JEE Advanced - Page 3 of 4 - Vidhyarthi Darpan

JEE Advanced 2012 Paper II Previous Year Paper

JEE Advanced 2012 Paper 2

Q. 1 A loop carrying current I lies in the x-y plane as shown in the figure. The unit vector k̂ is coming out of the plane of the paper. the magnetic moment of the current loop is

A. a²Ik̂

B. (Π/2+1)a²Ik̂

C. -(Π/2+1)a²Ik̂

D. (2Π+1)a²Ik̂

Q. 2 An infinitely long hollow conducting cylinder with inner radius R/2 and outer radius R carries a uniform current density along its length. the magnitude of the magnitude field, |B̅| as a function of the radial distance r from the axis is best represented by

A. A

B. B

C. C

D. D

Q. 3 A thin uniform cylindrical shell, closed at both ends, is partially filled with water. it is floating vertically in water in half-submerged state. if ρc is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

A. more than half-filled if ρc is less than 0.5

B. more than half-filled if ρc is less than 1.0

C. half-filled if ρc is more than 0.5

D. less than half-filled if ρc is less than 0.5

Q. 4 In the given circuit, a change of +80 μC is given to the upper plate of the 4 μF capacitor. Then in the steady state, the charge on the upper plate of the 3 μF capacitor is

A. +32 μC

B. +40 μC

C. +48 μC

D. +80 μC

Q. 5 Two moles of ideal helium gas are in a rubber balloon at 30°C. The balloon is fully expandable and can be assumed to require no energy in its expansion. the temperature of the gas in the balloon is slowly changed to 35°C. The amount heat required in raising the temperature is nearly (take R=8.31 J/mol.K)

A. 62 J

B. 104 J

C. 124 J

D. 208 J

Q. 6 Consider a disc rotating in the horizontal plane with a constant angular speed co about its, centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebblesPand are simultaneously projected at an angle towards. The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back onthe disc before the disc has completed y rotation, (ii) their range is less than half the disc radius, and (iii) w remains constant throughout. Then

A. P lands in the shaded region and in the unshaded region.

B. P lands in the unshaded region and Q in the shaded region

C. Both P and Q land in the unshaded region.

D. Both P and Q land in the shaded region

Q. 7 A student is performing the experiment of Resonance Column. The diameter of the column tube is 4 cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38 C in which the speed of sound is 336 mls. The zero of the meter scale coincides with the top end of the Resonance Column tube. When the first resonance occurs, the reading of the water level in the column is

A. 14.0 cm

B. 15.2 cm

C. 16.4 cm

D. 17.6 cm

Q. 8 Two identical discs of the same radius R are rotating about their axes in opposite

directions with the same constant angular speed w. The discs are in the same horizontal plane. At the time!= 0, the points P and Q are facing each other as shown in the figure. The relative speed between the two points Pand Q is vᵣ. In one time period (T ) of rotatin of the discs, v, as a function of time is best represented by

A. A

B. B

C. C

D. D

Questions: 9 – 10

Most materials have the refractive index, n > 1. So, when a light ray from the air enters a naturally occurring material, then by Snell’s law, sinθ₁/sinθ₂=n₂/n₁. It is understood that the refracted ray bends towards the normal. But it never emerges on the same side of the normal as the incident ray. According to electromagnetism, the refractive index of the medium is given by the relation, n=(c/v)=±√εᵣμᵣ, where c is the speed of electromagnetic waves in vacuum, v its speed in the medium, εᵣ, and μᵣ, are the relative permittivity and permeability of the medium respectively. In normal materials, both Sr and it, are positive, implying positive n for the medium. When both εᵣ and μᵣ are negative, one must choose the negative root of n. Such negative refractive index materials can now be artificially prepared and are called metamaterials. They exhibit significantly different optical behavior, without violating any physical laws. Since n is negative, it results in a change in the direction of propagation of the refracted light. However, similar to normal materials, the frequency of light remains unchanged upon refraction even in meta-materials.

Q. 9 For light incident from air on a meta-material, the appropriate ray diagram is

A. A

B. B

C. C

D. D

Q. 10 Choose the correct statement

A. (A) The speed of light in the meta-material is v = c|n|

B. (B) The speed of light in the meta-material is v =c/|n|

C. (B) The speed of light in the meta-material is v =c

D. (D) The wavelength of the light in the meta-material λₘ is given by λₘ=λₐᵢᵣ|n|, where

λₐᵢᵣ is the wavelength of the light in air.

Questions: 11 – 12

The β-decay process, discovered around 1900, is basically the decay of a neutron (n). In the laboratory, a proton (p) and an electron ( e⁻) are observed as the decay products of the neutron. Therefore, considering the decay of a neutron as a twobody decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has a continuous spectrum. Considering a three-body decay process, i.e. n —> p + e⁻ +vₑ around 1930, Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino(vₑ) to be massless and possessing negligible energy, and the neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is 0.8×106 eV. The kinetic energy carried by the proton is only the recoil energy.

Q. 11 What is the maximum energy of the anti-neutrino?

A. Zero

B. Much less than 0.8 x 10⁶ eV

C. Nearly 0.8 x 10⁶ eV

D. Much larger than 0.8 x 10⁶ eV

Q. 12 If the anti-neutrino had a mass of 3 eV/c² (where c is the speed of light) instead of zero mass, what should be the range of the kinetic energy, K, of the electron?

A. 0 ≤K≤ 0.8 x 10⁶ eV

B. 3.0 eV ≤ K≤0.8x 10⁶ eV

C. 3.0 eV ≤ K<0.8x 10⁶ eV

D. 0 ≤K< 0.8 x 10⁶ eV

Questions: 13 – 14

The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass. These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed) horizontally at its rim to a massless stick, as shown in the figure. When the disc— stick system is rotated about the origin on a horizontal frictionless plane with angular speed ω, the motion at any instant can be taken as a combination of (i) a rotation of the centre of mass of the disc about the z-axis, and (ii) a rotation of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the changed orientation of points P and Q). Both these motions have the same angular speed ω in this case. Now consider two similar systems as shown in the figure: Case (a) the disc with its face vertical and parallel to x-z plane; Case (b) the disc with its face making an angle of 45° with x-y plane and its horizontal diameter parallel to x-axis. In both the cases, the disc is welded at point P, and the systems are rotated with constant angular speed co about the z-axis.

Q. 13 Which of the following s statements about the instantaneous axis (passing through the centre of mass) is correct?

A. It is vertical for both the cases (a) and (b).

B. It is vertical for case (a); and is at 45° to the x-z plane and lies in the plane of the disc for case (b).

C. It is horizontal for case (a); and is at 45° to the x-z plane and is normal to the plane of the disc for case (b).

D. It is vertical for case (a); and is at 45° to thex-z plane and is normal to the plane of the disc for case (b).

Q. 14 Which of the following statements regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct?

A. It is √2ω for both the cases.

B. It is ω for case (a); and ω/√2 for case (b)

C. It is ω for case (a); and √2ω for case (b)

D. It is ω for both the cases

Q. 15 In the given circuit, the AC source has w = 100 rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)

A. The current through the circuit, I is 0.3 A

B. The current through the circuit, I is 0.3√2A

C. The voltage across 100Ω resistor =10√2V

D. The voltage across 50Ω resistor=10V

Q. 16 A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it. The correct statement(s) is(are)

A. The emf induced in the loop is zero if the current is constant.

B. The emf induced in the loop is finite if the current is constant.

C. The emf induced in the loop is zero if the current decreases at a steady rate

D. The emf induced in the loop is finite if the current decreases at a steady rate.

Q. 17 Six point charges are kept at the vertices of a regular hexagon of side L and centre O, as shown in the figure. Given that K=(1/4Πεo)q/L² which of the following statement(s) is(are) correct ?

A. The electric field at O is 6K along OD.

B. The potential at O is zero

C. The potential at all points on the line PR is same.

D. The potential at all points on the line ST is same.

Q. 18 Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are) correct ?

A. Both cylinders P and Q reach the ground at the same time.

B. Cylinder P has larger linear acceleration than cylinder Q.

C. Both cylinders reach the ground with same translational kinetic energy.

D. Cylinder Q reaches th ground with larger angular speed.

Q. 19 Two spherical planets P and Q have the same uniform density ρ, masses Mₚ and Mᵩ, and surface areas A and 4A, respectively. A spherical planet R also has uniform density ρ and its mass is ( Mₚ+ Mᵩ). The escape velocities from the planets P, Q, and R are Vₚ, Vᵩ, and Vᵣ, respectively. Then

A. Vᵩ > Vᵣ > Vₚ

B. Vᵣ > Vᵩ > Vₚ

C. Vᵣ /Vₚ =3

D. Vₚ / Vᵩ =1/2

Q. 20 The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed ω and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed ω/2. The ring and disc are separated by frictionless ball bearings. The system is in the x-z plane. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of 30° with the horizontal. Then with respect to the horizontal surface,

A. the point O has a linear velocity 3Rωî

B. the point P has a linear velocity 11/4Rωî+√3/4Rωk̂

C. the point P has a linear velocity 13/4Rωî-√3/4Rωk̂

D. the point P has a linear velocity (3-√3/4)Rωî+1/4Rωk̂

Q. 21 NiCl₂{P(C₂H₅)₂(C₆H5₅)}₂ exhibits temperature dependent magnetic behaviour paramagnetic/diamagnetic). The coordination geometries of Ni²⁺ in the paramagnetic and diamagnetic states are respectively

A. tetrahedral and tetrahedral

B. square planar and square planar

C. tetrahedral and square planar

D. square planar and tetrahedral

Q. 22 In the cyanide extraction process of silver from argentite ore, the oxidizing and reducing agents used are

A. O₂ and CO respectively

B. O₂ and Zn dust respectively

C. HNO₃ and Zn dust respectively

D. HNO₃ and CO respectively.

Q. 23 The reaction of white phosphorus with aqueous NaOH gives phosphine along with another phosphorus containing compound. The reaction type; the oxidation states of phosphorus in phosphine and the other product are respectively

A. redox reaction; — 3 and — 5

B. redox reaction; + 3 and + 5

C. disproportionation reaction; — 3 and + 5

D. disproportionation reaction; — 3 and + 3

Q. 24 The shape of XeO₂F₂ molecule is

A. trigonal bipyramidal

B. square planar

C. tetrahedral

D. see-saw

Q. 25 For a dilute solution containing 2.5 g of a non-volatile non-electrolyte solute in 100 g of water, the elevation in boiling point at 1 atm pressure is 2°C. Assuming concentration of solute is much lower than the concentration of solvent, the vapour pressure (mm of Hg) of the solution is (take kᵦ = 0.76 K kg mol⁻¹)

A. 724

B. 740

C. 736

D. 718

Q. 26 The compound that undergoes’decarboxylation most readily under mild condition is

A. A

B. B

C. C

D. D

Q. 27 Using the data provided, calculate the multiple bond energy (kJ mol⁻¹) of a C ≡ C bond in C₂H₂. That energy is (take the bond energy of a C-H bond as 350 kJ mol⁻¹)

2C (s) + H₂(g)——–> C₂H₂(g) ΔH= 225 kJ mol⁻¹

2C (s)——–> 2C (g) ΔH= 1410 kJ mol⁻¹

H₂(g)——–>2H(g) ΔH = 330 kJ mol⁻¹

A. 1165

B. 837

C. 865

D. 815

Q. 28 The major product H of the given reaction sequence is

A. A

B. B

C. C

D. D

Questions: 29 – 30

Bleaching powder and bleach solution are produced on a large scale and used in several house¬hold products. The effectiveness of bleach solution is often measured by iodometry.

Q. 29 Bleaching powder contains a salt of an oxoacid as one of its components. The anhydride of that oxoacid is

A. Cl₂O

B. Cl₂O₇

C. ClO₂

D. Cl₂O₆

Q. 30 25 mL of household bleach solution was mixed with 30 mL of 0.50 M KI and 10 mL of 4 N acetic acid. In the titration of the liberated iodine, 48 mL of 0.25 N Na₂S₂O₃ was used to reach the endpoint. The molarity of the household bleach solution is

A. 0.48M

B. 0.96M

C. 0.25M

D. 0.024M

Questions: 31 – 32

The electrochemical cell shown below is a concentration cell. M ∣ M²⁺ (saturated solution of a sparingly soluble salt, MX₂) ∥ M²⁺ (0.001 mol dm⁻³) ∣ M. The emf of the cell depends on the difference in concentrations of M²⁺ ions at the two electrodes. The emf of the cell at 298 K is 0.059 V.

Q. 31 The solubility product (Kₛₚ; mol³ dm⁻⁹) of MX₂; at 298 K based on the information available for the given concentration cell is (take 2.303 x R x 298/F = 0.059V)

A. 1 x 10¹⁵

B. 4 x 10⁻¹⁵

C. 1 x 10

D. 4 x 10⁻¹²

Q. 32 The value of ΔG (kJ mol⁻¹) for the given cell is (take 1F = 96500 C mot⁻¹)

A. -5.7

B. 5.7

C. 11.4

D. -11.4

Questions: 33 – 34

In the following reaction sequence, the compound J is an intermediate. J (C₉H₈O₂) gives effervescence on treatment with NaHCO₃ and a positive Baeyer’s test.

Q. 33 The compound I is

A. A

B. B

C. C

D. D

Q. 34 The compound K in figure 1 is

A. A

B. B

C. C

D. D

Q. 35 The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?

A. T₁ = T₂

B. T₃ > T₁

C. (w)isothermal > (w)adiabatic

D. (ΔU)isothermal > (ΔU)adiabatic

Q. 36 The given graphs / data I, II, III and IV represent general trends observed for different physisorption and chemisorption processes under mild conditions of temperature and pressure. Which of the following choice(s) about I, II, III and IV is (are) correct?

A. I is physisorption and II is chemisorption

B. I is physisorption and III is chemisorption

C. IV is chemisorption and II is chemisorption

D. IV is chemisorption and III is chemisorption

Q. 37 For the given aqueous reactions, which of the statement(s) is (are) true ?

A. The first reaction is a reoox reaction.

B. White precipitate is Zn₃[Fe(CN)₆]₂

C. Addition of filtrate to starch solution gives blue cofoui

D. White precipitate is soluble in NaOH solution.

Q. 38 With respect to graphite and diamond, which of the statement(s) given below is (are) correct ?

A. Graphite is harder than diamond.

B. Graphite has higher electrical conductivity than diamond.

C. Graphite has higher thermal conductivity than diamond.

D. Graphite has higher C-C bond order than diamond.

Q. 39 With reference to the scheme given, which of the given statment(s) , bout T, U, V and W is (are) correct ?

A. T is soluble in hot aqueous NaOH

B. U is optically active

C. Molecular formula of W is C₁₀H₁₈O₄

D. V gives effervescence on treatment with aqueous NaHCO₃

Q. 40 Which of the given statement(s) about N, O, P and Q with respect to M is (are) correct ?

A. M and N are non-mirror image stereoisomers

B. M and O are identical

C. M and P are enantiomers

D. M and Q are identical

Q. 41 The equation of a plane passing through the line of intersection of the planes x + 2y + 3z = 2 and x y + z = 3 and at a distance 2/√3 from the point (3, 1,-1) is

A. 5x— 11y + z = 17

B. √2x+y=3√2-1

C. x+y+z=√3

D. x-√2y=1-√2

Q. 42 Let PQR be a triangle of area Δ with a= 2, b =7/2 and c = 5/2 , where a, b and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R respectively. Then (2 sin P – sin 2P)/(2 sin P+sin 2P) equals

A. 3/4Δ

B. 45/4Δ

C. (3/4Δ)²

D. (45/4Δ)²

Q. 43 If a̅ and b̅ are vectors such that |a̅ + b̅| =√29 and âx(2î + 3ĵ + 4k̂)=(2î+3ĵ+4k̂) x b̅, then a possible value of (a̅ + b̅).(-7î + 2ĵ + 3k̂) is

A. 0

B. 3

C. 4

D. 8

Q. 44 If P is a 3 x 3 matrix such that Pᵀ =2P + I, where Pᵀ is the transpose of P and I is the 3 x 3 identity matrix, then there exists a column matrix

A. A

B. B

C. C

D. D

Q. 45 Choose the correct option:

A. -5/2 and 1

B. -1/2 and -1

C. -7/2 and 2

D. -9/2 and 3

Q. 46 Four fair dice D₁, D₂, D₃ and D₄, each having six faces numbered 1, 2, 3, 4, 5 and 6, are rolled simultaneously. The probability that D4 shows a number appearing on one of D₁, D₂ and D₃ is

A. 91/216

B. 108/216

C. 125/216

D. 127/216

Q. 47 The value of the integral is :

A. 0

B. Π²/2-4

C. Π²/2+4

D. Π²/2

Q. 48 Let a₁, a₂, a₃, … be in harmonic progression with a₁= 5 and a₂₀= 25. The least positive integer n for which aₙ < 0 is

A. 22

B. 23

C. 24

D. 25

Questions: 49 – 50

Let aₙ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let bₙ= the number of such n-digit integers ending with digit 1 and cₙ=the number of such n-digit integers ending with digit 0.

Q. 49 The value of b₆ is

A. 7

B. 8

C. 9

D. 11

Q. 50 Which of the following is correct?

A. a₁₇ =a₁₆ + a₁₅

B. c₁₇ = c₁₆ + c₁₅

C. b₁₇ = b₁₆ + c₁₆

D. a₁₇ =c₁₇ +b₁₆

Q. 51 Choose the correct option based on the figure .

Which of the following is true?

A. g is increasing on (1, ∞)

B. g is decreasing on (1, ∞)

C. g is increasing on (1, 2) and decreasing on (2,∞)

D. g is decreasing on (1, 2) and increasing on (2, ∞)

Q. 52 Choose the correct option based on the figure .

Consider the statements :

P : There exists some X E IR such that f(x)+2x= 2(1 +x²)

Q : There exists some x E IR such that 2f(x)+ 1= 2x(1 + x)

Then

A. both P and Q are true

B. P is true and Q is false

C. P is false and Q is true

D. both P and Q are false

Questions: 53 – 54

A tangent PT is drawn to the circle x² + y² = 4 at the point P (√3,1). A straight line L, perpendicular to PT is a tangent to the circle (x-3)² + y² = 1.

Q. 53 A possible equation of L is

A. x-√3y=1

B. x+√3y=1

C. x-√3y=-1

D. x+√3y=5

Q. 54 A common tangent of the two circles is

A. x=4

B. y=2

C. x+√3y=4

D. x+2√2y=6

Q. 55 For every integer n, let aₙ and bₙ be real numbers. Let function f: IR —> IR be given by f(x) = aₙ+sinπx, for x∈[2n,2n+1] = bₙ+cosπx, for x∈[2n-1,2n], for all integers of n. If f is continuous, then which of the following hold(s) for all n?

A. aₙ₋₁ – bₙ₋₁ =0

B. aₙ -bₙ =1

C. aₙ – bₙ₊₁=1

D. aₙ₋₁ – bₙ=-1

Q. 56 choose the correct one:

A. f has a local maximum at x = 2

B. f is decreasing on (2, 3)

C. there exists some c∈(0,α) such that f″(c)=0

D. f has a local minimum at x=3

Q. 57 If the straight lines x-1/2=y+1/k=z/2 and x+1/5=y+1/2=z/k are coplanar, then the plane(s) containing these two lines is(are)

A. y+2z=-1

B. y+z=-1

C. y-z=-1

D. y-2z=-1

Q. 58 X and Y be two events such that P(X∣Y)=1/2, P(Y∣X)=1/3 and P(X∩Y)=1/6.Which of the following is (are) correct?

A. P(X∪Y)=2/3

B. X and Y are independent

C. X and Y are not independent

D. P(xᶜ∩Y)=1/3

Q. 59 Choose the correct option:

A. -2

B. -1

C. 1

D. 2

Q. 60 Choose the correct option:

A. 1-√(3/2)

B. 1+√(3/2)

C. 1-√(2/3)

D. 1+√(2/3)

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

JEE Advanced 2012 Paper I Previous Year Paper

JEE Advanced 2012 Paper 1

Q. 1 A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed ω, as shown in the figure. At time t = 0, a small insect starts from O and moves with constant speed v with respect to the rod towards the other end. It reaches the end of the rod at t = T and stops. The angular speed of the system remains ω throughout. The magnitude of the torque (|τ̅|) on the system about O, as a function of time is best represented by which plot

A. A

B. B

C. C

D. D

Q. 2 Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures 2T and 3T respectively. The temperature of the middle (i.e. second) plate under steady state condition is

A. A

B. B

C. C

D. D

Q. 3 Consider a thin spherical shell of radius R with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field |E̅(r)| and the electric potential V(r) with the distance r from the centre, is best represented by which graph

A. A

B. B

C. C

D. D

Q. 4 In the determination of Young’s modulus Y = {4Mlg/(πld²)} by using Searle’s method, a wire of length L = 2 m and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length of the wire is observed. Quantities d and l are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable error of the Y measurement

A. due to the errors in the measurements of d and l are the same.

B. due to the error in the measurement of d is twice that due to the error in the

measurement of l.

C. due to the error in the measurement of l is twice that due to the error in the

measurement of d.

D. due to the error in the measurement old is four times that due to the error in the

measurement of l.

Q. 5 A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at t = 0. It then executes simple harmonic motion with angular frequency ω = π/3 rad/s. Simultaneously at t = 0, a small pebble is projected with speed v from point P at an angle of 45° as shown in the figure. Point P is at a horizontal distance of 10 m from O. If the pebble hits the block at t = 1 s, the value of v is (take g = 10 m/s²)

A. √50 m/s

B. √51 m/s

C. √52 m/s

D. √53 m/s

Q. 6 Young’s double slit experiment is carried out by using green, red and blue light, one color at a time. The fringe widths recorded are βG, βR and βB respectively. Then,

A. βG > βB > βR

B. βB > βG > βR

C. βR > βB > βG

D. βR > βG > βB

Q. 7 A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed ω. If the angular momentum of the system, calculated about O and P are denoted by L̅o and L̅p respectively, then

A. L̅o and L̅p do not vary with time

B. L̅o varies with time while L̅p remains constant

C. L̅o remains constant while L̅p varies with time

D. L̅o and L̅p both vary with time

Q. 8 A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds

A. 0.32

B. 0.45

C. 2.24

D. 3.16

Q. 9 Two large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage source of potential difference X. A proton is released at rest midway between the two plates. It is found to move at 45°to the vertical JUST after release. Then X is nearly

A. 1 x 10⁻⁵ V

B. 1 x 10⁻⁷ V

C. 1 x 10⁻⁹ V

D. 1 x 10⁻¹⁰ V

Q. 10 A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surfaces are of the same radius of curvature R = 14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be

A. – 280.0 cm

B. 40.0 cm

C. 21.5 cm

D. 13.3 cm

Q. 11 A cubical region of side a has its centre at the origin. lt encloses three fixed point charges, – q at (0, -a/4, 0), +3q at (0,0,0) and -q at (0 ,+a/4, 0). Choose the correct option(s).

A. The net electric flux crossing the plane x = +a/ 2 is equal to the net electric flux

crossing the plane x = – a/2.

B. The net electric flux crossing the plane y = +a/ 2 is more than the net electric flux

crossing the plane y = – a/2.

C. The net electric flux crossing the entire region is q/ε0

D. The net electric flux crossing the plane z = +a/ 2 is equal to the net electric flux

crossing the plane x = +a/ 2.

Q. 12 For the resistance network shown in the figure, choose the correct option(s).

A. The current through PQ is zero

B. I₁ = 3A

C. The potential at S is less than that at Q

D. I₂ = 2A

Q. 13 A small block of mass of 0.1 kg lies on a fixed inclined plane PQ which makes an angle θ with the horizontal. A horizontal force of 1 N acts on the block through its center of mass as shown in the figure. The block remains stationary if (take g = 10 m/s²)

A. θ = 45°

B. θ > 45° and a frictional force acts on the block towards P

C. θ > 45° and a frictional force acts on the block towards Q.

D. θ < 45° and a frictional force acts on the block towards Q.

Q. 14 Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields E̅ = Eo ĵ and B̅ = Bo ĵ. At time t: 0, this charge has velocity v̅ if in the x-y plane, making an angle θ with the x-axis. Which of the following option(s) is(are) correct for time t > 0?

A. If θ = 0°, the charge moves in a circular path in the x-z plane.

B. If θ = 0°, the charge undergoes helical motion with constant pitch along the y-axis

C. If θ = 10°, the charge undergoes helical motion with its pitch increasing with time,

along the y-axis.

D. If θ = 90°, the charge undergoes linear but accelerated motion along the y-axis.

Q. 15 A person blows into open-end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,

A. a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is open.

B. a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is open.

C. a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed.

D. a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed.

Q. 16 An infinitely long solid cylinder of radius R has a uniform volume charge density ρ. It has a spherical cavity of radius R/2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point P, which is at a distance 2R from the axis of the cylinder is given by the expression 23ρR/16kεo ? The value of k is

Q. 17 A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of the magnetic field at the point P is given by (N/12)μo aJ , then the value of N is

Q. 18 A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R, as shown in the figure. The moment of inertia of this lamina about axes passing through O and P is Io and Ip , respectively. Both these axes are perpendicular to the plane of the lamina. The ratio Ip/Io to the nearest integer is

Q. 19 A circular wire loop of radius R is placed in the x-y plane centered at the origin O. A square loop of side a (a << R) having two turns is placed with its center at z = √3 R along the axis of the circular wire loop, as shown in figure. The plane of the square loop makes an angle of 45° with respect to the z-axis. If the mutual inductance between the loops is given by value shown in the figure , then the value of p is

Q. 20 A proton is fired from very far away towards a nucleus with charge Q = 120 e, where e is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of the proton at its start is: (take the proton mass, mp = (5/3) x 10⁻²⁷ kg; h/e = 4.2 x 10⁻¹⁵ J.s/C; 1/(4πεo)= 9 x10⁹ m/F; fm=10⁻¹⁵ m)

A. 7 fm

B. 8 fm

C. 9 fm

D. 10 fm

Q. 21 In allene (C₃H₄), the type(s) of hybridisation of the carbon atoms is (are)

A. sp and sp³

B. sp and sp²

C. only sp²

D. sp² and sp³

Q. 22 For one mole of a van der Waals gas when b = 0 and T: 300 K, the PV vs 1/V plot is shown below. The value of the van der Waals constant a (atm.liter² mol-²) is

A. 1.0

B. 4.5

C. 1.5

D. 3.0

Q. 23 The number of optically active products obtained from the complete ozonolysis of the given compound is

A. 0

B. 1

C. 2

D. 4

Q. 24 A compound MpXq has cubic close packing (ccp) arrangement of X. Its unit cell structure is shown below. The empirical formula of the compound is

A. MX

B. MX₂

C. M₂X

D. M₅X₁₄

Q. 25 The number of aldol reaction(s) that occurs in the given transformation is

A. 1

B. 2

C. 3

D. 4

Q. 26 The colour of light absorbed by an aqueous solution of CuSO₄ is

A. orange-red

B. blue-green

C. yellow

D. violet

Q. 27 The carboxyl functional group (-COOH) is present in

A. picric acid

B. barbituric acid

C. ascorbic acid

D. aspirin

Q. 28 The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [ao is Bohr radius]

A. A

B. B

C. C

D. D

Q. 29 Which ordering of compounds is according to the decreasing order of the oxidation state of nitrogen?

A. A

B. B

C. C

D. D

Q. 30 As per IUPAC nomenclature, the name of the complex [Co(H₂0)₄(NH₃)₂]CI₃ is

A. Tetraaquadiaminecobalt (III) chloride

B. Tetraaquadiamminecobalt (III) chloride

C. Diaminetetraaquacobalt (III) chloride

D. Diamminetetraaquacobalt (III) chloride

Q. 31 Identify the binary mixture(s) that can be separated into individual compounds, by differential extraction, as shown in the given scheme.

A. A

B. B

C. C

D. D

Q. 32 Choose the correct reason(s) for the stability of the lyophobic colloidal particles

A. Preferential adsorption of ions on their surface from the solution

B. Preferential adsorption of solvent on their surface from the solution

C. Attraction between different particles having opposite charges on their surface

D. Potential difference between the fixed layer and the diffused layer of opposite charges around the colloidal particles

Q. 33 Which of the following molecules, in pure form, is (are) unstable at room temperature ?

A. A

B. B

C. C

D. D

Q. 34 Which of the following hydrogen halides react(s) with AgNo₃(aq) to give a precipitate that dissolves in Na₂S₂O₃(aq)

A. HCl

B. HF

C. HBr

D. HI

Q. 35 For an ideal gas, consider only P-V work in going from an initial state X to the final state Z. The final state Z can be reached by either of the two paths shown in the figure. Which of the following choice(s) is (are) correct ? [take ΔS as change in entropy and w as work done].

A. A

B. B

C. C

D. D

Q. 36 The substituents R₁ and R₂ for nine peptides are listed in the table given below. How many of these peptides are positively charged at pH = 7.0 ?

Q. 37 The periodic table consists of 18 groups. An isotope of copper, on bombardment with protons, undergoes a nuclear reaction yielding element X as shown below. To which group, element X belongs in the periodic table

Q. 38 When the following aldohexose exists in its D-configuration, the total number of

stereoisomers in its pyranose form is

Q. 39 29.2% (w/w) HCI stock solution has a density of 1.25 g m/L . The molecular weight of HCI is 36.5 g/mol. The volume (mL) of stock solution required to prepare a 200 mL solution of 0.4 M HCI is

Q. 40 An organic compound undergoes first-order decomposition. The time taken for its decomposition to 1/8 and 1/10 of its initial concentration are t(1/8) and t(1/10) respectively. What is the value of [t(1/8)/t(1/10)] x 10 ? (take log 2 = 0.3)

Q. 41 The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least One ball is

A. 75

B. 150

C. 210

D. 243

Q. 42 Find the value of f.

A. differentiable both at x = 0 and at x = 2

B. differentiable at x = 0 but not differentiable at x = 2

C. not differentiable at x = 0 but differentiable at x = 2

D. differentiable neither at x = 0 nor at x = 2

Q. 43 The function f : [0, 3] → [1, 29], defined by f(x) = 2x³ – 15x² + 36x + 1, is

A. one-one and onto

B. onto but not one-one

C. one-one but not onto

D. neither one-one nor onto

Q. 44 Choose the correct option:

A. a = 1, b = 4

B. a = 1, b = -4

C. a = 2, b = -3

D. a = 2, b = 3

Q. 45 Let z be a complex number such that the imaginary part of z is nonzero and a = z² + z + 1 is real. Then a cannot take the value

A. -1

B. 1/3

C. 1/2

D. 3/4

Q. 46 The ellipse E₁ : x²/9 + y²/4 = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E₂ passing through the point (0, 4) circumscribes the rectangle R. The eccentricity of the ellipse E₂ is

A. √2/2

B. √3/2

C. 1/2

D. 3/4

Q. 47 Let P = [aij] be a 3×3 matrix and let Q = [bij], where bij = 2(i+j) x aij for 1 ≤ i, j ≤ 3. If the determinant of P is 2, then the determinant of the matrix Q is

A. 2¹⁰

B. 2¹¹

C. 2¹²

D. 2¹³

Q. 48 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 49 The point P is the intersection of the straight line joining the points Q(2,3,5) and R(1, – 1, 4) with the plane 5x – 4y – z = 1. If S is the foot of the perpendicular drawn from the point T(2, 1,4) to QR, then the length of the line segment PS is

A. 1/√2

B. √2

C. 2

D. 2√2

Q. 50 The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x – 5y = 20 to the circle x² + y² = 9 is

A. 20(x² + y²) – 36x + 45y = 0

B. 20(x² + y²) + 36x – 45y = 0

C. 36(x² + y²) – 20x + 45y = 0

D. 36(x² + y²) + 20x – 45y = 0

Q. 51 Choose the correct option:

A. 0 < φ < π/2

B. π/2 < φ < 4π/3

C. 4π/3 < φ < 3π/2

D. 3π/2< φ < 2π

Q. 52 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 53 A ship is fitted with three engines E₁, E₂ and E₃. The engines function independently of each other with respective probabilities 1/2, 1/4 and 1/4. For the ship to be operational at least two of its engines must function. Let X denote the event that the ship is operational and let X₁, X₂ and X₃ denote respectively the events that the engines E₁, E₂ and E₃ are functioning. Which of the following is (are) true?

A. A

B. B

C. C

D. D

Q. 54 Tangents are drawn to the hyperbola x²/9 – y²/4 = 1 , parallel to the straight line 2x – y = 1. The points of contact of the tangents on the hyperbola are

A. (9/2√2 , 1/√2)

B. (-9/2√2 , -1/√2)

C. (3√3 , -2√2)

D. (-3√3 , 2√2)

Q. 55 If y (x) satisfies the differential equation y’ – y tan x = 2x sec x and y (0) = 0, then

A. A

B. B

C. C

D. D

Q. 56 Let f: IR → IR be defined as f (x) = |x| + |x² -1| The total number of points at which f attains either a local maximum or a local minimum is

Q. 57 The value of the expression given in the figure is:

Q. 58 Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3. lf p(1)= 6 and p(3) = 2, then p'(0) is

Q. 59 If a̅, b̅ and c̅ are unit vectors satisfying |a̅ – b̅|² + |b̅ – c̅|² + |c̅ – a̅|² = 9, then | 2a̅ + 5b̅ + 5c̅| is

Q. 60 Let S be the focus of the parabola y² = 8x and let PQ be the common chord of the circle x² +y² – 2x – 4y = 0 and the given parabola. The area of the triangle PQS is

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

JEE Advanced 2011 Paper II Previous Year Paper

JEE Advanced 2011 Paper 2

Q. 1 Oxidation states of the metal in the minerals haematite and magnetite, respectively, are

A. II, III in haematite and III in magnetite

B. II, III in haematite and II in magnetite

C. II in haematite and II, III in magnetite

D. III in haematite and II, III in magnetite

Q. 2 Among the following complexes (K-P), K₃[Fe(CN)₆] (K), [Co(NH₃)₆]Cl₃ (L), Na₃[Co(oxalate)₃] (M), [Ni(H₂O)₆]Cl₂ (N), K₂[Pt(CN)₄] (O) and [Zn(H₂O)₆](NO₃)₂ (P) the diamagnetic complexes are

A. K, L, M, N

B. K, M, O, P

C. L, M, O, P

D. L, M, N, O

Q. 3 Passing H₂S gas into a mixture of Mn²⁺, Ni²⁺, Cu²⁺ and Hg²⁺ ions in an acidified aqueous solution precipitates

A. CuS and HgS

B. MnS and CuS

C. MnS and NiS

D. NiS and HgS

Q. 4 Consider the following cell reaction:

2Feᵣ + O2ᵤ +4H⁺ᵥₓ → 2Fe²ᵥₓ + 2H₂O(l) E° = 1.67 V

At [Fe²⁺] = 10⁻³ M, P(O₂) = 0.1 atm and pH = 3, the cell potential at 25°C is

A. 1.47 V

B. 1.77 V

C. 1.87 V

D. 1.57 V

Q. 5 The freezing point (in °C) of a solution containing 0.1g of K₃[Fe(CN)₆] (Mol. Wt. 329) in 100g of water (Kᵣ = 1.86 K kg mol⁻¹) is

A. -2.3 x 10⁻²

B. -5.7 x 10⁻²

C. -5.7 x 10⁻²

D. -1.2 x 10⁻²

Q. 6 Amongst the compounds given in figure (A), (B), (C), (D), the one that would form a brilliant colored dye on treatment with NaNO₂ in dil. HCl followed by addition to an alkaline solution of β-naphthol is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 7 The major product of the reaction shown in figure is

A. a hemiacetal

B. an acetal

C. an ether

D. an ester

Q. 8 The carbohydrate shown in figure is:

A. a ketohexose

B. an aldohexose

C. an α – furanose

D. an α – pyranose

Q. 9 Reduction of the metal centre in aqueous permanganate ion involves

A. 3 electrons in neutral medium

B. 5 electrons in neutral medium

C. 3 electrons in alkaline medium

D. 5 electrons in acidic medium

Q. 10 The equilibrium 2Cuᶦ⇔ Cuᵒ + Cuᶦᶦ in aqueous medium at 25 °C shifts towards the left in the presence of

A. NO₃⁻

B. Cl⁻

C. SCN⁻

D. CN⁻

Q. 11 For the first order reaction:

2 N₂O₅(g) → 4NO₂(g) + O₂(g)

A. the concentration of the reactant decreases exponentially with time.

B. the half-life of the reaction decreases with increasing temperature.

C. the half-life of the reaction depends on the initial concentration of the reactant.

D. the reactant proceeds to 99.6% completion in eight half-life duration.

Q. 12 The correct functional group X and the reagent / reaction conditions Y in the following scheme given in figure (1) are

A. X = COOCH₃, Y = H₂ / Ni /heat

B. X = CONH₂, Y = H₂ / Ni / heat

C. X = CONH₂, Y = Br₂ / NaOH

D. X = CN, Y = H₂ / Ni / heat

Q. 13 Among the following, the number of compounds that can react with PCl₅ to give POCl₃ is O₂, CO₂, SO₂, H₂O, H₂SO₄, P₄O₁₀.

Q. 14 The volume (in mL) of 0.1 M AgNO₃ required for complete precipitation of chloride ions present in 30 mL of 0.01 M solution of [Cr(H₂O)₅Cl]Cl₂, as silver chloride is close to

Q. 15 In 1 L saturated solution of AgCl [Ksp (AgCl) = 1.6 x 10⁻¹⁰], 0.1 mol of CuCl [Ksp (CuCl) = 1.0 x 10⁻⁶] is added. The resultant concentration of Ag⁺ in the solution is 1.6 x 10⁻ⁿ. The value of “n” is:

Q. 16 The number of hexagonal faces that are present in a truncated octahedron is

Q. 17 The maximum number of isomers (including stereoisomers) that are possible on

monochlorination of the compound shown in figure (1), is

Q. 18 The total number of contributing structures showing hyperconjugation (involving C-H bonds) for the carbocation given in figure (1) is

Q. 19 Match the transformations in Column I with appropriate options in Column II given in figure (1):

Column I	Column II
(A)	CO2(s) CO2(g)	(p)	Phase transition
(B)	CaCO3(s) CaO(s) +CO2(g)	(r)	H is positive
(C)	2 H. H2 (g)	(s)	S is positive
(D)	P(white, solid) P(red, soild)	(t)	S is negative

A. A – p,s ; B – p,q ; C – q ; D – p,t

B. A – p,r,s ; B – r,s ; C – t ; D – p,q,t

C. A – p,r ; B – r ; C – p ; D – p,q

D. A – r,s ; B – p,q ; C – t ; D – q,t

Q. 20 Match the reactions in column I with appropriate types of steps/reactive intermediate involved in these reactions as given in column II given in figure (1):

A. A – r,s,t ; B – p,s ; C – r,s ; D -q,r

B. A – s,t ; B – p,s ; C – p,t ; D – q,r

C. A – p,t ; B – r,s ; C – p,s ; D – q,r

D. A – r,s ; B – p,q ; C – r,s ; D – p,r

Q. 21 A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence θ. The reflected (R) and transmitted (T) intensities, both as function of θ, are plotted which is given in (1). The correct sketch among (A), (B), (C), (D) is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 22 A satellite is moving with a constant speed ‘V’ in a circular orbit about the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is:

A. 1/2mV²

B. mV²

C. 3/2mV²

D. 2mV²

Q. 23 A long insulated copper wire is closely wound as a spiral of ‘N’ turns. (Given in figure (1)). The spiral has inner radius ‘a’ and outer radius ‘b’. The spiral lies in the X-Y plane and a steady current ‘I’ flows through the wire. The Z – component of the magnetic field at the center of the spiral is

A. μ0N I /2(b – a) ln (b/a)

B. μ0N I /2(b – a) ln (b+a/b-a)

C. μ0N I /2b ln (b/a)

D. μ0N I /2b ln (b+a/b-a)

Q. 24 A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x1(t) A sinωt and x2(t) = A sin(ωt + 2π/3). Adding a third sinusoidal displacement x3(t) = B sin(ωt + ø) brings the mass to a complete rest. The values of B and ø are

A. √2A, 3π/4

B. A, 4π/3

C. √3A, 5π/6

D. A, π/3

Q. 25 Which of the field patterns (A), (B), (C), (D) is valid for electric field as well as for magnetic field?

A. (A)

B. (B)

C. (C)

D. (D)

Q. 26 A ball of mass 0.2kg rests on a vertical post of height 5m(Given in figure (1)). A bullet of mass 0.1 kg, traveling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity V of the bullet is

A. 250 m/s

B. 250√2 m/s

C. 400 m/s

D. 500 m/s

Q. 27 The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is

A. 0.9%

B. 2.4%

C. 3.1%

D. 4.2%

Q. 28 A wooden block shown in figure (1) performs SHM on a frictionless surface with frequency, v₀. The block carries a charge +Q on its surface. If now a uniform electric field is switched on as shown in figure (1), then the SHM of the block will be

A. of the same frequency and with shifted mean position.

B. of the same frequency and with the same mean position.

C. of changed frequency and with shifted mean position.

D. of changed frequency and with the same mean position.

Q. 29 Two solid spheres A and B of equal volumes shown in figure but of different densities dA and dB are connected by a string. They are fully immersed in a fluid of density of density dF. They get arranged into an equilibrium state as shown in the figure (1) with a tension in the string. The arrangement is possible only if

A. dA < dF

B. dB > dF

C. dA > dF

D. dA + dB = 2 dF

Q. 30 A series R-C circuit is connected to AC voltage source. Consider two cases; (A) and C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current IR through the resistor and voltage VC across the capacitor are compared in the two cases. Which of the following is/are true?

A. (A)

B. (B)

C. (C)

D. (D)

Q. 31 Which of the following statement(s) is/are correct?

A. If the electric field due to a point charge varies as r⁻²⁵ instead of r⁻², then the Gauss

law will still be valid.

B. The Gauss law can be used to calculate the field distribution around an electric dipole.

C. If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same.

D. The work done by the external force in moving a unit positive charge from a point A at potential VA to point B at potential VB is (VB – VA).

Q. 32 A thin ring of mass 2 kg and radius 0.5 m shown in figure (1) is rolling without slipping on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20m/s in the opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision

A. the ring has pure rotation about its stationary CM.

B. the ring comes to a complete stop.

C. friction between the ring and the ground is to the left.

D. there is no friction between the ring and the ground

Q. 33 A train is moving along a straight line with a constant acceleration ‘a’. A boy standing in the train throws a ball forward with a speed of 10 m/s, at an angle of 60° to the horizontal. The boy has to move forward by 1.15m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s², is

Q. 34 A block of mass 0.18 kg shown in figure is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is rest and the spring is unstretched. An impulse is given to the block as shown in figure (1). The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block in m/s is V = N/10. Then N is

Q. 35 Two batteries of different emfs and different internal resistances are connected as shown in figure (1). The voltage across AB in volts is

Q. 36 Water (with refractive index = 4/3) in a tank shown in figure is 18cm deep. Oil of refractive index 7/4 lies on water making a convex surface of radius of curvature ‘R = 6cm’ as shown. Consider oil to act as a thin lens. An object ‘S’ is placed 24cm above water surface. The location of its image is at ‘x’ cm above the bottom of the tank. Then ‘x’ is

Q. 37 A series R-C combination is connected to an AC voltage of angular frequency ω = 500 radian/s. If the impedance of the R-C circuit is R√1.25, the time constant (in millisecond) of the circuit is

Q. 38 A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is A x 10ⁿ (where 1 < A < 10). The value of ‘n’ is

Q. 39 One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the P-V diagram given in figure (1). Column II gives the characteristics involved in the cycle. Match them with each of the processes given in Column I. (Given in figure (2)).

A. A – p, r ,t ; B – p,r ; C – q,s ; D – r,t

B. A – p,q,r ; B – p,t ; C – q,t ; D – q,t

C. A – p ; B – r,t ; C – p,t ; D – p,q

D. A – q,r ; B – p,s ; C – p,s ; D – p,t

Q. 40 Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as λ₁. Match each system with statements given in Column II describing the nature and wavelength of the standing waves. (Given in figure (1)).

A. A – p,t ; B – p,s ; C – q,s ; D – q,r

B. A – p,r ; B – s,t ; C – q,r ; D – p,s

C. A – q,r ; B – p,t ; C – p,q ; D – s,t

D. A – p,t ; B – p,q ; C – q,s ; D – q,r

Q. 41 Let P(6, 3) be a point on the hyperbola x² / a³ – y² / b² = 1. If the normal at the point P intersects the x-axis at (9, 0), then the eccentricity of the hyperbola is

A. √5/2

B. √3/2

C. √2

D. √3

Q. 42 A value of b for which the equations

x² + bx – 1 = 0

x² + x + b = 0

have one root in common is

A. -√2

B. -i√3

C. i√5

D. √2

Q. 43 Let ω ≠ 1 be a cube root of unity and S be the set of all non-singular matrices of the form given in figure where each of a, b, and c is either ω or ω². Then the number of distinct matrices in the set S is

A. 2

B. 6

C. 4

D. 8

Q. 44 The circle passing through the point (-1, 0) and touching the y-axis at (0, 2) also passes through the point

A. (-3/2, 0)

B. (-5/2, 2)

C. (-3/2, 5/2)

D. (-4, 0)

Q. 45 Find the value of θ in the equation given in figure .

A. ±π/4

B. ±π/3

C. ±π/6

D. ±π/2

Q. 46 Let f : [-1, 2] → [0, ∞) be a continuous function such that f(x) = f(1-x) for all x ∈ [-1, 2]. The value of R₁ is given in the figure (1) and R² be the area of the region bounded by y = f(x), x = -1, x = 2, and the x-axis. Then

A. R₁ = 2R₂

B. R₁ = 3R₂

C. 2R₁ = R₂

D. 3R₁ = R₂

Q. 47 Let f(x) = x² and g(x) = sinx for all x ∈ R. Then the set of all x satisfying (f ∘ g ∘ g ∘ f)(x) = (g ∘ g ∘ f)(x), where (f ∘ g)(x) = f(g(x)), is

A. ±√nπ, n ∈ {0, 1, 2, ……….}

B. ±√nπ, n ∈ {1, 2, …………}

C. π/2 + 2nπ, n ∈ {…………….., -2, -1, 0, 1, 2, ………}

D. 2nπ, n ∈ {…………….., -2, -1, 0, 1, 2, ………}

Q. 48 Let (x, y) be any point on the parabola y² = 4x. Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio 1: 3. Then the locus of P is

A. x² = y

B. y² = 2x

C. y² = x

D. x² = 2y

Q. 49 If the value of f(x), given in the figure (1), then

A. f(x) is continuous at x = -π/2

B. f(x) is not differentiable at x = 0

C. f(x) is differentiable at x = 1

D. f(x) is differentiable at x = -3/2

Q. 50 Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the probability of none of them occurring is 2/25. If P(T) denotes the probability of occurrence of the event T, then

A. P(E) = 4/5, P(F) = 3/5

B. P(E) = 1/5, P(F) = 2/5

C. P(E) = 2/5, P(F) = 1/5

D. P(E) = 3/5, P(F) = 4/5

Q. 51 Let L be a normal to the parabola y² = 4x. If L passes through the point (9, 6), then L is given by

A. y – x + 3 = 0

B. y + 3x – 33 = 0

C. y + x – 15 = 0

D. y – 2x + 12 = 0

Q. 52 Let f : (0, 1) → R be defined by f(x) = b – x / 1 – bx, where b is a constant such that 0 < b < 1. Then

A. f is not invertible on (0, 1)

B. f ≠ f⁻¹ on (0, 1) and f'(b) = 1/f'(0)

C. f = f⁻¹ on (0, 1) and f'(b) = 1 / f'(0)

D. f⁻¹ is differentiable on (0, 1)

Q. 53 Let ω = e^iπ/3, and a, b, c, x, y, z be non-zero complex number such that

a + b + c = x

a + bω + cω² = y

a + bω² + cω = z

Then the value of |x|² + |y|² + |z|² / |a|² + |b|² + |c|² is

Q. 54 The number of distinct real roots of x⁴ – 4x³ + 12x³ + x – 1 = 0 is

Q. 55 Let y'(x) + y(x)g'(x) = g(x)g'(x), y(0) = 0, x ∈ R, where f'(x) denotes df(x) / dx and g(x) is a given non-constant differentiable function on R with g(0) = g(2) = 0. Then the value of y(2) is

Q. 56 Let M be a 3 x 3 matrix satisfying the information given in figure , then the sum of the diagonal entries of M is

Q. 57 Let a = -î – k̂, b = -î + ĵ and c = î + 2ĵ + 3k̂ be three given vectors. If r is a vector such that r x b = c x b and r . a = 0, then the value of r . b is

Q. 58 The straight line 2x – 3y = 1 divides the circular region x² + y² ≤ 6 into two parts. If S = {(2, 3/4), (5/2, 3/4), (1/4, 1/4), (1/8, 1/4)}, then the number of point(s) in S lying inside the smaller part is

Q. 59 Match the statements given in Column I with the values given in Column II. (Given in figure).

A. A – p ; B – p,q ; C – s ; D – q,r

B. A – q ; B – q,s ; C – p ; D – r,t

C. A -q ;B – p,q,r,s,t ; C -s ; D – t

D. A – p ; B – p,s ; C – q ; D – p,t

Q. 60 Match the statement given in column I with the intervals/union of intervals given in Column II (given in figure (1)).

A. A -p ; B – q ; C – r ; D – s

B. A – p,q ; B – r,s ; C – r ; D – s

C. A – s ; B – t ; C – p , D – r

D. A – s ; b – t ; C – r ; D – r

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

JEE Advanced 2011 Paper I Previous Year Paper

JEE Advanced 2011 Paper 1

Q. 1 Extra pure N₂ can be obtained by heating

A. A

B. B

C. C

D. D

Q. 2 Geometrical shapes of the complexes formed by the reaction of Ni₂+ with Cl- , CN- and H₂0, respectively, are

A. octahedral, tetrahedral and square planar

B. tetrahedral, square planar and octahedral

C. square planar, tetrahedral and octahedral

D. octahedral, square planar and octahedral

Q. 3 Bombardment of aluminum by α-particle leads to its artificial disintegration in two ways, (i) and (ii) as shown. Products X, Y and 2 respectively are

A. proton, neutron, positron

B. neutron, positron, proton

C. proton, positron, neutron

D. positron, proton, neutron

Q. 4 Dissolving 120 g of urea (mol. wt. 60) in 1000 g of water gave a solution of density 1.15 g/mL. The molarity of the solution is

A. 1.78 M

B. 2.00 M

C. 2.05 M

D. 2.22 M

Q. 5 AgNO₃ (aq.) was added to an aqueous KCl solution gradually and the conductivity of the solution was measured. The plot of conductance (A) versus the volume of AgNO₃ is

A. (P)

B. (Q)

C. (R)

D. (S)

Q. 6 Among the following compounds, the most acidic is

A. p-nitrophenol

B. p-hydroxybenzoic acid

C. o-hydroxybenzoic acid

D. p-toluic acid

Q. 7 The major product of the following reaction is

A. A

B. B

C. C

D. D

Q. 8 Extraction of metal from the ore cassiterite involves

A. carbon reduction of an oxide ore

B. self-reduction of a sulphide ore

C. removal of copper impurity

D. removal of iron impurity

Q. 9 The correct statement(s) pertaining to the adsorption of a gas on a solid surface is (are)

A. Adsorption is always exothermic.

B. Physisorption may transform into chemisorption at high temperature.

C. Physisorption increases with increasing temperature but chemisorption decreases

with increasing temperature.

D. Chemisorption is more exothermic than physisorption, however it is very slow due to higher energy of activation.

Q. 10 According to kinetic theory of gases

A. collisions are always elastic.

B. heavier molecules transfer more momentum to the wall of the container.

C. only a small number of molecules have very high velocity.

D. between collisions, the molecules move in straight lines with constant velocities.

Q. 11 Amongst the given options, the compound(s) in which all the atoms are in one plane in all the possible conformations (if any), is (are)

A. A

B. B

C. C

D. D

Questions: 12 – 14

When a metal rod M is dipped into an aqueous colourless concentrated solution of compound N, the solution turns light blue. Addition of aqueous NaCl to the blue solution gives a white precipitate 0. Addition of aqueous NH₃ dissolves O and gives an intense blue solution

Q. 12 The metal rod M is

A. Fe

B. Cu

C. Ni

D. Co

Q. 13 The compound N is

A. AgNO₃

B. Zn(NO₃)₂

C. Al(NO₃)₂

D. Pb(NO₃)₂

Q. 14 The final solution contains

A. [Pb(NH₃)₄]₂- and [CoCl₄]₂⁻

B. [Al(NH₃)₄]₃+ and [Cu(NH₃)₄]₂⁺

C. [Ag(NH₃)₂]⁺ and [Cu(NH₃)₄]₂⁺

D. [Ag(NH₃)₂]⁺ and [Ni(NH₃)₆]₂⁺

Questions: 15 – 16

An acyclic hydrocarbon P, having molecular formula CsHm, gave acetone as the only organic product through the following sequence of reactions, in which Q is an intermediate organic compound.

Q. 15 Choose the correct option

A. A

B. B

C. C

D. D

Q. 16 Choose the correct option

A. A

B. B

C. C

D. D

Q. 17 The difference in the oxidation numbers of the two types of sulphur atoms in Na₂S₄O₆ is

Q. 18 Reaction of Br₂ with Na₂CO₃ in aqueous solution gives sodium bromide and sodium bromate with evolution of CO₂ gas. The number of sodium bromide molecules involved in the balanced chemical equation is

Q. 19 The maximum number of electrons that can have principal quantum number, n = 3, and spin quantum number, ms = -1/2, is

Q. 20 The work function (Φ) of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metal is

Q. 21 To an evacuated vessel with movable piston under external pressure of 1 atm., 0.1 mol of He and 1.0 mol of an unknown compound (vapour pressure 0.68 atm. at 0°C) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at 0°C is close to

Q. 22 The total number of alkenes possible by dehydrobromination of 3-bromo-3-

cyclopentylhexane using alcoholic KOH is

Q. 23 A decapeptide (Mol. Wt. 796) on complete hydrolysis gives glycine (Mol. Wt. 75), alanine and phenylalanine. Glycine contributes 47.0 % to the total weight of the hydrolysis products. The number of glycine units present in the decapeptide is

Q. 24 A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall building which reflects the sound waves. The speed of sound in air is 320 m/s. The frequency of the siren heard by the car driver is

A. 8.50 kHz

B. 8.25 kHz

C. 7.75 kHz

D. 7.50 kHz

Q. 25 5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T1, the work done in the process is

A. 9/8 RT1

B. 3/2 RT1

C. 15/8 RT1

D. 9/2 RT1

Q. 26 Consider an electric field E̅ = Eo x̂, where Eo is a constant. The flux through the shaded area (as shown in the figure) due to this field is

A. 2Eo a²

B. √2Eo a²

C. Eo a²

D. Eo a²/√2

Q. 27 The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 Å. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is

A. 1215 Å

B. 1640 Å

C. 2430 Å

D. 4687 Å

Q. 28 A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) is

A. 9

B. 18

C. 27

D. 36

Q. 29 A meter bridge is set-up as shown, to determine an unknown resistance ‘X’ using a standard 10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of ‘X’ is

A. 10.2 ohm

B. 10.6 ohm

C. 10.8 ohm

D. 11.1 ohm

Q. 30 A 2 μF capacitor is charged as shown in figure. The percentage of its stored energy dissipated after the switch 8 is turned to position 2 is

A. 0 %

B. 20 %

C. 75 %

D. 80 %

Q. 31 A spherical metal shell A of radius RA and a solid metal sphere B of radius RB (< RA) are kept far apart and each is given charge ‘+Q’. Now they are connected by a thin metal wire. Then

A. A

B. B

C. C

D. D

Q. 32 An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?

A. They will never come out of the magnetic field region.

B. They will come out travelling along parallel paths.

C. They will come out at the same time.

D. They will come out at different times.

Q. 33 A composite block is made of slabs A, B, C, D and E of different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat ‘Q’ flows only from left to right through the blocks. Then in steady state

A. heat flow through A and E slabs are same.

B. heat flow through slab E is maximum.

C. temperature difference across slab E is smallest.

D. heat flow through C = heat flow through B + heat flow through D.

Q. 34 A metal rod of length ‘L’ and mass ‘m’ is pivoted at one end. A thin disk of mass ‘M’ and radius ‘R’ (< L) is attached at its center to the free end of the rod. Consider two ways the disc is attached: (case A) The disc is not free to rotate about its center and (case B) the disc is free to rotate about its center. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is (are) true?

A. Restoring torque in case A = Restoring torque in case B

B. Restoring torque in case A < Restoring torque in case B

C. Angular frequency for case A > Angular frequency for case B.

D. Angular frequency for case A < Angular frequency for case B.

Questions: 35 – 37

Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis. The phase space diagram is x(t) vs. p(t) curve in this plane. The arrow on the curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which position or momentum upwards (or to right) is positive and downwards (or to left) is negative.

Q. 35 Choose the correct option

A. A

B. B

C. C

D. D

Q. 36 Choose the correct option

A. A

B. B

C. C

D. D

Q. 37 Choose the correct option

A. A

B. B

C. C

D. D

Questions: 38 – 39

A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let ‘N’ be the number density of free electrons, each of mass ‘m’. When the electrons are subjected to an electric field, they are displaced relatively away from the heavy positive ions. if the electric field becomes zero, the electrons begin to oscillate about the positive ions with a natural angular frequency ‘ωp’, which is called the plasma frequency. To sustain the oscillations, a time varying electric field needs to be applied that has an angular frequency ω, where a part of the energy is absorbed and a part of it is reflected. As ω approaches ωp, all the free electrons are set to resonance together and all the energy is reflected. This is the explanation of high reflectivity of metals.

Q. 38 Taking the electronic charge as ‘e’ and the permittivity as ‘εo’, use dimensional analysis to determine the correct expression for ωp.

A. √(Ne/mεo)

B. √(mεo/Ne)

C. √(Ne²/mεo)

D. √(mεo/Ne²)

Q. 39 Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons N ≈ 4 x 10²⁷ m-³. Take ε0 ≈ 10⁻¹¹ and m ≈ 10⁻³⁰, where these quantities are in proper SI units.

A. 800 nm

B. 600 nm

C. 300 nm

D. 200 nm

Q. 40 A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. The stick applies a force of 2 N on the ring and rolls it without slipping with an acceleration of 0.3 m/s². The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is (P/10). The value of P is

Q. 41 A block is moving on an inclined plane making an angle 45° with the horizontal and the coefficient of friction is μ. The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N = 10 μ, then N is

Q. 42 Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side ‘a ’. The surface tension of the soap film is γ. The system of charges and planar film are in equilibrium, (value of a given in the figure, where ‘k’ is a constant. Then N is

Q. 43 Steel wire of length ‘L’ at 40°C is suspended from the ceiling and then a mass ‘m’ is hung from its free end. The wire is cooled down from 40°C to 30°C to regain its original length ‘L’. The coefficient of linear thermal expansion of the steel is 10⁻⁵/ °C, Young’s modulus of steel is 10¹¹ N/m² and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of ‘m’ in kg is nearly

Q. 44 The activity of a freshly prepared radioactive sample is 10¹⁰ disintegrations per second, whose mean life is 10⁹ s. The mass of an atom of this radioisotope is 10⁻²⁵ kg. The mass (in mg) of the radioactive sample is

Q. 45 A long circular tube of length 10 m and radius 0.3 m carries a current I along its curved surface as shown. A wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as I = Io cos (300 t) where Io is constant. It the magnetic moment of the loop is N μo Io sin (300 t) , then ‘N’ is

Q. 46 Four solid spheres each of diameter √5 cm and mass 0.5 kg are placed with their centers at the corners of a square of side 4 cm. The moment of inertia of the system about the diagonal of the square is N x 10⁻⁴ kg-m² , then N is

Q. 47 Let (x₀, y₀) be the solution of the following equations. Then x₀ is

A. 1/6

B. 1/3

C. 1/2

D. 6

Q. 48 Choose the correct option.

A. A

B. B

C. C

D. D

Q. 49 Let a̅ = î + ĵ + k̂ , b̅ = î – ĵ + k̂ and c̅ = î – ĵ – k̂ be three vectors. A vector v̅ in the plane of a̅ and b̅ , whose projection on c̅ is 1/√3, is given by,

A. î – 3ĵ + 3k̂

B. -3î – 3ĵ – 3k̂

C. 3î – ĵ + 3k̂

D. î + 3ĵ – 3k̂

Q. 50 Let P = {θ: sinθ – cosθ = √2 cosθ} and Q= {θ: sinθ + cosθ = √2 cosθ} be two sets. Then

A. P ⊂ Q and Q – P ≠ ∅

B. Q ⊄ P

C. P ⊄ Q

D. P = Q

Q. 51 Let the straight line x = b divide the area enclosed by y = (1 – x)², y=0 , and x = 0 into two parts R₁ (0 ≤ x ≤ b) and R₂ (b ≤ x ≤ 1) such that R₁ – R₂= 1/4. Then b equals

A. 3/4

B. 1/2

C. 1/3

D. 1/4

Q. 52 Let α and β be the roots of x² – 6x – 2 = 0 with α > β. If an = αⁿ – βⁿ, for n ≥ 1 , then the value of expression in the image is

A. 1

B. 2

C. 3

D. 4

Q. 53 A straight line L through the point (3, -2) is inclined at an angle 60° to the line √3x + y = 1. If L also intersects the x-axis, then the equation of L is

A. y + √3x + 2 – 3√3 = 0

B. y – √3x + 2 + 3√3 = 0

C. √3y – x + 3 + 2√3 = 0

D. √3y + x – 3 + 2√3 = 0

Q. 54 The vector(s) which is/are coplanar with vectors î + ĵ + 2k̂ and î + 2ĵ + k̂ , and perpendicular to the vector î + ĵ + k̂ is/are

A. ĵ – k̂

B. -î + ĵ

C. î – ĵ

D. -ĵ + k̂

Q. 55 Let M and N be two 3×3 non-singular skew-symmetric matrices such that MN = NM. if Pᵗ denotes the transpose of P, then the value of the expression given in the image is?

A. M²

B. -N²

C. -M²

D. MN

Q. 56 Let the eccentricity of the hyperbola x²/a² – y²/b² = 1 be reciprocal to that of the ellipse x² + 4y² = 4.If the hyperbola passes through a focus of the ellipse, then

A. the equation of the hyperbola is x²/3 – y²/2 = 1

B. a focus of the hyperbola is (2, 0)

C. the eccentricity of the hyperbola is √5/3

D. the equation of the hyperbola is x² – 3y² = 3

Q. 57 Let f : ℝ → ℝ be a function such that f(x+y) = f(x) + f(y), Ɐx, y∈R If f (x) is differentiable at x = 0, then

A. (x) is differentiable only in a finite interval containing zero

B. f (x) is continuous Ɐx ∈ ℝ

C. f’(x) is constant Ɐx ∈ ℝ

D. f (x) is differentiable except at finitely many points

Questions: 58 – 60

Let a, b and c be three real numbers satisfying

Q. 58 If the point P(a, b, c), with reference to (E), lies on the plane 2x+ y+ z =1, then the value of 7a +b+c is

A. 0

B. 12

C. 7

D. 6

Q. 59 Choose the correct option:

A. -2

B. 2

C. 3

D. -3

Q. 60 Choose the correct option:

A. 6

B. 7

C. 6/7

D. ∞

Questions: 61 – 62

Let U₁ and U₂ be two urns such that U₁ contains 3 white and 2 red balls, and U₂ contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U₁ and put into U₂. However, if tail appears then 2 balls are drawn at random from U₁ and put into U₂. Now 1 ball is drawn at random from U₂.

Q. 61 The probability of the drawn ball from U₂ being white is

A. 13/30

B. 23/30

C. 19/30

D. 11/30

Q. 62 Given that the drawn ball from U₂ is white, the probability that head appeared on the coin is

A. 17/23

B. 11/23

C. 15/23

D. 12/23

Q. 63 Consider the parabola y² = 8x. Let Δ₁ be the area of the triangle formed by the end points of its Latus rectum and the point P(1/2, 2) on the parabola, and Δ₂ be the area of the triangle formed by drawing tangents at P and at the end points of the Latus rectum. Then Δ₁/Δ₂ is

Q. 64 Answer the following question:

Q. 65 The positive integer value of n > 3 satisfying the equation is

Q. 66 Let f : [1,∞) -> [2,∞) be a differentiable function such that f(1) = 2. If the expression in figure is true for all x ≥ , then the value of f(2) is

Q. 67 If z is any complex number satisfying |z – 3 – 2i| ≤ 2, then the minimum value of |2z – 6 + 5i|

Q. 68 Answer the following question:

Q. 69 Answer the following:

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	D	B	A	C	D	C	A	ACD	ABD	ABCD
Question	11	12	13	14	15	16	17	18	19	20
Answer	BC	B	A	C	D	B	5	5	9	4
Question	21	22	23	24	25	26	27	28	29	30
Answer	7	5	6	A	A	C	A	D	B	D
Question	31	32	33	34	35	36	37	38	39	40
Answer	ABCD	BCD	ACD	AD	D	C	B	C	B	4
Question	41	42	43	44	45	46	47	48	49	50
Answer	5	3	3	1	6	9	C	A	C	D
Question	51	52	53	54	55	56	57	58	59	60
Answer	B	C	B	AD	ABCD	BD	BCD	D	A	B
Question	61	62	63	64	65	66	67	68	69
Answer	B	D	2	3 OR 9	7	6	5	8	1

JEE Advanced 2010 Paper II Previous Year Paper

JEE Advanced 2010 Paper 2

Q. 1 The complex showing a spin-only magnetic moment of 2.82 B.M is

A. A

B. B

C. C

D. D

Q. 2 The species having pyramidal shape is

A. A

B. B

C. C

D. D

Q. 3 Choose the correct option

A. A

B. B

C. C

D. D

Q. 4 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 5 The packing efficiency of the two-dimensional square unit cell shown below is

A. 39.27%

B. 68.02%

C. 74.05%

D. 78.54%

Q. 6 Assuming that Hund’s rule is violated. the bond order and magnetic nature of the diatomic molecule B₂ is

A. 1 and diamagnetic

B. 1 and paramagnetic

C. 0 and diamagnetic

D. 0 and paramagnetic

Q. 7 The total number of diprotic acids among the following is

Q. 8 Total number of geometrical isomers for the complex is

Q. 9 Among the following. the number of elements showing only one non-zero oxidation state is O, Cl, F, N, P, Sn Tl, Na, Ti

Q. 10 Silver (atomic weight = 108 g/mol) has a density of 10.5 g cm-³. The number of silver atoms on a surface of area 10⁻¹² m² can be expressed in scientific notation as y x 10ˣ. The value of x is

Q. 11 One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is Wₛ and that along the dotted line path is W􀀁. then the integer closest to the ratio W􀀁/Wₛ is

Questions: 12 – 14

Two aliphatic aldehydes P and Q react in the presence of aqueous K₂CO₃ to give compound R, which upon treatment with HCN provides compound S. On acidification and heating, S gives the product shown below

Q. 12 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 13 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 14 Choose the correct option:

A. A

B. B

C. C

D. D

Questions: 15 – 17

The hydrogen-like species Li²⁺ is in a spherically symmetric state S₁ with one radial node. Upon absorbing light the ion undergoes transition to a state S₂. The state S₂ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.

Q. 15 The state S₁ is

A. 1s

B. 2s

C. 2p

D. 3s

Q. 16 Energy of the state S₁ in units of the hydrogen atom ground state energy is

A. 0.75

B. 1.50

C. 2.25

D. 4.50

Q. 17 The orbital angular momentum quantum number of the state S₂ is

A. 0

B. 1

C. 2

D. 3

Q. 18 Match the reactions in Column I with appropriate options in Column II.

A. A – r, s ; B – t ; C – p, q ; D – r

B. A – q, s ; B – t ; C – p, q ; D – r

C. A – p, q ; B – t ; C – q, s ; D – r

D. A – r, s ; B – r ; C – p, q ; D – t

Q. 19 All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II.

A. A – p, s ; B – p, q, r, t ; C – p, q ; D – p

B. A – p, s ; B – p, q, r, t ; C – p, q ; D – p, r

C. A – p, q ; B – p, q, r, t ; C – p, s ; D – p

D. A – p, r ; B – p, q, r, t ; C – p, q ; D – p, s

Q. 20 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 21 Let S = {1. 2. 3. 4}. The total number of unordered pairs of disjoint subsets of S is equal to

A. 25

B. 34

C. 42

D. 41

Q. 22 Choose the correct option:

A. 1

B. 1/3

C. 1/2

D. 1/e

Q. 23 If the distance of the point P(1, -2, 1) from the plane x + 2y – 22 = a. where a > 0, is 5, then the foot of the perpendicular from P to the plane is

A. (8/3, 4/3, -7/3)

B. (4/3, -4/3, 1/3)

C. (1/3, 2/3, 10/3)

D. (2/3, -1/3, 5/2)

Q. 24 Two adjacent sides of a parallelogram ABCD are given by

AB =2i + 10j + 11k and AD = -i + 2j + 2k

The side AD is rotated by an acute angle a in the plane of the parallelogram so that AD becomes AD’. If AD’ makes a right angle with the side AB. then the cosine of the angle a is given by

A. 8/9

B. √17/9

C. 1/9

D. 4√5/9

Q. 25 A signal which can be green or red with probability 4/5 and 1/5 respectively. is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 3/4. If the signal received at station B is green, then the probability that the original signal was green is

A. 3/5

B. 6/7

C. 20/23

D. 9/20

Q. 26 Two parallel chords of a circle of radius 2 are at a distance √3 +1 apart. If the chords subtend at the center angles of π/k and 2π/k where k > 0, then the value of [k] is [Note : [k] denotes the largest integer less than or equal to k]

Q. 27 Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively. Suppose a = 6, b = 10 and the area of the triangle is 15√3. If ∠ACB is obtuse and if r denotes the radius of the incircle of the triangle. then r² is equal to

Q. 28 Answer the following:

Q. 29 Answer the following:

Q. 30 Answer the following:

Questions: 31 – 33

Consider the polynomial

f(x) = 1 + 2x + 3x² + 4x³

Let s be the sum of all distinct real roots of fix) and let t = |s|.

Q. 31 The real number s lies in the interval

A. (-1/4, 0)

B. (-11, -3/4)

C. (-3/4, -1/2)

D. (0, 1/4)

Q. 32 The area bounded by the curve y = f(x) and the lines x = 0, y = 0 and x = t, lies in the interval

A. (3/4, 3)

B. (24/64, 11/16)

C. (9, 10)

D. (0, 21/64)

Q. 33 The function f ‘(x) is

A. increasing in (-t, -1/4) and decreasing in (-1/4, t)

B. decreasing in (-t, -1/4) and increasing in (-1/4, t)

C. increasing in (-t, t)

D. decreasing in (-t, t)

Questions: 34 – 36

Tangents are drawn from the point P(3, 4) to the ellipse x²/9 + y²/4 = 1 touching the ellipse at points A and B.

Q. 34 The coordinates of A and B are

A. (3, 0) and (0, 2)

B. (-8/5, 2√161/15) and (-9/5, 8/5)

C. (-8/5, 2√161/15) and (0, 2)

D. (3, 0) and (-9/5, 8/5)

Q. 35 The orthocenter of the triangle PAB is

A. (5, 8/7)

B. (7/5, 25/8)

C. (11/5, 8/5)

D. (8/25, 7/5)

Q. 36 The equation of the locus of the point whose distances from the point P and the line AB are equal is

A. 9x² + y² – 6xy – 54x – 62y + 241 = 0

B. x² + 9y² + 6xy – 54x + 62y – 241 = 0

C. 9x² + 9y² – 6xy – 54x – 62y – 241 = 0

D. x² + y² – 2xy + 27x + 31y – 120 = 0

Q. 37 Match the statements in Column-I with those in Column-II.

[Note: Here z takes values in the complex plane and Im z and Re z denote respectively, the imaginary part and the real part of z.]

A. A – p, r; B – q ; C – p, s, t ; D – q, r, s, t

B. A – p, r, s, t ; B – p ; C – p, s, t ; D – q, r

C. A – q, r; B – p ; C – p, s, t ; D – q, r, s, t

D. A – q, r ; B – p ; C – s, t ; D – r, s, t

Q. 38 Match the statements in Column-I with those in Column-II.

A. A – t ; B – p, r ; C – q, s ; D – r

B. A – t ; B – q, s ; C – p, r ; D – r

C. A – r ; B – p, r ; C – q, s ; D – t

D. A – r ; B – q, s ; C – p, r ; D – t

Q. 39 A Vernier caliper has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers. the least count is

A. 0.02 mm

B. 0.05 mm

C. 0.1 mm

D. 0.2 mm

Q. 40 A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the Wire is 50 N and the speed of sound is 320 m/s. the mass of the string is

A. 5 grams

B. 10 grams

C. 20 grams

D. 40 grams

Q. 41 A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is

A. virtual and at a distance of 16 cm from the mirror

B. real and at a distance of 16 cm from the mirror

C. Virtual and at a distance of 20 cm from the mirror

D. real and at a distance of 20 cm from the mirror

Q. 42 A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force F(t) in the x-direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is

A. 4.50 J

B. 7.50 J

C. 5.06 J

D. 14.06 J

Q. 43 A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength 81π/7 x 10⁵ V/m. When the field is switched off, the drop is observed to fall with terminal velocity 2 x 10⁻³ m/s. Given g = 9.8 m/s²,. viscosity of the air = 1.8 x 10⁻⁵ Ns m-² and the density of oil = 900 kg/m³, the magnitude of q is

A. 1.6 x 10⁻¹⁹ C

B. 3.2 x 10⁻¹⁹ C

C. 4.8 x 10⁻¹⁹ C

D. 8.0 x 10⁻¹⁹ C

Q. 44 A uniformly charged thin spherical shell of radius R carries uniform surface charge density of σ per unit area. It is made of two hemispherical shells held together by pressing them with force F (see figure). F is proportional to

A. A

B. B

C. C

D. D

Q. 45 A diatomic ideal gas is compressed adiabatically to 1/32 of its initial volume. In the initial temperature of the gas is Tᵢ (in Kelvin) and the final temperature is aTᵢ. the value of a is

Q. 46 At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V ?

[Take ln 5 = 1.6, ln 3 = 1.1]

Q. 47 Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from 25/3 m to 50/7 m in 30 seconds. What is the speed of the object in km per hour ?

Q. 48 A large glass slab (μ = 5/ 3) of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R ?

Q. 49 To determine the half life of a radioactive element. a student plots a graph of ln|dN(t)/dt| versus t. Here dN(t)/dt is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is Years

Questions: 50 – 52

When liquid medicine of density ρ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the chopper is pressed. a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.

Q. 50 If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius R (assuming r <

A. 2πrT

B. 2πRT

C. 2πr²T/R

D. 2πR²T/r

Q. 51 If r = 5 x 10^(-4) ρ =10 kg/m³. g=10 m/s², T=0.11N/m, the radius of the drop when it detaches from the dropper is approximately

A. 1.4 x 10-³ m

B. 3.3 x 10-³ m

C. 2.0 x 10-³ m

D. 4.1 x 10-³ m

Q. 52 After the drop detaches. its surface energy is

A. 1.4 x 10⁻⁶ J

B. 2.7 x 10⁻⁶ J

C. 5.4 x 10⁻⁶ J

D. 8.1 x 10⁻⁶ J

Questions: 53 – 55

The key feature of Bohr’s theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr’s quantization condition.

Q. 53 A diatomic molecule has moment of inertia I. By Bohr’s quantization condition its rotational energy in the nth level (n = 0 is not allowed) is

A. 1/n² x (h²/(8π²I))

B. 1/n x (h²/(8π²I))

C. n x (h²/(8π²I))

D. n² x (h²/(8π²I))

Q. 54 It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to 4/π x 10¹¹ Hz. Then the moment of inertia of CO molecule about its center of mass is close to (Take h = 2 x 10³⁴ J s)

A. 2.76 x 10⁻⁴⁶ kg m²

B. 1.87 x 10⁻⁴⁶ kg m²

C. 4.67 x 10⁻⁴⁷ kg m²

D. 1.17 x 10⁻⁴⁷ kg m²

Q. 55 In a CO molecule. the distance between C (mass = 12 a.m.u.) and 0 (mass = 16 a.m.u.) where 1 a.m.u = (5/3) x 10⁻²⁷ is close to

A. 2.4 x 10⁻¹⁰ m

B. 1.9 x 10⁻¹⁰ m

C. 1.3 x 10⁻¹⁰ m

D. 4.4 x 10⁻¹¹ m

Q. 56 Two transparent media of refractive indices μ₁ and μ₃ have a solid lens shaped transparent material of refractive index μ₂ between them as shown in figures in Column II. A traversing these media is also shown in the figures. In Column I different relationship between μ₁, μ₂ and μ₃ are given. Match them to the ray diagrams shown in Column

A. A – p, r ; B – q, s, t ; C – p, r, t ; D – q, s

B. A – q, s ; B – q, s, t ; C – p, r, t ; D – p, r

C. A – p, r ; B – p, r, t ; C – q, s, t ; D – q, s

D. A – q, s ; B – q, s, t ; C – p, r, t ; D – p, r

Q. 57 You are given many resistances. capacitors and inductors. These are connected to variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column II. When a current (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage V₁ and V₂. (indicated in circuits) are related as shown in column I. Match the two

A. A – r, s, t ; B – q, r, s, t ; C – p, q; D – q, r, s, t

B. A – r, t ; B – r, s, t ; C – p, q; D – q, r, s, t

C. A – s, t ; B – q, r, s, t ; C – p, q; D – q, r, s

D. A – r, s, t ; B – q, r ; C – p, q; D – q, r

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

JEE Advanced 2010 Paper I Previous Year Paper

JEE Advanced 2010 Paper 1

Q. 1 The correct structure of ethylenediaminetetraacetic acid (EDTA) among the structures (A), (B), (C), (D) is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 2 The ionization isomer of [Cr(H₂O)₄Cl(NO₂)]Cl is

A. [Cr(H₂O)₄(O₂N)]Cl₂

B. [Cr(H₂O)₄Cl₂](NO₂)

C. [Cr(H₂O)₄Cl(ONO)]Cl

D. [Cr(H2O)4Cl2(NO2)] . H2O

Q. 3 The synthesis of 3-octyne is achieved by adding a bromoalkane into a mixture of sodium amide and an alkyne. The bromoalkane and alkyne respectively are

A. BrCH₂CH₂CH₂CH₂CH₃ and CH₃CH₃C ≡ CH

B. BrCH₂CH₂CH₃ and CH₃CH₂CH₂C ≡ CH

C. BrCH₂CH₂CH₂CH₂CH₃ and CH₃C ≡ CH

D. BrCH₂CH₂CH₂CH₃ and CH₃CH₂C ≡ CH

Q. 4 The correct statement about the disaccharide shown in figure (1) is

A. Ring (a) is pyranose with α – glycosidic link

B. Ring (a) is furanose with α – glycosidic link

C. Ring (b) is furanose with α – glycosidic link

D. Ring (b) is pyranose with β- glycosidic link

Q. 5 In the reaction given in figure (1) , the products among (A), (B), (C), (D) are

A. (A)

B. (B)

C. (C)

D. (D)

Q. 6 Plots showing the variation of the rate constant (k) with temperature (T) are given in (A), (B), (C), (D). The plot that follows Arrhenius equation is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 7 The species which by definition has ZERO standard molar enthalpy of formation at 298 K is

A. Br₂ (g)

B. Cl₂ (g)

C. H₂O (g)

D. CH₄ (g)

Q. 8 The bond energy (in kcal mol⁻¹) of a C-C single bond is approximately

A. 1

B. 10

C. 100

D. 1000

Q. 9 The reagent(s) used for softening the temporary hardness of water is(are)

A. Ca₃(PO₄)₂

B. Ca(OH)₂

C. Na₂CO₃

D. NaOCl

Q. 10 In the reaction given in figure (1), the intermediate(s) among (A), (B), (C), (D) is(are)

A. (A)

B. (B)

C. (C)

D. (D)

Q. 11 In the Newman projection for 2, 2-dimethybutane given in figure (1), X and Y can respectively be

A. H and H

B. H and C₂H₅

C. C₂H₅ and H

D. CH₃ and CH₃

Q. 12 Among the following, the intensive property is (properties are)

A. molar conductivity

B. electromotive force

C. resistance

D. heat capacity

Q. 13 Aqueous solutions of HNO₃, KOH, CH₃COOH, and CH₃COONa of identical concentrations are provided. The pair(s) of solutions which form a buffer upon mixing is(are)

A. HNO₃ and CH₃COOH

B. KOH and CH₃COONa

C. HNO₃ and CH₃COONa

D. CH₃COOH and CH₃COONa

Questions: 14 – 16

Copper is the most noble of the first row transition metals and occur in small deposits in several countries. Ores of copper include chalcanthite (CuSO₄ . 5H₂O), atacamite (Cu₂Cl(OH)₃), Cuprite (Cu₂O), copper glance (Cu₂S) and malachite (Cu₂(OH)₂CO₃). However, 80% of the world copper production comes from the ore chalcopyrite (CuFeS₂). The extraction of copper from chalcopyrite involves partial roasting, removal of iron and self-reduction.

Q. 14 Partial roasting of chalcopyrite produces

A. Cu₂S and FeO

B. Cu₂O and FeO

C. CuS and Fe₂O₃

D. Cu₂O and Fe₂O3₃

Q. 15 Iron is removed from chalcopyrite is

A. FeO

B. FeS

C. Fe₂O₃

D. FeSiO₃

Q. 16 In self-reduction, the reducing species is

A. S

B. O²⁻

C. S²⁻

D. SO₂

Questions: 17 – 18

The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in higher processes such as transmission of nerve impulses and maintaining the ion balance. A simple model for such a concentration cell involving a metal M is:

M(s) | M⁺(aq; 0.05 molar) || M⁺(aq; 1 molar) | M(s) For the above electrolytic cell the magnitude of the cell potential |E Cell| = 70 mV

Q. 17 For the above cell

A. E cell < 0; ΔG > 0

B. E cell > 0; ΔG < 0

C. E cell < 0; ΔG⁰ > 0

D. E cell > 0; ΔG⁰ < 0

Q. 18 If the 0.05 molar solution of M⁺ is replaced by a 0.0025 molar M⁺ solution, then the magnitude of the cell potential would be

A. 35 mV

B. 70 mV

C. 140 mV

D. 700 mV

Q. 19 The total number of basic groups in the following form of lysine given in figure is

Q. 20 The total number of cyclic isomers possible for a hydrocarbon with the molecular formula C₄H₆ is

Q. 21 In the figure given , the total number of intramolecular aldol condensation products formed from ‘Y’ is

Q. 22 Amongst the following compounds given in figure (1), the total number of compounds soluble in aqueous NaOH is

Q. 23 Amongst the following, the total number of compounds whose aqueous solution turns red litmus paper blue is

KCN, K₂SO₄, (NH₄)2C₂O₄, NaCl, Zn(NO₃)₂, FeCl₃, K₂CO₃, NH₄NO₃, LiCN

Q. 24 Based on VSEPR theory, the number of 90 degree F-Br-F angles in BrF₅ is

Q. 25 The value of n in the molecular formula BenAl₂Si₆O₁₈ is

Q. 26 A student performs a titration with different burettes and finds titre values of 25.2 mL, 25.25 mL and 25.0 mL. The number of significant figures in the average titre value is

Q. 27 The concentration of R in the reaction R → P was measured as a function of time and the following data is obtained given in figure . The order of the reaction is

Q. 28 The number of neutrons emitted when ²³⁵₉₂U undergoes controlled nuclear fission to ¹⁴²₅₄Xe and ⁹⁰₃₈Sr is

Q. 29 If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression a/c sin2C + c/a sin 2A is

A. 1/2

B. √3/2

C. 1

D. √3

Q. 30 Equation of the plane containing the straight line x/2 = y/3 = z/4 and perpendicular to the plane containing the straight lines x/3 = y/4 = z/2 and x/4 = y/2 = z/3 is

A. x + 2y – 2z = 0

B. 3x + 2y – 2z = 0

C. x – 2y + z = 0

D. 5x + 2y – 4z = 0

Q. 31 Let ω be a complex cube root of unity with ω ≠ 1. A fair die is thrown three times. If r₁, r₂ and r₃ are the numbers obtained on the die, then the probability that ωʳ₁ + ωʳ₂ + ωʳ₃ = 0 is

A. 1/18

B. 1/9

C. 2/9

D. 1/36

Q. 32 Let P, Q, R and S be the points on the plane with position vectors -2î – ĵ, 4î, 3î + 3ĵ and -3î + 2ĵ respectively. The quadrilateral PQRS must be a

A. parallelogram, which is neither a rhombus nor a rectangle

B. square

C. rectangle, but not a square

D. rhombus, but not a square

Q. 33 The number of 3 x 3 matrices A (given in figure ), whose entries are either 0 and 1 and for which the system A has exactly two distinct solutions, is

A. 0

B. 2⁹ – 1

C. 168

D. 2

Q. 34 Find the value of the equation given in figure (1).

A. 0

B. 1/12

C. 1/24

D. 1/64

Q. 35 Let p and q be real numbers such that p ≠ 0, p³ ≠ q and p³ ≠ -q. If α and β are nonzero complex numbers satisfying α + β = -p and α³ + β³ = q, then a quadratic equation having α/β and β/α as its roots is

A. (p³ + q)x² – (p³ + 2q)x + (p³ + q) = 0

B. (p³ + q)x² – (p³ – 2q)x + (p³ + q) = 0

C. (p³ – q)x² – (5p³ – 2q)x + (p³ – q) = 0

D. (p³ – q)x² – (5p³ + 2q)x + (p³ – q) = 0

Q. 36 Let f, g and h be real – valued functions defined on the interval [0, 1] by f(x) = e^x^2 + e^-x^2, g(x) = xe^x^2 + e^-x^2 and h(x) = x^2e^-x^2 + e^-x^2. If a, b and c denote, respectively, the absolute maximum of f, g and h on [0, 1], then

A. a = b and c ≠ b

B. a = c and a ≠ b

C. a ≠ b and c ≠ b

D. a = b = c

Q. 37 Let A and B be two distinct points on the parabola y² = 4x. If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be

A. -1/r

B. 1/r

C. 2/r

D. -2/r

Q. 38 Let ABC be a triangle such that ∠ACB = π/6 and let a, b and c denote the lengths of the sides opposite to A, B and C respectively. The value(s) of x for which a = x² + x + 1, b = x² – 1 and c = 2x + 1 is (are)

A. -(2 + √3)

B. 1 + √3

C. 2 + √3

D. 4√3

Q. 39 Let z₁ and z₂ be two distinct complex numbers and let z = (1 – t)z₁ + tz₂ for some real number t with 0 < t < 1. If Arg(w) denotes the principal argument of a nonzero complex number w, then which is the correct option among (A), (B), (C), (D)

A. (A)

B. (B)

C. (C)

D. (D)

Q. 40 Let f be a real-valued function defined on the interval (0, ∞) by f(x) given in figure (1). Then which of the following statement(s) is (are) true?

A. f”(x) exists for all x ∈ (0, ∞)

B. f'(x) exists for all x ∈ (0, ∞) and f’ is continuous on (0, ∞), but not differentiable on (0, ∞)

C. there exists α > 1 such that |f'(x)| < |f(x)| for all x ∈ (0, ∞)

D. there exists β > 1 such that |f(x)| + |f'(x)| ≤ β for all x ∈ (0, ∞)

Q. 41 Find the value(s) of the equation given in figure (1):

A. 22/7 – π

B. 2/105

C. 0

D. 71/15 – 3π/2

Questions: 42 – 44

Let p be an odd prime number and Tp be the following set of 2 x 2 matrices (given in figure (1):

Q. 42 The number of A in Tp such that A is either symmetric or skew – symmetric or both, and det (A) divisible by p is

A. (p – 1)²

B. 2 (p – 1)

C. (p-1)² + 1

D. 2p – 1

Q. 43 The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is

[NOTE: The trace of a matrix is the sum of its diagonal entries.]

A. (p – 1)(p² – p + 1)

B. p³ – (p – 1)²

C. (p – 1)²

D. (p – 1)(p² – 2)

Q. 44 The number of A in Tp such that det (A) is not divisible by p is

A. 2p³

B. p³ – 5p

C. p³ – 3p

D. p³ – p²

Questions: 45 – 46

The circle x² + y² – 8x = 0 and hyperbola x²/⁹ – y²/⁴ = 1 intersect at the points A and B.

Q. 45 Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

A. 2x – √5y – 20 = 0

B. 2x – √5y + 4 = 0

C. 3x – 4y + 8 = 0

D. 4x – 3y + 4 = 0

Q. 46 Equation of the circle with AB as its diameter is

A. x² + y² – 12x + 24 = 0

B. x² + y² + 12x + 24 = 0

C. x² + y² + 24x – 12 = 0

D. x² + y² – 12x – 24 = 0

Q. 47 The number of values of θ in the interval (-π/2, π/2) such that θ ≠ nπ/5 for n = 0, ±1, ±2 and tanθ = cot5θ as well as sin 2θ = cos 4θ is

Q. 48 The maximum value of the expression 1 / (sin²θ + 3sinθcosθ + 5cos²θ) is

Q. 49 If a⃗ and b⃗ are vectors in space given by a⃗ = î – 2ĵ/√5 and b⃗ = 2î + ĵ + 3k̂/√14, then the value of (2a⃗ + b⃗) . [(a⃗ x b⃗) x (a⃗ – 2b⃗)] is

Q. 50 The line 2x + y = 1 is tangent to the hyperbola x²/a² – y²/b² = 1. If this line passes through the point of intersection of the nearest directrix and the x-axis, then the eccentricity of the hyperbola is

Q. 51 If the distance between the plane Ax – 2y + z = d and the plane containing the lines x-1/2 = y- 2/3 = z-3/4 and x-2/3 = y-3/4 = z-4/5 is √6, then |d| is

Q. 52 For any real number x, let |x| denote the largest integer less than or equal to x. Let f be a real valued function defined on the interval [-10, 10] by f(x) = { x – [x], if [x] is odd, 1 + [x] – x, if [x] is even. Then the value of the equation given in figure (1)

Q. 53 Let ω be the complex number cos 2π/3 + i sin 2π/3. Then the number of distinct complex numbers z satisfying the determinant given in figure (1), is equal to

Q. 54 Let Sk, k = 1, 2, …….., 100, denote the sum of the infinite geometric series whose first term is k-1/k! and the common ratio is 1/k. Then find the value of the equation given in figure (1)

Q. 55 The number of all possible values of θ, where 0 < θ < π, for which the system of equations (y + z) cos 3θ = (xyz) sin 3θ

x sin 3θ = 2 cos 3θ/y + 2 sin 3θ/z

(xyz) sin 3θ = (y + 2z) cos 3θ + y sin 3θ

have a solution (xo, yo, zo) with yo zo ≠ 0, is

Q. 56 Let f be a real – valued differentiable function on R (the set of all real numbers) such that f(1) = 1. If the y-intercept of the tangent at any point P(x, y) on the curve y = f(x) is equal to the cube of the abscissa of P, then the value of f(-3) is equal to

Q. 57 Consider a thin square sheet of side L and thickness t, made of a material of resistivity ρ. The resistance between two opposite faces, shown by the shaded areas in the figure (1) is

A. directly proportional to L

B. directly proportional to t

C. independent of L

D. independent of t

Q. 58 A real gas behaves like an ideal gas if its

A. pressure and temperature are both high

B. pressure and temperature are both low

C. pressure is high and temperature is low

D. pressure is low and temperature is high

Q. 59 Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100W, 60W and 40W bulbs have filament resistances R₁₀₀, R₆₀ and R₄₀, respectively, the relation between these resistances is

A. 1/R₁₀₀ = 1/R₄₀ + 1/R₆₀

B. R₁₀₀ = R₄₀ = R₆₀

C. R₁₀₀ > R₆₀ > R₄₀

D. 1/R₁₀₀ > 1/R₆₀ > 1/R₄₀

Q. 60 To verify Ohm’s law, a student is provided with a test resistor RT, a high resistance R₁, a small resistance R₂, two identical galvanometers G₁ and G₂, and a variable voltage source V. The correct circuit to carry out the experiment among figure (A), (B), (C), (D) is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 61 An AC voltage source of variable angular frequency ω and fixed amplitude Vo is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When ω is increased

A. the bulb glows dimmer

B. the bulb glows brighter

C. total impedance of the circuit is unchanged

D. total impedance of the circuit increases

Q. 62 A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of circle. The tension in the wire is

A. IBL

B. IBL/π

C. IBL/2π

D. IBL/4π

Q. 63 A block of mass m is on an inclined plane of angle θ. The coefficient of friction between the block and the plane is μ and tan θ > μ. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P₁ = mg(sinθ – μ cosθ) to P₂ = mg(sinθ + μ cosθ), the frictional force f versus P graph will look like

A. (A)

B. (B)

C. (C)

D. (D)

Q. 64 A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is

A. 2GM/7R (4√2 – 5)

B. -2GM/7R (4√2 – 5)

C. GM/4R

D. 2GM/5R (√2-1)

Q. 65 A few electric field lines for a system of two charges Q₁ and Q₂ fixed at two different points on the x-axis are shown in the figure . These lines suggest

A. |Q₁| > |Q₂|

B. |Q₁| < |Q₂|

C. at a finite distance to the left of Q1 the electric field is zero

D. at a finite distance to the right of Q2 the electric field is zero

Q. 66 A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stopwatch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true?

A. Error Δt in measuring T, the time period, is 0.05 seconds

B. Error ΔT in measuring T, the time period , is 1 second

C. Percentage error in the determination of g is 5%

D. Percentage error in the determination of g is 2.5%

Q. 67 A point mass of 1 kg collides elastically with a stationary point mass of 5kg. After their collision, the 1 kg mass reverse its direction and moves with a speed of 2 ms⁻¹. Which of the following statement(s) is (are) correct for the system of theses two masses?

A. Total momentum of the system is 3 kg ms⁻¹

B. Momentum of 5 kg mass after collision is 4 kg ms⁻¹

C. Kinetic energy of the centre of mass is 0.75 J

D. Total kinetic energy of the system is 4J

Q. 68 A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60° (see figure (1)). If the refractive index of the material of the prism is √3, which of the following is (are) correct?

A. The ray gets totally internally reflected at face CD

B. The ray comes out through face AD

C. The angle between the incident ray and the emergent ray is 90°

D. The angle between the incident ray and the emergent ray is 120°

Q. 69 One mole of an ideal gas in initial stage A undergoes a cyclic process ABCD, as shown in the figure (1). Its pressure at A is P₀. Choose the correct option(s) from the following

A. Internal energies at A and B are the same

B. \Work done by the gas in process AB is P₀V₀ ln 4

C. Pressure at C is P₀/4

D. Temperature at C is T₀/4

Questions: 70 – 72

When a particle of mass m moves on the x-axis in a potential of the form V(x) = kx², it performs simple harmonic motion. The corresponding time period is proportional to √m/k, as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different from kx² and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x-axis. Its potential energy is V(x) = αx⁴ (α > 0) for |x| near the origin and becomes a constant equal to Vo for |x| ≥ X₀. (See figure (1)).

Q. 70 If the total energy of the particle is E, it will perform periodic motion only if

A. E < 0

B. E > 0

C. V₀ > E > 0

D. E > V₀

Q. 71 For periodic motion of small amplitude A, the time period T of this particle is proportional to

A. A√m/α

B. 1/A√m/α

C. A√α/m

D. 1/A√α/m

Q. 72 The acceleration of this particle for |x| > X₀ is

A. proportional to V₀

B. proportional to V₀/mX₀

C. proportional to √V₀/mX₀

D. Zero

Questions: 73 – 74

Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature Tc(0). An interesting property of superconductors is that their critical temperature becomes smaller than Tc(0) if they are placed in a magnetic field, i.e., the critical temperature Tc(B) is a function of the magnetic field strength B. The dependence of Tc(B) on B is shown in the figure (1).

Q. 73 In the graphs (A), (B), (C), (D), the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B1 (solid line) and B₂ (dashed line). If B2 is larger than B₁, which of the following graphs shows the correct variation of R with T in these fields?

A. (A)

B. (B)

C. (C)

D. (D)

Q. 74 A superconductor has Tc (0) = 100 K. When a magnetic field of 7.5 Tesla is applied, its Tc decreases to 75 K. For this material one can definitely say that when

A. B = 5 Tesla, Tc (B) = 80 K

B. B = 5 Tesla, 75 K < Tc (B) < 100 K

C. B = 10 Tesla, 75 K < Tc (B) < 100 K

D. B = 10 Tesla, Tc (B) = 70 K

Q. 75 The focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25 cm in front of it to 50 cm, the magnification of its image changes from m₂₅ to m₅₀. The ratio m₂₅/m₅₀ is

Q. 76 An α-particle and a proton are accelerated from rest by a potential difference of 100V. After this, their de Broglie wavelengths are λα and λp respectively. The ratio λα/λp, to the nearest integer, is

Q. 77 When two identical batteries of internal resistance 1Ω each are connected in series across a resistor R, the rate of heat produced in R is J₁. When the same batteries are connected in parallel across R, the rate is J₂. If J₁ = 2.25 J₂ then the value of R in Ω is

Q. 78 Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperature T₁ and T₂, respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B?

Q. 79 When two progressive waves y₁ = 4sin(2x – 6t) and y₂ = 3sin(2x – 6t – π/2) are superimposed, the amplitude of the resultant wave is

Q. 80 A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its cross-sectional area is 4.9 x 10⁻⁷ m². If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s⁻¹. If the Young’s modulus of the material of the wire is n x 10⁹ Nm⁻², the value of n is

Q. 81 A binary star consists of two stars A (mass 2.2Ms) and B (mass 11Ms), where Ms is the mass of the sun. They are separated by the distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is

Q. 82 Gravitational acceleration on the surface of a planet is √6/11 g, where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is ⅔ times that of the earth. If the escape speed on the surface of the earth is taken to be 11kms⁻¹, the escape speed on the surface of the planet in kms⁻¹ will be

Q. 83 A piece of ice (heat capacity = 2100 J kg⁻¹ °C⁻¹ and latent heat = 3.36 x 10⁵ J kg⁻¹) of mass m grams is at -5°C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is

Q. 84 A stationary source is emitting sound at a fixed frequency fo, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of fo. What is the difference in the speeds of the cars (in km per hour) to the nearest integer? The cars are moving at constant speeds much smaller than the speed of sound which is ms⁻¹

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	C	B	D	A	D	A	B	C	B	AC
Question	11	12	13	14	15	16	17	18	19	20
Answer	BD	AB	CD	A	D	C	B	C	2	5
Question	21	22	23	24	25	26	27	28	29	30
Answer	1	4	3	0 OR 8	3	3	0	4	D	C
Question	31	32	33	34	35	36	37	38	39	40
Answer	C	A	A	B	B	D	CD	B	ACD	BC
Question	41	42	43	44	45	46	47	48	49	50
Answer	A	D	C	D	B	A	3	2	5	2
Question	51	52	53	54	55	56	57	58	59	60
Answer	6	4	1	3	3	9	C	D	D	C
Question	61	62	63	64	65	66	67	68	69	70
Answer	B	C	A	A	AD	AC	AC	ABC	ABCD	C
Question	71	72	73	74	75	76	77	78	79	80
Answer	B	D	A	B	6	3	4	9	5	4
Question	81	82	83	84
Answer	6	3	8	7