T ; D – R

B. A – Q ; B – P,S ; C – R,T ; D – P,Q,S,T

C. A – R,T ; B – P,Q,S ; C – P,Q,S ; D – P,Q,S,T

D. A – P,S ; B-P,Q,S ; C- P,S ; D -P,Q

 

Q. 41 The number of distinct solutions of the equation 5/4 cos²(2x) + cos⁴x + sin⁴x + cos⁶x + sin⁶x = 2 in the interval [0, 2pi] is

 

Q. 42 Let the curve C be the mirror image of the parabola y² = 4x with respect to the line x + y + 4 = 0. If A and B are the points of intersection of C with the line y = -5, then the distance between A and B is

 

Q. 43 The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0.96, is

 

Q. 44 Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of m/n is

 

Q. 45 If the normals of the parabola y² = 4x drawn at the end points of its latus rectum are tangents to the circle (x-3)² + (y+2)² = r², then the value of r² is

 

Q. 46 Let f : R —> R be a function defined by

f(x) = [x], x <=2

f(x) = 0, x > 2

where [x] is the greatest integer less than or equal to x. The value of (4I – 1) is

 

Q. 47 A cylindrical container is to be made from certain solid material with the following constraints: It has a fixed inner volume of V mm^3, has a 2 mm thick solid wall and is open at the top. The bottom of the container is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of the container. If the volume of the material used to make the container is minimum when the inner radius of the container is 10 mm, then the value of V/250pi is

 

Q. 48 For a is an element of [0, 1/2], if F'(a) + 2 is the area of the region bounded by x = 0, y = 0, y = f(x) and x = a, then f(0) is

 

Q. 49 Let X and Y be two arbitrary, 3×3, non-zero, skew-symmetric matrices and Z be an arbitrary 3×3, non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?

A. Y³Z⁴ – Z⁴Y³

B. X⁴⁴ + Y⁴⁴

C. X⁴Z³ – Z³X⁴

D. X²³ + Y²³

 

Q. 50 Which of the following values of a satisfy the equation

A. -4

B. 9

C. -9

D. 4

 

Q. 51 In R³, consider the planes P₁ : y = 0 and P₂ : x + z = 1. Let P₃ be a plane, different from P₁ and P₂, which passes through the intersection of P₁ and P₂. If the distance of the point (0, 1, 0) from P₃ is 1 and the distance of a point (a, b, c) from P₃ is 2, then which of the following relations is (are) true?

A. 2a + b + 2c + 2 = 0

B. 2a – b + 2c + 4 = 0

C. 2a + b – 2c – 10 = 0

D. 2a – b + 2c – 8 = 0

 

Q. 52 In R³, let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two planes P₁ : x + 2y – z + 1 = 0 and P₂ : 2x – y + z = 0. Let M be the locus of the feet of the perpendiculars drawn from the points on L to the plane P₁. Which of the following points lie(s) on M?

A. (0, -5/6, -2/3)

B. (-1/6, -1/3, 1/6)

C. (-5/6, 0, 1/6)

D. (-1/3, 0, 2/3)

 

Q. 53 Let P and Q be distinct points on the parabola y² = 2x such that a circle with PQ as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle OPQ is 3√2, then which of the following is (are) the coordinates of P?

A. 4 , 2√2

B. 9 , 3√2

C. 1/4 , 1⁄√2

D. 1 , √2

 

Q. 54 Let y(x) be a solution of the differential equation (1 + eˣ)y’+ yeˣ = 1. If y(0) = 2, then which of the following statements is (are) true?

A. y(-4) = 0

B. y(-2) = 0

C. y(x) has a critical point in the interval (-1, 0)

D. y(x) has no critical point in the interval (-1, 0)

 

Q. 55 Consider the family of all circles whose centers lie on the straight line y = x. If this family of circles is represented by the differential equation Py” + Qy’ + 1 = 0, where P, Q are functions of x, y and y’ (here y’ = dy/dx, y” = d²y/dx²), then which of the following statements is (are) true?

A. P = y + x

B. P = y – x

C. P + Q = 1 – x + y + y’ + (y’)²

D. P – Q = x + y – y’ – (y’)²

 

Q. 56 Let g : R—>R be a differentiable function with g(0) = 0, g'(0) = 0 and g'(0) = 0 and g'(1) is not = 0. Let

f(x) = xg(x)/|x|, x is not = 0

f(x) = 0, x = 0

and h(x) = e^|x| for all x is element of R. Let (f . h)(x) denote f(h(x)) and (h . f)(x) denote h(f(x)). Then which of the following is (are) true?

A. f is differentiable at x = 0

B. h is differentiable at x = 0

C. f . h is differentiable at x = 0

D. h . f is differentiable at x = 0

 

Q. 57 Let f(x) = sin(pi/6 sin(pi/2 sinx)) for all x is element of R and g(x) = pi/2 sinx for all x element of R. Let (f . g)(x) denote f(g(x)) and (g . f)(x) denote g(f(x)). Then which of the following is (are) true?

A. Range of f is [-1/2, 1/2]

B. Range of f . g is [-1/2, 1/2]

C. lim(x—>0) f(x)/g(x) = pi/6

D. There is an x element of R such that (g . f)(x) = 1

 

Q. 58 Let PQR be a triangle. Let a = QR, b = RP and c = PQ. If |a| = 12, |b| = 4√3 and b.c = 24, then which of the following is (are) true?

A. |c|²/2 – |a| = 12

B. |c|²/2 + |a| = 30

C. |a x b + c x a| = 48√3

D. a.b = -72

 

Q. 59 Match the column

A. A – P,Q ; B – P,Q ; C – P,Q,S,T ; D – Q,T

B. A – P,S ; B – R,T ; C – S,T ; D – Q,T

C. A – R,T ; B – P,S ; C – S,T ; D – P,T

D. A – P,Q ; B – R,S ; C – S,T ; D – Q,S

 

Q. 60 Match the column

A. A – P,Q,T ; B – S,R ; C – P,T ; D – R

B. A – P,R,S ; B – P ; C – P,Q; D – S,T

C. A – P,T ; B – Q,R ; C – S,R ; D – R

D. A – Q,S ; B – S,T ; C – P,T D – S

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	6	2	2	7	2	3	3	7	BC	ACD
Question	11	12	13	14	15	16	17	18	19	20
Answer	BD	CD	C	B	ABC	ABD	B	AC	A	C
Question	21	22	23	24	25	26	27	28	29	30
Answer	2	9	8	4	4	3	4	1	BD	A
Question	31	32	33	34	35	36	37	38	39	40
Answer	D	A	C	ABC	BCD	AB	B	A	B	C
Question	41	42	43	44	45	46	47	48	49	50
Answer	8	4	8	5	2	0	4	3	CD	BC
Question	51	52	53	54	55	56	57	58	59	60
Answer	BD	AB	AD	AC	BC	AD	ABC	ACD	A	B