**JEE Advanced 2014 Paper 2**

Q. 1 A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following describes the variation of its kinetic energy K with time t most appropriately? The figures are only illustrative and not to scale.

A. A

B. B

C. C

D. D

Q. 2 A wire which passes through the hole in a small bead is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is

A. Always radially outwards

B. Always radially inwards

C. Radially outwards initially and radially inwards later

D. Radially inwards initially and radially outwards later

Q. 3 During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at 40.0 cm using a standard resistance of 90 Ω, as shown in the figure. The least count of the scale used in the metre bridge is 1 mm. The unknown resistance is

A. 60 ± 0.15 Ω

B. 135 ± 0.56 Ω

C. 60 ± 0.25 Ω

D. 135 ± 0.23 Ω

Q. 4 Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii R/2, R and 2R respectively as shown in figure. If magnitudes of the electric fields at point P at a distance R from the center of spheres 1, 2 and 3 are E₁, E₂ and E₃ respectively then

A. E₁>E₂>E₃

B. E₃>E₁>E₂

C. E₂>E₁>E₃

D. E₃>E₂>E₁

Q. 5 A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter 11.54 mm on top of the block. The refractive index of the liquid is

A. 1.21

B. 1.30

C. 1.36

D. 1.42

Q. 6 Parallel rays of light of intensity l = 912 Wm⁻² are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant σ = 5.7 x 10⁻⁸ Wm⁻² K⁻⁴ and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to

A. 330 K

B. 660 K

C. 990 K

D. 1550 K

Q. 7 A metal surface is illuminated by the light of two different wavelengths 248 nm and 310 nm. The maximum speed of the photoelectrons corresponding to these wavelengths is u₁ and u₂ respectively. If the ratio u₁:u₂ = 2:1 and hc = 1240 eV nm, the work function of the metal is nearly

A. 3.7 eB

B. 3.2 eV

C. 2.8 eV

D. 2.5 eV

Q. 8 If λᵤ is the wavelength of Kₐ X-ray line of copper (atomic number 29) and λₘₒ is the wavelength of the Kₐ X-ray line of molybdenum (atomic number 42), then the ratio λᵤ/λₘₒ is close to

A. 1.99

B. 2.14

C. 0.50

D. 0.48

Q. 9 A planet of radius R = 1/10 x (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth $/5 on it and lower a wire of the same length and of linear mass density 10⁻³ kgm⁻¹ into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth = 6 x 10⁶m and the acceleration to gravity on Earth is 10 ms⁻²)

A. 96 N

B. 108 N

C. 120 N

D. 150 N

Q. 10 A glass capillary tube is in the shape of a truncated cone with an apex angle α so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height h, where the radius of its cross section is b. If the surface tension of water is S, its density is p, and its contact angle with glass is θ, the value of h will be (g is the acceleration due to gravity)

A. (2S/bpg)cos (θ – α)

B. (2S/bpg)cos (θ + α)

C. (2S/bpg)cos (θ – α/2)

D. (2S/bpg)cos (θ + α/2)

Questions: 11 – 12

In the figure a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. The lower compartment of the container is filled with 2 moles of an ideal monatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. The heat capacities per mole of an ideal monatomic gas are Cᵥ – 3/2R, Cₚ = 5/2R and those for an ideal diatomic gas are Cᵥ = 5/2, Cₚ = 7/2R

Q. 11 Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the final temperature of the gases will be

A. 550 K

B. 525 K

C. 513 K

D. 490 K

Q. 12 Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. Then total work done by the gases till the time they achieve equilibrium will be

A. 250 R

B. 200 R

C. 100 R

D. -100 R

Questions: 13 – 14

A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm respectively. The upper end of the container is open to the atmosphere.

Q. 13 If the piston is pushed at a speed of 5 mms⁻¹, the air comes out of the nozzle with a speed of

A. 0.1 ms⁻¹

B. 1 ms⁻¹

C. 2 ms⁻¹

D. 8 ms⁻¹

Q. 14 If the density of air is Pₐ and that of the liquid Pl, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to

A. √Pₐ/Pₗ

B. √PₐPₗ

C. √Pₗ/Pₐ

D. Pₗ

Questions: 15 – 16

The figure shows a circular loop of radius a with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is d. The loop and the wires are carrying the same current I. The current in the loop is in the counter-clockwise direction if seen from above.

Q. 15 When d ≈ a but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height h above the loop. In that case

A. Current in wire 1 and wire 2 is the direction PQ and RS respectively and h ≈ a

B. Current in wire 1 and wire 2 is the direction PQ and SR respectively and h ≈ a

C. Current in wire 1 and wire 2 is the direction PQ and SR respectively and h ≈ 1.2a

D. Current in wire 1 and wire 2 is the direction PQ and RS respectively and h ≈ 1.2a

Q. 16 Consider d>>a and the loop is rotated about its diameter parallel to the wires by 30° from the position shown in the figure. If the current in the wires are in the opposite directions, the torque on the loop at its new positions will be (assume that the net field due to the wires is constant over the loop)

A. μ₀I²a²/d

B. μ₀I²a²/2d

C. √3 μ₀I²a²/d

D. √3 μ₀I²a²/2d

Q. 17 Four charges Q₁, Q₂, Q₃ and Q₄ of same magnitude are fixed along the x axis at x = -2a, -a, +a and +2a respectively. A positive charge q is placed on the positive y axis at a distance b > 0. Four options of the signs of these charges are given in List I. The direction of the forces on the charge q is given in List II. Match List I and II and select the correct answer.

A. P-3, Q-1, R-4, S-2

B. P-4, Q-2, R-3, S-1

C. P-3, Q-1, R-2, S-4

D. P-4, Q-2, R-1, S-3

Q. 18 Four combinations of two thin lenses are given in list I. The radius of curvature of all curved surfaces is r and the refractive index of all the lenses is 1.5. Match lens combinations in List I with their focal length in List II and select the correct answer.

A. P-1, Q-2, R-3, S-4

B. P-2, Q-4, R-3, S-1

C. P-4, Q-1, R-2, S-3

D. P-2, Q-1, R-3, S-4

Q. 19 A block of mass m₁ = 1 kg another mass m₂ = 2 kg, are placed together (see figure) on an inclined plane with angle of inclination θ. Various values of θ are given in List I. The coefficient of friction between the block m₁ and the plane is always zero. The coefficient of static and dynamic friction between the blocks m₂ are given. Match the correct expression of the friction in List II and the angles given in List I, and choose the correction. The acceleration due to gravity is denoted by g. [Useful information: tan(5.5°) ≈ 0.1; tan(11.5°) ≈ 0.2; tan(16.5°) ≈ 0.3]

A. P-1, Q-1, R-1, S-3

B. P-2, Q-2, R-2, S-3

C. P-2, Q-2, R-2, S-4

D. P-2, Q-2, R-3, S-3

Q. 20 A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance of 1.2 m from the person. In the following, state of the lift’s motion is given in List I and the distance where the water jet hits the floor of the lift is given in List II. Match the statements from List I with those in List II and select the correct answer.

A. P-2, Q-3, R-2, S-4

B. P-2, Q-3, R-1, S-4

C. P-1, Q-1, R-1, S-4

D. P-2, Q-3, R-1, S-1

Q. 21 The acidic hydrolysis of ether (X) shown below is fastest when

A. One phenyl group is replaced by a methyl group

B. One phenyl group is replaced by a para-methoxyphenyl group

C. Two phenyl groups are replaced by two para-methoxyphenyl groups

D. No structural change is made to X.

Q. 22 Isomers of hexane, based on their branching, can be divided into three distinct classes as shown in the figure. the correct order of their boiling point is

A. I >II>III

B. III >II>I

C. II >III>I

D. III >I>II

Q. 23 The major product in the following reaction is

A. A

B. B

C. C

D. D

Q. 24 Hydrogen peroxide in its reaction with KIO₄ and NH₂OH respectively, is acting as a

A. Reducing agent, oxidising agent

B. Reducing agent, reducing agent

C. Oxidising agent, oxidising agent

D. Oxidising agent, reducing agent

Q. 25 The product formed in the reaction SOCl₂ with white phosphorus is

A. PCl₃

B. SO₂Cl₂

C. SCl₃

D. POCl₃

Q. 26 Under ambient conditions, the total number of gases released as products in the final step of the reaction scheme shown below is

A. 0

B. 1

C. 2

D. 3

Q. 27 For the identification of β – naphthol using dye test, it is necessary to use

A. Dichloromethane solution of β-naphthol

B. Acidic solution of β-naphthol

C. Neutral solution of β-naphthol

D. Alkaline solution of β-naphthol

Q. 28 For the elementary reaction M → N, the rate of disappearance of M increases by a factor of 8 upon doubling the concentration of M. The order of the reaction with respect to M I s

A. 4

B. 3

C. 2

D. 1

Q. 29 For the process H₂O (l) → H₂O (g) at T = 100°C and 1 atmosphere pressure, the correct choice is

A. ΔS.system > 0 and ΔS.surroundings > 0

B. ΔS.system > 0 and ΔS.surroundings < 0

C. ΔS.system < 0 and ΔS.surroundings > 0

D. ΔS.system < 0 and ΔS.surroundings < 0

Q. 30 Assuming 2s – 2p mixing is NOT operative, the paramagnetic species among the following is

A. Be₂

B. B₂

C. C₂

D. N₂

Questions: 31 – 32

Schemes 1 and 2 describe sequential transformation of alkynes M and N.

consider only the major products formed in each step for both the schemes.

Q. 31 The product X is

A. A

B. B

C. C

D. D

Q. 32 The correct statement with respect to product Y is

A. It gives positive Tollens test and is a functional isomer of X

B. It gives positive Tollens test and is a geometrical isomer of X

C. It gives a positive iodoform test and is a functional isomer of X

D. It gives a positive iodoform test and is a geometrical isomer of X

Questions: 33 – 34

An aqueous solution of metal ion M1 reacts separately with reagents Q and R in excess to give tetrahedral and square planar complexes, respectively. And aqueous solution of another metal ion M2 always reforms tetrahedral complexes with these reagents. Aqueous solution of M2 on reaction with reagent S gives white precipitate which dissolves in excess of S. The reactions are summarized in the figure given below.

Q. 33 M1, Q and R respectively are

A. Zn²⁺, KCN and HCl

B. Ni²⁺, HCl and KCN

C. Cd²⁺, KCN and HCl

D. Co²⁺, HCL and KCN

Q. 34 Reagent S is

A. K₄[Fe(CN)₆]

B. Na₂HPO₄

C. K₂CrO₄

D. KOH

Questions: 35 – 36

X and Y are two volatile liquids with molar weights of 10 g mol⁻¹ and 40 g mol⁻¹ respectively. two cotton plugs, one soaked in X and the other soaked in Y, are simultaneously placed at the ends of a tube of length L = 24 cm, as shown in the figure. The tube is filled with an inert gas at 1 atmosphere pressure and a temperature of 300 K. Vapours of X and Y react to form a product which is first observed at a distance d cm from the plug soaked in X. take X and Y to have equal molecular diameters and assume ideal behaviour of the inert gas and the two vapours.

Q. 35 The value of d in cm (shown in figures) as estimated from Graham’s law is

A. 8

B. 12

C. 16

D. 20

Q. 36 The experimental value of d is found to be smaller than the estimate obtained using Graham’s law. This is due to

A. Larger mean free path for X as compared to that of Y

B. Larger mean free path for Y as compared to that of X

C. Increased collision frequency of Y with the inert gas as compared to that of X with the inert gas

D. Increased collision frequency of X with the inert gas as compared to that of Y with the inert gas

Q. 37 Different possible thermal decomposition pathways for peroxy esters are shown below. Match each pathway from List I with an appropriate structure from List II and select the correct answer.

A. P-1, Q-3, R-4, S-2

B. P-2, Q-4, R-3, S-1

C. P-4, Q-1, R-2, S-3

D. P-3, Q-2, R-1, S-4

Q. 38 Match the four starting materials (P, Q, R, S) given in List I with the corresponding reaction schemes (I, II, III, IV) provided in List II and select the correct answer.

A. P-1, Q-4, R-2, S-3

B. P-3, Q-1, R-4, S-2

C. P-3, Q-4, R-2, S-1

D. P-4, Q-1, R-3, S-2

Q. 39 Match each coordination compound in List I with an appropriate pair of characteristics from List __ and select the correct answer. {en = H₂NCH₂CH₂NH₂; atomic numbers: Ti = 22;

Cr = 24; Co = 27; Pt = 78}

A. P-4, Q-2, R-3, S-1

B. P-3, Q-1, R-4, S-2

C. P-2, Q-1, R-3, S-4

D. P-1, Q-3, R-4, S-2

Q. 40 Match the orbital overlap figures shown in List I with the description given in List Ii and select the correct answer.

A. P-2, Q-1, R-3, S-4

B. P-4, Q-3, R-1, S-2

C. P-2, Q-3, R-1, S-4

D. P-4, Q-1, R-3, S-2

Q. 41 The function y = f(x) is the solution of the differential equation in the image in (-1, 1) satisfying f(0) = 0. Then the value of the integral in the image is

A. π/3 – √3/2

B. π/3 – √3/4

C. π/6 – √3/4

D. π/6 – √3/2

Q. 42 The value of the integral in the image is equal to

A. A

B. B

C. C

D. D

Q. 43 Coefficient of x¹¹ in the expansion of (1 + x²)⁴(1 + x³)⁷(1 + x⁴)¹² is

A. 1051

B. 1106

C. 1113

D. 1120

Q. 44 Let f:[0, 2] → R be function which is continuous on [0, 2] and is differentiable on (0, 2) with f(0) = 1. Let the integral in the image, for x ϵ [0, 2]. If F’(x) = f’(x) for all x ϵ (0, 2), then F(2) equals

A. e² – 1

B. e⁴ – 1

C. e – 1

D. e⁴

Q. 45 The common tangents to the circle x² + y² = 2 and the parabola y² = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is

A. 3

B. 6

C. 9

D. 15

Q. 46 For x ϵ (0, π) the equation sin x + 2 sin 2x – sin 3x = 3 has

A. Infinitely many solutions

B. Three solutions

C. One solution

D. No solution

Q. 47 In a triangle the sum of two sides is x and the product of the same two sides is y. I f x² – c² = y, where c is the third side of the triangle, then the ratio of the in-radius to the circumradius of the triangle is

A. 3y/2x(x+c)

B. 3y/2c(x+c)

C. 3y/4x(x+c)

D. 3y/4c(x+c)

Q. 48 Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done is

A. 264

B. 265

C. 53

D. 67

Q. 49 Three boys and two girls stand in a queue. The probability that the number of boys ahead of every girl is at least one more than the number of girls ahead of her is

A. 1/2

B. 1/3

C. 2/3

D. 3/4

Q. 50 The quadratic equation p(x) = 0 with real coefficients has purely imaginary roots. Then the equation p(p(x)) = 0 has

A. Only purely imaginary roots

B. All real roots

C. Two real and two purely imaginary roots

D. Neither real nor purely imaginary roots

Questions: 51 – 52

Let a, r, s, t be nonzero real numbers. Let P(at², 2at), Q, R(ar², 2ar) and S(as², 2as) be distinct points on the parabola y² = 4ax. Suppose that PQ is the focal chord and lines QR and PK are parallel, where K is the point (2a, 0).

Q. 51 The value of r is

A. -1/t

B. (t²+1)/t

C. 1/t

D. (t²-1)/t

Q. 52 If st = 1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is

A. (t²+1)²/2t³

B. a(t²+1)²/2t³

C. a(t²+1)²/t³

D. a(t²+2)²/t³

Questions: 53 – 54

Given that for each a ϵ (0, 1), the equation in the image exists. Let the limit be g(a). In addition, it is given that the function g(a) is differentiable on (0, 1).

Q. 53 The value of g(1/2) is

A. π

B. 2π

C. π/2

D. π/4

Q. 54 The value of g’(1/2) is

A. π/2

B. π

C. -π/2

D. 0

Questions: 55 – 56

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3, 4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let xᵢ be the number on the card drawn from the i^th box, I = 1, 2, 3.

Q. 55 The probability that x₁ + x₂ + x₃ is odd, is

A. 29/105

B. 53/105

C. 57/105

D. 1/2

Q. 56 The probability that x₁, x₂, x₃ are in an arithmetic progression is

A. 9/105

B. 10/105

C. 11/105

D. 7/105

Q. 57 Match the elements of List I and List II.

A. P-1, Q-2, R-4, S-3

B. P-2, Q-1, R-3, S-4

C. P-1, Q-2, R-3, S-4

D. P-2, Q-1, R-4, S-3

Q. 58 P-3, Q-2, R-4, S-1

A. P-3, Q-2, R-4, S-1

B. P-2, Q-3, R-4, S-1

C. P-3, Q-2, R-1, S-4

D. P-2, Q-3, R-1, S-4

Q. 59 Match the elements of List I and List II.

A. P-4, Q-3, R-2, S-1

B. P-2, Q-4, R-3, S-1

C. P-4, Q-3, R-1, S-2

D. P-2, Q-4, R-1, S-3

Q. 60 Let f₁:R → R, f₂:[0, ∞) → R, f₃:R → R and f₄:R → [0, ∞) be defined by equations in the image. Match the elements of List I and List II.

A. P-3, Q-1, R-4, S-2

B. P-1, Q-3, R-4, S-2

C. P-3, Q-1, R-2, S-4

D. P-1, Q-3, R-2, S-4

Answer Sheet |
||||||||||

Question |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |

Answer | B | D | C | C | C | A | A | B | B | D |

Question |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |

Answer | D | D | C | A | C | B | A | B | D | C |

Question |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |

Answer | C | B | D | A | A | C | D | B | B | C |

Question |
31 |
32 |
33 |
34 |
35 |
36 |
37 |
38 |
39 |
40 |

Answer | A | C | B | D | C | D | A | C | B | C |

Question |
41 |
42 |
43 |
44 |
45 |
46 |
47 |
48 |
49 |
50 |

Answer | B | A | C | B | D | D | B | C | A | D |

Question |
51 |
52 |
53 |
54 |
55 |
56 |
57 |
58 |
59 |
60 |

Answer | D | B | A | D | B | C | C | D | A | D |

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