Engineering Entrance Exam - Page 3 of 5

JEE Advanced 2014 Paper II Previous Year Paper

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 λ􀀁ᵤ 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 λ􀀁ᵤ/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

JEE Advanced 2014 Paper I Previous Year Paper

JEE Advanced 2014 Paper 1

Q. 1 At time t = 0, terminal A in the circuit shown in the figure is connected to B by a key and an alternating current I(t) = I₀cos(wt), with I₀ = 1A and w = 500 rad s⁻¹ starts flowing in it with the initial direction shown in the figure. At t = 7π/6w, the key is switched from B to D. Now

onwards only A and D are connected. A total charge Q flows from the battery to charge the capacitor fully. If C = 20μF, R = 10 Ω and the battery is ideal with emf of 50V, identify the correct statement(s).

A. Magnitude of the maximum charge on the capacitor before t = 7π/6w is 1×10⁻³ C.

B. The current in the left part of the circuit just before t = 7π/6w is clockwise.

C. Immediately after A is connected to D, the current in R is 10A.

D. Q = 2×10⁻³ C.

Q. 2 A light source, which emits two wavelengths λ₁ = 400 nm and λ₂ = 600 nm, is used in a Young’s double slit experiment. If recorded fringe widths for λ₁ and λ₂ are β₁ and β₂, number of fringes for them within a distance y on one side of the central maximum are m₁ and m₂, respectively, then

A. β₁ > β₂

B. m₁ > m₂

C. From the central maximum, 3rd maximum of λ₂ overlaps with 5th minimum of λ₁

D. The angular separation of fringes of λ₁ is greater than λ₂

Q. 3 One end of a taut string of length 3m along the x-axis is fixed at x = 0. The speed of the waves in the string is 100 ms⁻¹. The other end of the string is vibrating in the y-direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is (are)

A. y(t) = A sin πx/6 cot 50πt/3

B. y(t) = A sin πx/3 cos 100πt/3

C. y(t) = A sin 5πx/6 cos 250πt/3

D. y(t) = A sin 5πx/2 cos 250πt

Q. 4 A parallel plate capacitor has a dielectric slab of dielectric constant K between its plates that covers 1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is C while that of the portion with di-electric in between is C₁. When the capacitor is charged, the plate area covered by the dielectric gets charge Q₁ and the rest of the area gets charge Q₂. The electric field in the dielectric is E₁ and that in the other portion is E₂. Choose the correct option(s), ignoring edge effects.

A. E₁/E₂ = 1

B. E₁/E₂ = 1/K

C. Q₁/Q₂ = 3/K

D. C₁/C₂ = 2+K/K

Q. 5 Let E₁(r), E₂(r) and E₃(r) be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density x, and an infinite plane with uniform surface charge density d. If E₁(r₀) = E₂(r₀) = E₃(r₀) at a given distance r₀, then

A. Q = 4σπ(r₀)²

B. r₀ = x/2πσ

C. E₁(r₀/2) = 2E₂(r₀/2)

D. E₂(r₀/2) = 4E₃(r₀/2)

Q. 6 A student is performing an experiment using a resonance column and a tuning fork of frequency 244 s⁻¹. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is (0.350 + or 0.005)m, the gas in the tube is (Useful information: Root of 167RT = 640 J¹/² mole⁻¹/², √140RT = 590 J¹/² mole⁻¹/². The molar masses M in grams are given in the options. Take the values of root of 10/M for each gas as given there.)

A. Neon (M = 20, √(10/20) = 7/10)

B. Nitrogen (M = 28, √(10/28) = 3/5)

C. Oxygen (M = 32, √(10/32) = 9/16)

D. Argon (M = 36, √(10/36) = 17/32)

Q. 7 Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the temperature of 0.5kg water by 40K. This heater is replaced by a new heater having two wires of the same material, each of length L and diameter 2d. The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by 40K?

A. 4 if wires are in parallel

B. 2 if wires are in series

C. 1 if wires are in series

D. 0.5 if wires are in parallel

Q. 8 In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle θ with the horizontal floor. The coefficient of friction between the wall and the ladder is μ₁ and that between the floor and the ladder is μ₂. The normal reaction of the wall on the ladder is N₁ and that of the floor is N₂. If the ladder is about to slip, then

A. μ₁ = 0, μ₂ ≠ 0 and N₂ tanθ = mg/2

B. μ₁ ≠ 0, μ₂ = 0 and N₁ tanθ = mg/2

C. μ₁ ≠ 0, μ₂ ≠ 0 and N₂ = mg/(1+μ₁μ₂)

D. μ₁ = 0, μ₂ ≠ 0 and N₁ tanθ = mg/2

Q. 9 A transparent thin film of uniform thickness and refractive index n₁ = 1/4 is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index n₂ = 1.5, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f₁ from the film, while rays of light traversing from glass to air get focused at distance f₂ from the film. Then

A. |f₁| = 3R

B. |f₁| = 2.8R

C. |f₂| = 2R

D. |f₂| = 1.4R

Q. 10 Two ideal batteries of emf V₁ and V₂ and three resistances R₁, R₂ and R₃ are connected as shown in the figure. The current in resistance R₂ would be zero if

A. V₁ = V₂ and R₁ = R₂ = R₃

B. V₁ = V₂ and R₁ = 2R₂ = R₃

C. V₁ = 2V₂ and 2R₁ =2 R₂ = R₃

D. 2V₁ = V₂ and 2R₁ = R₂ = R₃

Q. 11 Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 degrees and 60 degrees with respect to the horizontal respectively as shown in the figure. The speed of A is 100√3 m/2. At time t = 0 s, an observer in A finds B at a distance of 500m. This observer sees B moving with a constant velocity perpendicular to the line of motion of

A. If at t = t₀, A just escapes being hit by B, t₀ in seconds is

Q. 12 During Searle’s experiment, zero of the Vernier scale lies between 3.20 x 10⁻² m and 3.25 x 10⁻² m of the main scale. The 20th division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of 2 kg is applied to the wire, the zero of the Vernier scale still lies between 3.20 x 10⁻² m and 3.25 x 10⁻² m of the main scale but now the 45th division of Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is 2 m and its cross-sectional area is 8 x 10⁻⁷ m². The least count of the Vernier scale is 1.0 x 10⁻⁵ m. The maximum percentage error in the Young’s modulus of the wire is

Q. 13 A uniform circular disc of mass 1.5 kg and radius 0.5 m is initially at rest on a horizontal frictionless surface. Three forces of equal magnitude F = 0.5 N are applied simultaneously along the three sides of an equilateral triangle XYZ with its vertices on the perimeter of the disc (see figure). One second after applying the forces, the angular speed of the disc in rad s⁻¹ is

Q. 14 Two parallel wires in the plane of the paper are distance X₀ apart. A point charge is moving with speed u between the wires at a distance X₁ from one of the wires. When the wires carry current of magnitude I in the same direction, the radius of curvature of the path of the point charge is R₁. In contrast, if the currents I in the two wires have directions opposite to each other, the radius of curvature of the path is R₂. If X₀/X₁ = 3, the value of R₁/R₂ is

Q. 15 To find the distance d over which a signal can be seen clearly in foggy conditions, a railway engineer uses dimensional analysis and assumes that the distance depends on the mass density p of the fog, intensity (power/area) S of the light from the signal and its frequency f. The engineer finds that d is proportional to S¹/ⁿ. The value of n is

Q. 16 A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990 ohm resistance, it can be converted into a voltmeter of range 0 – 30 V. If connected to a 2n/249 ohm resistance, it becomes an ammeter of range 0 – 1.5 A. The value of n is

Q. 17 Consider an elliptically shaped rail PQ in the vertical plane with OP = 3m and OQ = 4m. A block of mass 1kg is pulled along the rail from P to Q with a force of 18 N, which is always parallel to line PQ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is (n x 10) Joules. The value of n is (take acceleration due to gravity = 10 m/s⁻²)

Q. 18 A rocket is moving in a gravity free space with a constant acceleration of 2 m/s² along +x direction (see figure). The length of a chamber inside the rocket is 4m. A ball is thrown from the left end of the chamber in +x direction with a speed of 0.2 m/s from its right end relative to the rocket. The time in seconds when the two balls hit each other is

Q. 19 A horizontal circular platform of radius 0.5 m and mass 0.45 kg is free to rotate about its axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg are attached to the platform at a distance 0.25 m from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the balls horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the balls have horizontal speed of 9 m/s with respect to the ground. The rotational speed of the platform in rad/s after the balls leave the platform is

Q. 20 A thermodynamic system is taken from an initial state i with internal energy Uᵢ = 100 J to the final state f along two different paths iaf and ibf, as schematically shown in the figure. The work done by the system along the paths af, ib and bf are Wₐ􀀁 = 200 J, Wᵢᵦ= 50 J and Wᵦ􀀁 = 100 J respectively. The heat supplied to the system along the path iaf, ib and bf are Qᵢₐ􀀁, Qᵢᵦ and Qᵦ􀀁 respectively. If the internal energy of the system in the state b is Uᵦ = 200 J and Qᵢₐ􀀁 = 500 J, the ratio Qᵦ􀀁/Qᵢᵦ is

Q. 21 The correct combination of names for isomeric alcohols with molecular formula C₄H₁₀O is/are

A. tert-butanol and 2-methylpropan-2-ol

B. tert-butanol and 1, 1=dimethylethan-1-ol

C. n-butanol and butan-1-ol

D. isobutyl alcohol and 2-methylpropan-1-ol

Q. 22 The reactivity of compound Z with different halogens under appropriate conditions is given. The observed pattern of electrophilic substitution can be explained by

A. the steric effect of the halogen

B. the steric effect of the tert-butyl group

C. the electronic effect of the phenolic group

D. the electronic effect of the tert-butyl group

Q. 23 In the reaction shown, the major product(s) formed is/are

A. (A)

B. (B)

C. (C)

D. (D)

Q. 24 An ideal gas in a thermally insulated vessel at internal pressure = P₁, volume – V₁ and absolute temperature = T₁ expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are P₂, V₂ and T₂, respectively. For this expansion,

A. q = 0

B. T₂ = T₁

C. P₂V₂ = P₁V₁

D. P₂V₂ʸ = P₁V₁ʸ

Q. 25 Hydrogen bonding plays a central role in the following phenomena:

A. Ice floats in water

B. Higher Lewis basicity of primary amines than tertiary amines in aqueous solutions

C. Formic acid is more acidic than acetic acid

D. Dimerisation of acetic acid in benzene

Q. 26 In a galvanic cell, the salt bridge

A. does not participate chemically in the cell reaction.

B. stops the diffusion of ions from one electrode to another.

C. is necessary for the occurrence of the cell reaction.

D. ensures mixing of the two electrolytic solutions.

Q. 27 Upon heating with Cu₂S, the reagent(s) that give copper metal is/are

A. CuFeS₂

B. CuO

C. Cu₂O

D. CuSO₄

Q. 28 The correct statement(s) for orthoboric acid is/are

A. It behaves as a weak acid in water due to self ionization.

B. Acidity of its aqueous solution increases upon addition of ethylene glycol.

C. It has a three dimensional structure due to hydrogen bonding.

D. It is a weak electrolyte in water.

Q. 29 For the reaction:

I⁻ + ClO₃⁻ + H₂SO₄ —–> Cl⁻ + H₂SO₄⁻ + I₂

The correct statement(s) in the balanced equation is/are:

A. Stoichiometric coefficient of HSO₄⁻ is 6.

B. Iodide is oxidized.

C. Sulphur is reduced.

D. H₂O is one of the products.

Q. 30 The pair(s) of reagents that yield paramagnetic species is/are

A. Na and excess of NH₃

B. K and excess of O₂

C. Cu and dilute HNO₃

D. O₂ and 2-ethylanthraquinol

Q. 31 Consider all possible isometric ketones, including stereoisomers, of MW = 100. All these isomers are independently reacted with NaBH4 (NOTE: stereoisomers are also reacted separately). The total number of ketones that give a racemic product(s) is/are

Q. 32 A list of species having the formula XZ₄ is given below.

XeF₄, SF₄, SiF₄, BF₄⁻, BrF₄⁻, [Cu(NH₃)₄]²⁺, [FeCl₄]²⁻, [CoCl₄]²⁻ and [PtCl4]²⁻ Defining shape on the basis of the location of X and Z atoms, the total number of species having a square planar shape is

Q. 33 Among PbS, CuS, HgS, MnS, Ag2S, NiS, CoS, Bi₂S₃ and SnS₂, the total number of BLACK coloured sulfides is

Q. 34 The total number(s) of stable conformers with non-zero dipole moment for the following compound is (are)

Q. 35 Consider the following list of reagents:

Acidified K₂Cr₂O₇, alkaline KMnO₄, CuSO₄, H₂O₂, Cl₂, O₃, FeCl₃, HNO₃ and Na₂S₂O₃. The total number of reagents that can oxidise aqueous iodide to iodine is

Q. 36 The total number of distinct naturally occurring amino acids obtained by complete acidic hydrolysis of the peptide shown is

Q. 37 In an atom, the total number of electrons having quantum numbers n = 4, |mₗ| = 1 and mₛ = -1/2 is

Q. 38 If the value of Avogadro number is 6.023 x 10²³ mol⁻¹ and the value of Boltzmann constant is 1.380 x 10⁻²³ J/K, then the number of significant digits in the calculated value of the universal gas constant is

Q. 39 A compound H₂X with molar weight of 80 g is dissolved in a solvent having density of 0.4 g ml⁻¹. Assuming no change in volume upon dissolution, the molality of a 3.2 molar solution is

Q. 40 MX₂ dissociates into M²⁺ and X⁻ ions in an aqueous solution, with a degree of dissociation (alpha) of 0.5. The ratio of the observed depression of freezing point of the aqueous solution to the value of the depression of freezing point in the absence of ionic dissociation is

Q. 41 Let M and N be two 3×3 matrices such that MN = NM. Further, if M ≠ N² and M² = N⁴, then

A. determinant of (M² + MN²) is 0

B. there is a 3×3 non-zero matrix U such that (M² + MN²)U is the zero matrix

C. determinant of (M² + MN²) ≥ 1

D. for a 3×3 matrix U, if (M² + MN²) U equals the zero matrix then U is the zero matrix

Q. 42 For every pair of continuous functions f, g:[0, 1] —> ℝ such that max {f(x): x ∈ [0, 1]} = max{g(x):x is ∈ [0, 1]}, the correct statement(s) is (are):

A. (f(c))² + 3f(c) = (g(c))² + 3g(c) for some c ∈ [0, 1]

B. (f(c))² + f(c) = (g(c))² + 3g(c) for some c ∈ [0, 1]

C. (f(c))² + 3f(c) = (g(c))² + g(c) for some c ∈ [0, 1]

D. (f(c))² = (g(c))² for some c ∈ [0, 1]

Q. 43 f:(0, infinity) —-> ℝ is given. Then

A. f(x) is monotonically increasing on [1, ∞ )

B. f(x) is monotonically decreasing on (0, 1)

C. f(x) + f(1/x) = 0, for all x ∈ (0, ∞)

D. f(2ˣ) is an odd function of x on ℝ

Q. 44 Let a is an element of ℝ and let f: ℝ —-> ℝ be given by f(x) = x⁵ – 5x + a. Then

A. f(x) has three real roots if a > 4

B. f(x) has only one real root if a > 4

C. f(x) has three real roots if a < -4

D. f(x) has three real roots is -4 < a < 4

Q. 45 Let f:[a, b] —> [1, infinity) be a continuous function and let g : ℝ—> ℝbe defined as Then

A. g(x) is continuous but not differentiable at a

B. g(x) is differentiable on ℝ

C. g(x) is continuous but not differentiable at b

D. g(x) is continuous and differentiable at either a or b but not both

Q. 46 Let f:(-π/2, π/2) —-> ℝ be given by f(x) = (log(secx + tanx))³ Then

A. f(x) is an odd function

B. f(x) is a one-one function

C. f(x) is an onto function

D. f(x) is an even function

Q. 47 From a point P(λ, λ, λ) perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1 and y = -x, z = -1. If P is such that angle QPR is a right angle, then the possible value(s) of λ is (are)

A. √2

B. 1

C. -1

D. – √ 2

Q. 48 Let x, y and z be three vectors each of magnitude √2 and the angle between each pair of them is π⁄ 3. If a is a nonzero vector perpendicular to x and yxz and b is a nonzero vector perpendicular to y and z × x, then

A. b = (b.z)(z-x)

B. a = (a.y)(y-z)

C. a.b = -(a.y)(b.z)

D. a = (a.y)(z-y)

Q. 49 A circle S passes through the point (0, 1) and is orthogonal to the circles (x-1)² + y² = 16 and x² + y² = 1. Then

A. radius of S is 8

B. radius of S is 7

C. centre of S is (-7, 1)

D. centre of S is (-8, 1)

Q. 50 Let M be a 2×2 symmetric matrix with integer entries. Then M is invertible is

A. the first column of M is the transpose of the second row of M

B. the second row of M is the transpose of the first column of M

C. M is a diagonal matrix with nonzero entries in the main diagonal

D. the product of entries in the main diagonal of M is not the square of an integer

Q. 51 Let a, b, c be positive integers such that b/a is an integer. If a, b, c are in geometric progression and the arithmetic mean of a, b, c is b+2, then the value of a² + a – 14/a+1 is

Q. 52 Let n ≥ 2 be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of n is

Q. 53 Let n₁ < n₂ < n₃ < n₄ < n₅ be positive integers such that n₁ + n₂ + n₃ + n₄ + n₅ = 20. Then the number of such distinct arrangements (n₁, n₂, n₃, n₄, n₅) is

Q. 54 Let f : ℝ—> ℝ and g : ℝ—> ℝ be respectively given by f(x) = |x| + 1 and g(x) = x² + 1. Define h :

ℝ—> ℝ by

h(x) = max{f(x), g(x)} if x <= 0,

h(x) = min{f(x), g(x)} if x > 0.

The number of points at which h(x) is not differentiable is

Q. 55 The value of the given integral is

014x3d2dx2(1-x2)5dx

Q. 56 The slope of the tangent to the curve (y-x⁵)² = x(1+x²)² at the point (1, 3) is

Q. 57 The largest value of the nonnegative integer a for which the given condition applies is

Q. 58 Let f:[0, 4π] —> [0, π] be defined by f(x) = cos⁻¹(cosx). The number of points x ∈ [0, 4π] satisfying the equation f(x) = 10-x/10 is

Q. 59 For a point P in the plane, let d₁(P) and d₂(P) be the distances of the point P from the lines x – y = 0 and x + y = 0 respectively. The area of the region R consisting of all points P lying in the first quadrant of the plane and satisfying 2 ≤ d₁(P) + d₂(P) ≤ 4, is

Q. 60 Let a, b, and c be three non-coplanar unit vectors such that the angle between every pair of them is π/3. If axb + bxc = pa + qb + rc, where p, q and r are scalars, then the value of (p² + 2q² + r²)/q² is

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	CD	ABC	ACD	AD	C	D	BD	CD	AC	ABD
Question	11	12	13	14	15	16	17	18	19	20
Answer	5	4	2	3	3	5	4	2 OR8	4	2
Question	21	22	23	24	25	26	27	28	29	30
Answer	ACD	ABC	A	ABC	ABD	AC	BCD	BD	ABD	ABC
Question	31	32	33	34	35	36	37	38	39	40
Answer	5	4	6 OR 7	3	7	1	6	4	8	2
Question	41	42	43	44	45	46	47	48	49	50
Answer	AB	AD	ACD	BD	AC	ABC	C	ABC	BC	CD
Question	51	52	53	54	55	56	57	58	59	60
Answer	4	5	7	3	2	8	0	3	6	4

JEE Advanced 2013 Paper II Previous Year Paper

JEE Advanced 2013 Paper 2

Q. 1 Using the expression 2d sinθ = λ, one calculates the values of d by measuring the corresponding angles θ in the range 0 to 90°. The wavelength λ is exactly known and the error in θ is constant for all values of θ. As θ increases from 0°.

A. the absolute error in d remains constant

B. the absolute error in d increases

C. the fractional error in d remains constant

D. the fractional error in d decreases

Q. 2 Two non conducting spheres of radii R₁ and R₂ and carrying uniform volume charge densities +p and -p respectively, are placed such that they partially overlap, as shown in figure (1). At all points in the overlapping region

A. The electrostatic field is zero

B. The electrostatic potential is constant

C. The electrostatic field is constant in magnitude

D. The electrostatic field has same direction

Q. 3 The figure (1) shows the variation of specific heat capacity (C) of a solid as a function of temperature (T). The temperature is increased continuously from 0 to 500 K at a constant rate. Ignoring any volume change, the following statement(s) is (are) correct to a reasonable approximation.

A. the rate at which heat is absorbed in the range 0 – 100 K varies linearly with temperature (T).

B. heat absorbed in increasing the temperature from 0 – 100 K is less than the heat required for increasing the temperature from 400 – 500 K.

C. there is no change in the rate of heat absorption in the range 400 – 500 K.

D. the rate of heat absorption increases in the range 200 – 300 K

Q. 4 The radius of the orbit of an electron in a Hydrogen – like atom is 4.5 ao, where ao is the Bohr radius. Its orbital angular momentum is 3h / 2π. It is given that h is Planck constant and R is Rydberg constant. The possible wavelength(s), when the atom de-excites, is (are)

A. 9 / 32R

B. 9 / 16R

C. 9 / 5R

D. 4 / 3R

Q. 5 Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are)

A. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 4√GM/L

B. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 2√GM/L

C. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is √2GM/L

D. The energy of the mass m remains constant

Q. 6 A particle of mass m is attached to one end of a massless spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u₀. When the speed of the particle is 0.5 u₀, it collides elastically with a rigid wall. After this collision

A. the speed of the particle when it returns to its equilibrium position is u₀

B. the time at which the particle passes through the equilibrium position for the first time is t = π√m/k

C. the time at which the maximum compression of the spring occurs is t = 4π/3 √m/k

D. the time at which the particle passes through the equilibrium position for the second time is t = 5π/3√m/k

Q. 7 A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. The cylinder is placed co-axially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady current I. Consider a point P at a distance r from the common axis. The correct statement(s) is (are)

A. In the region 0 < r < R, the magnetic field is non-zero.

B. In the region R < r < 2R, the magnetic field is along the common axis.

C. In the region R < r < 2R, the magnetic field is tangential to the circle of radius r, centered on the axis.

D. In the region r > 2R, the magnetic field is non-zero.

Q. 8 Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. A wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency f₁. An observer in the other vehicle hears the frequency of the whistle to be f₂. The speed of sound in still air is V. The correct statement(s) is (are)

A. If the wind blows from the observer to the source, f₂ > f₁.

B. If the wind blows from the source to the observer,f₂ > f₁

C. If the wind blows from the observer to the source, f₂ < f₁

D. If the wind blows from the source to the observer, f₂ < f₁.

Questions: 9 – 10

A point charge Q is moving in a circular orbit of radius R in the x-y plane with an angular velocity ω. This can be considered as equivalent to a loop carrying a steady current Qω / 2π. A uniform magnetic field along the positive z-axix is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant γ.

Q. 9 The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is

A. BR / 4

B. BR / 2

C. BR

D. 2BR

Q. 10 The charge in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is

A. -⋎BQR²

B. -⋎(BQR² / 2)

C. -⋎(BQR²/ 2)

D. -⋎BQR²

Questions: 11 – 12

The mass of a nucleus (A)(Z)X is less than the sum of masses of (A-Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into light nuclei of masses m₁ and m₂ only if (m₁ + m₂) < M. Also two light nuclei of masses m₃ and m₄ can undergo complete fusion and form a heavy nucleus of mass M’ only if (m₃ + m₄) > M’. The masses of some neutral atoms are given in table

Q. 11 The correct statement is

A. The nucleus (6)(3)Li can emit an alpha particle

B. The nucleus (210)(84)P0 can emit a proton

C. Deutron and alpha particle can undergo complete fusion

D. The nuclei (70)(30)Zn and (82)(34)Se can undergo complete fusion

Q. 12 The Kinetic energy (in keV) of alpha particle, when the nucleus (210)(84)Po at rest undergoes alpha decay, is

A. 5319

B. 522

C. 5707

D. 5818

Questions: 13 – 14

A small block of mass 1 kg is released from rest at the top of a rough track. The track is a circular arc of radius 40m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure (1), is 150 J. (Take the acceleration due to gravity, g =10ms⁻²).

Q. 13 The speed of the block when it reaches the point Q is:

A. 5 ms⁻¹

B. 10 ms⁻¹

C. 10√3 ms⁻¹

D. 20 ms⁻¹

Q. 14 The magnitude of the normal reaction that acts on the block at the point Q is:

A. 7.5 N

B. 8.6 N

C. 11.5 N

D. 22. 5 N

Questions: 15 – 16

A thermal power plant produces electric power of 600 kW at 4000 V, which is to be transported to a place 20 km away from the power plant for consumers’ usage. It can be transported either directly with a cable of large current carrying or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformer, the dissipation is much smaller. In this method, a step-up transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers’ end, a step-down transformer is used to supply power to the consumers ta the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformer are ideal with a power factor unity. All the currents and voltages mentioned are rms values.

Q. 15 If the direct transmission method with a cable of resistance 0.4 Ω km⁻¹ is used, the power dissipation (in %) during transmission is:

A. 20

B. 30

C. 40

D. 50

Q. 16 In the method using the transformers, assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is 1 : 10. If the power to the consumers has to be supplied at 200 V, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is:

A. 200 : 1

B. 150 : 1

C. 100 : 1

D. 50 : 1

Q. 17 Match list I with list II (given in figure (1)) and select the correct answer using the codes given below:

List I	List II
P.	Boltzamnn constant	1.	ML2T-1
Q.	Coefficient of viscosity	2.	ML-1T-1
R.	Planck constant	3.	MLT-3K-1
S.	Thermal conductivity	4.	ML2T-2K-1

A. P3, Q1, R2, S4

B. P3, Q2, R1, S4

C. P4, Q2, R1, S3

D. P4, Q1, R2, S3

Q. 18 A right-angled prism of refractive index μ₁ is placed in a rectangular block of refractive index μ₂, which is surrounded by a medium of refractive index μ₃, as shown in figure (1). A ray of light ‘e’ enters the rectangular block at normal incidence. Depending upon the relationship between μ₁, μ₂ and μ₃, it takes one of the four possible paths ‘ef’, ‘eg’, ‘eh’ or ‘ei’. Match the paths in List I with conditions of refractive indices in List II (given in figure (2)) and select the correct answer using the codes given below:

A. P2, Q3, R1, S4

B. P1, Q2, R4, S3

C. P4, Q1, R2, S3

D. P2, Q3, R4, S1

Q. 19 Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process (given if figure (1)) and then select the correct answer using the codes given below the lists:

A. P4, Q2, R1, S3

B. P1, Q3, R2, S4

C. P2, Q1, R4, S3

D. P4, Q3, R2, S1

Q. 20 One mole of a monatomic ideal gas is taken along two cyclic processes E → F → G → E and E → F → H → E as shown in the PV diagram given in figure (1). The processes involved are purely isochoric, isobaric, isothermal or adiabatic. Match the paths in List I with the magnitudes of the work done in List II (given in figure (2)) and select the correct answer using the codes given below:

A. P4, Q3, R2, S1

B. P4, Q3, R1, S2

C. P3, Q1, R2, S4

D. P1, Q3, R2, S4

Q. 21 The correct statement(s) about O₃ is (are) :

A. O – O bond lengths are equal.

B. Thermal decomposition of O₃ is endothermic.

C. O₃ is diamagnetic in nature.

D. O₃ has a bent structure

Q. 22 In the nuclear transmutation given in figure (1), (X, Y) is (are) :

A. (γ, n)

B. (p, D)

C. (n, D)

D. (γ, p)

Q. 23 The carbon-based reduction method is NOT used for the extraction of:

A. tin from SnO₂

B. iron from Fe₂O₃

C. aluminium from Al₂O₃

D. magnesium from MgCO₃ . CaCO₃

Q. 24 The thermal dissociation equilibrium of CaCO₃(s) is studied under different conditions. CaCO₃(s) ⇔ CaO(s) + C0₂(g)

A. ΔH is dependent on T

B. K is independent of the initial amount of CaCO₃

C. K is dependent on the pressure of CO₂ at a given T

D. ΔH is independent of the catalyst, if any.

Q. 25 The Ksp of Ag2CrO4 is 1.1 x 10⁻¹² at 298 K. The solubility (in mol/L) of Ag₂CrO₄ in a 0.1 M AgNO₃ solution is

A. 1.1 x 10⁻¹¹

B. 1.1 x 10⁻¹⁰

C. 1.1 x 10⁻¹²

D. 1.1 x 10⁻⁹

Q. 26 In the following reactions given in figure (1), the product(s) formed is(are) (given in figure (2)):

A. P(major)

B. Q(minor)

C. R(minor)

D. S(major)

Q. 27 The major product(s) among the structure (P), (Q), (R), (S) (given in figure (1)) of the following reaction (given in figure (2)) is(are) :

A. P

B. Q

C. R

D. S

Q. 28 After completion of the reactions (I and II) (given in figure), the organic compound(s) in the reaction mixtures (given in figure (1)) is (are) :

A. Reaction I: P and Reaction II: P

B. Reaction I: U, acetone and Reaction II: Q, acetone

C. Reaction I: T, U, acetone and Reaction II: P

D. Reaction I: R, acetone and Reaction II: S, acetone

Questions: 29 – 30

A fixed mass ‘m’ of a gas is subjected to transformation of states from K to L to M to N and back to K as shown in figure (1):

Q. 29 The succeeding operations that enable this transformation of states are:

A. Heating, cooling, heating, cooling

B. Cooling, heating, cooling, heating

C. Heating, cooling, cooling, heating

D. Cooling, heating, heating, cooling

Q. 30 The pair of isochoric processes among the transformation of states is

A. K to L and L to M

B. L to M and N to K

C. L to M and M to N

D. M to N and N to K

Questions: 31 – 32

The reactions of Cl₂ gas with cold-dilute and hot-concentrated NaOH in water give sodium salts of two (different) oxoacids of chlorine, P and Q, respectively. The Cl₂ gas reacts with SO₂ gas, in presence of charcoal, to give a product R. R reacts with white phosphorous to give a compound S. On hydrolysis, S gives an oxoacid of phosphorous, T.

Q. 31 P and Q, respectively, are the sodium salts of

A. hypochlorus and chloric acids

B. hypochlorus and chlorus acids

C. chloric and perchloric acids

D. chloric and hypochlorus acids

Q. 32 R, S and T, respectively, are:

A. SO₂Cl₂, PCl₅ and H₃PO₄

B. SO₂Cl₂, PCl₃ and H₃PO₃

C. SOCl₂, PCl₃ and H₃PO₂

D. SOCl₂, PCl₅ and H₃PO₄

Questions: 33 – 34

An aqueous solution of a mixture of two inorganic salts, when treated with dilute HCl, gave a precipitate (P) and a filtrate (Q). The precipitate P was found to dissolve in hot water. The filtrate (Q) remained unchanged when treated with H₂S in a dilute mineral acid medium. However, it gave a precipitate (R) with H₂S in an ammoniacal medium. The precipitate R gave a coloured solution (S), when treated with H₂0₂ in an aqueous NaOH medium.

Q. 33 The precipitate P contains

A. Pb²⁺

B. Hg₂²⁺

C. Ag⁺

D. Hg²⁺

Q. 34 The coloured solution S contains

A. Fe₂(SO₄)₃

B. CuSO₄

C. ZnSO₄

D. Na₂CrO₄

Questions: 35 – 36

P and Q are isomers of dicarboxylic acid C₄H₄O₄. Both decolourize Br₂ / H₂O. On heating, P forms the cyclic anhydride. Upon treatment with dilute alkaline KMnO₄, as well as Q, Q could produce one or more than one from S, T and U. (GivEn in figure(1)).

Q. 35 Compounds formed from P and Q are, respectively:

A. Optically active S and optically active pair (T, U)

B. Optically inactive S and optically inactive pair (T, U)

C. Optically active pair (T, U) and optically active S

D. Optically inactive pair (T, U) and optically inactive S

Q. 36 In the reaction sequences given in figure (2), V and W are, respectively (among the options (A), (B), (C), (D) given in figure (3)).

A. (A)

B. (B)

C. (C)

D. (D)

Q. 37 Match the chemical conversions in List I with the appropriate reagents in List II given in figure (1) and select the correct answer using the code given below:

Q. 38 The unbalanced chemical reactions given in List I show missing reagent or condition (?) which are provided in List II (Given in figure (1)). Match List I with List II and select the correct answer using the code given below:

A. P4, Q2, R3, S1

B. P3, Q2, R1, S4

C. P1, Q4, R2, S3

D. P3, Q4, R2, S1

Q. 39 The standard reduction potential data at 25° C is given below:

E° (Fe³⁺, Fe²⁺) = +0.77 V;

E° (Fe²⁺, Fe) = -0.44 V;

E° (Cu²⁺, Cu) = +0.34 V;

E° (Cu⁺, Cu) = +0.52 V

E° [O₂(g) + 4H⁺ + 4e⁻ → 2H₂O] = +1.23 V;

E° [O₂(g) + 2H₂0 + 4e⁻ → 4OH⁻] = +0.40 V;

E° (Cr³⁺, Cr) = -0.74 V;

E° (Cr²⁺, Cr) = -0.91 V;

Match E° of the redox pair in List I with the values given in List II (given in figure (1)) and select the correct answer using the code below:

A. P4, Q1, R2, S3

B. P2, Q3, R4, S1

C. P1, Q2, R3, S4

D. P3, Q4, R1, S2

Q. 40 An aqueous solution of X is added slowly to an aqueous solution of Y as shown in List I. The variation in conductivity of these reactions is given in List II (Both the Lists are given in figure (1)). Match List I and List II and select the correct answer using the code given below.

Q. 41 Let w = √3 + i / 2 and P = {wⁿ : n = 1, 2, 3, …..}. Further H₁ = {z ∈ C : Re z > 1/2} and H₂ = {z ∈ C : Re z < -1/2}, where C is the set of all complex numbers. If z₁ ∈ P ∩ H₁, z₂ ∈ P ∩ H₂ and O represents the origin, then ∠ z₁ Oz₂ =

A. π / 2

B. π / 6

C. 2π / 3

D. 5π / 6

Q. 42 If 3ˣ = 4ˣ⁻¹, then x =

A. 2 log₃2 / 2 log₃2 – 1

B. 2 / 2 – log₂3

C. 1 / 1 – log₄3

D. 2 log₂3 / 2 log₂3 – 1

Q. 43 Let ω be a complex cube root of unity with ω ≠ 1 and P = [Pᵢⱼ] be a n x n matrix with Pᵢⱼ = ωᶦ⁺ʲ. Then P² ≠ 0, when n =

A. 57

B. 55

C. 58

D. 56

Q. 44 The function f(x) = 2 |x| + |x + 2| – ||x + 2| – 2 |x|| has a local minimum or a local maximum at x =

A. -2

B. -2 / 3

C. 2

D. 2 / 3

Q. 45 For a ∈ R (the set of all real numbers), a ≠ -1, in the equation given in figure (1), then a =

A. 5

B. 7

C. -15 / 2

D. -17 / 2

Q. 46 Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length 2√7 on y-axis is (are):

A. x² + y² – 6x + 8y + 9 = 0

B. x² + y² – 6x + 7y + 9 = 0

C. x² + y² – 6x – 8y + 9 = 0

D. x² + y² – 6x – 7y + 9 = 0

Q. 47 Two lines L1 : x = 5, y / 3 – α = z / -2 and L2 : α, y / -1 = z / 2 – α are coplanar. Then α can take value(s):

A. 1

B. 2

C. 3

D. 4

Q. 48 In a triangle PQR, P is the largest angle and cos P = 1 / 3. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle

is (are)

A. 16

B. 18

C. 24

D. 22

Questions: 49 – 50

Let S = S₁ ∩ S₂ ∩ S₃, where

S₁ = {z ∈ C : |z| < 4}

S₂ = {z ∈ C : lm [(z – 1 + √3i) / (1 – √3i)] > 0}

S₃ = {z ∈ C : Re z > 0}

Q. 49 Area of S:

A. 10π / 3

B. 20π / 3

C. 16π / 3

D. 32π / 3

Q. 50 Find the value of the question given in figure (1):

A. 2-√3 / 2

B. 2+√3 / 2

C. 3-√3 / 2

D. 3+√3 / 2

Questions: 51 – 52

A box B₁ contains 1 white ball, 3 red balls and 2 black balls. Another box B₂ contains 2 white balls, 3 red balls and 4 black balls. A third box B₃ contains 3 white balls, 4 red balls and 5 black balls.

Q. 51 If 1 ball is drawn from each of the boxes B₁, B₂ and B₃, the probability that all 3 drawn balls are of the same colour is:

A. 82 / 648

B. 90 / 648

C. 558 / 648

D. 566 / 648

Q. 52 If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B₂ is:

A. 116 / 181

B. 126 / 181

C. 65 / 181

D. 55 / 181

Questions: 53 – 54

Let f: [0, 1] → R (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0) = f(1) and satisfies f”(x) – 2f'(x) + f(x) ≥ eˣ, x ∈ [0, 1].

Q. 53 Which of the following is true for 0 < x < 1?

A. 0 < f(x) < ∞

B. -1/2 < f(x) < 1/2

C. -1/4 < f(x) < 1

D. -∞ < f(x) < 0

Q. 54 If the function eˣ f(x) assumes its minimum in the interval [0, 1] at x = 1/4, which of the following is true?

A. f'(x) < f(x), 1/4 < x < 3/4

B. f'(x) > f(x), 0 < x < 1/4

C. f'(x) < f(x), 0 < x < 1/4

D. f'(x) < f(x), 3/4 < x < 1

Questions: 55 – 56

Let PQ be a focal chord of the parabola y² = 4ax. The tangents to the parabola at P and Q meet at a point lying on the line y = 2x + a, a > 0

Q. 55 Length of chord PQ is

A. 7a

B. 5a

C. 2a

D. 3a

Q. 56 If chord PQ subtends an angle θ at the vertex of y² = 4ax, then tan θ =

A. 2/3√7

B. -2/3√7

C. 2/3√5

D. -2/3√5

Q. 57 A line L : y = mx + 3 meets y-axis at E(0, 3) and the arc of the parabola y² = 16x, 0 ≤ y ≤ 6 at the point F(x₀, y₀). The tangent to the parabola at F(x₀, y₀) intersects the y-axis at G(0, y₁). The slope m of the line L is chosen such that the area of the triangle EFG has a local maximum. Match List I with List II (given in figure (1)) and select the correct answer using the code given below:

A. P4, Q1, R2, S3

B. P3, Q4, R1, S2

C. P1, Q3, R2, S4

D. P1, Q3, R4, S2

Q. 58 Match List I with List II (given in figure (1)) and select the correct answer using the code given below:

A. P4, Q3, R1, S2

B. P4, Q3, R2, S1

C. P3, Q4, R2, S1

D. P3, Q4, R1, S2

Q. 59 Consider the lines L1 : x – 1 /2 = y / -1 = z + 3 / 1, L2 : x – 4 / 1 = y + 3 / 1 = z + 3 / 2 and the planes P1 : 7x + y + 2z = 3, P2 : 3x + 5y – 6z = 4. Let ax + by + cz = d be the equation of the plane passing through the point of intersection of lines L1 and L2, and perpendicular to planes P₁ and P₂. Match List – I with List -II (given in figure (1)) and select the correct answer using the code given below:

A. P3, Q2, R4, S1

B. P1, Q3, R4, R2

C. P3, Q2, R1, S4

D. P2, Q4, R1, S3

Q. 60 Match List – I with List – II (given in figure (1)) and select the correct answer using the code given below:

A. P4, Q2, R3, S1

B. P2, Q3, R1, S4

C. P3, Q4, R1, S2

D. P1, Q4, R3, S2

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

JEE Advanced 2013 Paper I Previous Year Paper

JEE Advanced 2013 Paper 1

Q. 1 The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is

A. 5.112 cm

B. 5.124 cm

C. 5.136 cm

D. 5.148 cm

Q. 2 A ray of light travelling in the direction (1/2)(î + √3ĵ) is incident on a plane mirror. After reflection, it travels along the direction (1/2)(î – √3ĵ). The angle of incidence is

A. 30°

B. 45°

C. 60°

D. 75°

Q. 3 In the Young’s double slit experiment using a monochromatic light of wavelength λ, the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is

A. A

B. B

C. C

D. D

Q. 4 Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is

A. 1 : 4

B. 1 : 2

C. 6 : 9

D. 8 : 9

Q. 5 Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity K and the other 2K. The temperature difference between the ends along the xaxis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is

A. 2.0 s

B. 3.0 s

C. 4.5 s

D. 6.0 s

Q. 6 A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 x 10⁸ m/s. The final momentum of the object is

A. 0.3 x 10⁻¹⁷ kg m/s

B. 1.0 x 10⁻¹⁷ kg m/s

C. 3.0 x 10⁻¹⁷ kg m/s

D. 9.0 x 10⁻¹⁷ kg m/s

Q. 7 A particle of mass m is projected from the ground with an initial speed uo at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed uo. The angle that the composite system makes with the horizontal immediately after the collision is

A. π/4

B. π/4 + α

C. π/2 – α

D. π/2

Q. 8 The work done on a particle of mass m by a force (given in the image, K being a constant of appropriate dimensions), when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is

A. 2Kπ/a

B. Kπ/a

C. Kπ/2a

D. 0

Q. 9 One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is

A. 0.25

B. 0.50

C. 2.00

D. 4.00

Q. 10 The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is ⅔ times the wavelength in free space. The radius of the curved surface

A. 1 m

B. 2 m

C. 3 m

D. 6 m

Q. 11 A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, y(x, t) = (0.01 m) sin [(62.8 m⁻¹) x] cos [(628 s⁻¹) t]. Assuming π= 3.14, the correct statement(s) is (are)

A. The number of nodes is 5.

B. The length of the string is 0.25 m.

C. The maximum displacement of the midpoint of the string, from its equilibrium

position is 0.01 m.

D. The fundamental frequency is 100 Hz.

Q. 12 A solid sphere of radius R and density ρ is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3ρ. The complete arrangement is placed in a liquid of density 2ρ and is allowed to reach equilibrium. The correct statement(s) is (are)

A. A

B. B

C. C

D. D

Q. 13 A particle of mass M and positive charge Q, moving with a constant velocity u̅1 = 4î m/s enters a region of uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x = 0 to x = L for all values of y. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity u̅2 = 2(√3î + ĵ) m/s. The correct statement(s) is (are)

A. The direction of the magnetic field is -z direction.

B. The direction of the magnetic field is +z direction.

C. The magnitude of the magnetic field is 50πM/3Q units

D. The magnitude of the magnetic field is 100πM/3Q units

Q. 14 Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities ρ₁ and ρ₂ respectively, touch each other. The net electric field at a distance 2R from the center of the smaller sphere, along with the line joining the centers of the spheres, is zero. The ratio ρ₁/ρ₂ can be

A. -4

B. -32/25

C. 32/25

D. 4

Q. 15 In the circuit shown in the figure, there are two parallel plate capacitors each of

capacitance C. The switch S₁ is pressed first to fully charge the capacitor C₁ and then released. The switch S₂ is then pressed to charge the capacitor C₂. After some time, S₂ is released and then S₃ is pressed. After some time,

A. the charge on the upper plate of C₁ is 2CV0.

B. the charge on the upper plate of C₁ is CV0.

C. the charge on the upper plate of C₂ is 0.

D. the charge on the upper plate of C₂ is -CV0.

Q. 16 The work functions of Silver and Sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for Silver to that of Sodium is

Q. 17 A freshly prepared sample of a radioisotope of half-life 1386 s has activity 10³ disintegrations per second. Given that In 2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 80 s after

preparation of the sample is

Q. 18 A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in ms-1) of the particle is zero, the speed (in m/s) after 5 s is

Q. 19 A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 10 rad s-I about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius 0.2 m, are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in rad/s) of the system is

Q. 20 A bob of mass m, suspended by a string of length l1, is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l2, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio l1/l2 is

Q. 21 The compound that does NOT liberate CO₂, on treatment with aqueous sodium

bicarbonate solution, is

A. Benzoic acid

B. Benzenesulphonic acid

C. Salicylic acid

D. Carbolic acid (Phenol)

Q. 22 Concentrated nitric acid, upon long standing, turns yellow-brown due to the formation of

A. NO

B. NO₂

C. N₂O

D. N₂O₄

Q. 23 Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25 °C. For this process, the correct statement is

A. The adsorption requires activation at 25 °C.

B. The adsorption is accompanied by a decrease in enthalpy.

C. The adsorption increases with increase of temperature.

D. The adsorption is irreversible.

Q. 24 Sulfide ores are common for the metals

A. Ag, Cu and Pb

B. Ag, Cu and Sn

C. Ag, Mg and Pb

D. Al, Cu and Pb

Q. 25 The arrangement of X- ions around A+ ion in solid AX is given in the figure (not drawn to scale). If the radius of X- is 250 pm, the radius of A⁺ is

A. 104 pm

B. 125 pm

C. 183 pm

D. 57 pm

Q. 26 Upon treatment with ammoniacal H₂S, the metal ion that precipitates as a sulfide is

A. Fe(III)

B. Al(III)

C. Mg(II)

D. Zn(II)

Q. 27 The standard enthalpies of formation of CO₂(g), H₂0(l) and glucose(s) at 25 °C are -400 kJ/mol, -300 kJ/mol and -1300 kJ/mol, respectively. The standard enthalpy of combustion per gram of glucose at 25 °C is

A. + 2900 kJ

B. – 2900 kJ

C. – 16.11 kJ

D. + 16.11 kJ

Q. 28 Consider the following complex ions, P, Q and R.

The correct order of the complex ions, according to their spin-only magnetic moment

values (in B.M.) is

A. R<Q<P

B. Q<R<P

C. R<P<Q

D. Q<P<R

Q. 29 In the reaction,

P + Q → R + S

the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The

concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is

A. 2

B. 0

C. 3

D. 1

Q. 30 KI in acetone, undergoes SN₂ reaction with each of P, Q, R and S. The rates of the reaction vary as

A. P>Q>R>S

B. S>P>R>Q

C. P>R>Q>S

D. R>P>S>Q

Q. 31 The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is(are)

A. A

B. B

C. C

D. D

Q. 32 Among P, Q, R and S, the aromatic compound(s) is/are

A. P

B. Q

C. R

D. S

Q. 33 The hyperconjugative stabilities of tert-butyl cation and 2-butene, respectively, are due to

A. A

B. B

C. C

D. D

Q. 34 Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s) is(are)

A. A

B. B

C. C

D. D

Q. 35 The initial rate of hydrolysis of methyl acetate (1M) by a weak acid (HA, 1M) is 1/100 th of that of a strong acid (HX, 1M), at 25 °C. The kₐ of HA is

A. 1 x 10⁻⁴

B. 1 x 10⁻⁵

C. 1 x 10⁻⁶

D. 1 x 10⁻³

Q. 36 The total number of carboxylic acid groups in the product P is

Q. 37 A tetrapeptide has —COON group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine (Phe) and alanine (Ala), on complete hydrolysis. For this tetrapeptide, the number of possible sequences (primary structures) with —NH₂ group attached to a chiral center is

Q. 38 EDTA⁴⁻ is ethylenediaminetetraacetate ion. The total number of N-Co-O bond angles in [Co(EDTA)]¹⁻ complex ion is

Q. 39 The total number of lone-pairs of electrons in melamine is

Q. 40 The atomic masses of He and Ne are 4 and 20 a.m.u., respectively. The value of the de Broglie wavelength of He gas at -73 °C is “M” times that of the de Broglie wavelength of Ne at 727 °C. M is

Q. 41 Pick the correct option:

A. 1/√2

B. 1/2

C. 1/√7

D. 1/3

Q. 42 Four persons independently solve a certain problem correctly with probabilities 1/2, 3/4, 1/4, 1/8. Then the probability that the problem is solved correctly by at least one of them is

A. 235/236

B. 21/256

C. 3/256

D. 253/256

Q. 43 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 44 The number of points in (-∞, ∞), for which x² – x sinx – cosx = 0, is

A. 6

B. 4

C. 2

D. 0

Q. 45 The area enclosed by the curves y = sin x + cos x and y = |cos x – sin x| over the interval [0 , π/2] is

A. 4(√2 – 1)

B. 2√2 (√2 – 1)

C. 2(√2 + 1)

D. 2√2 (√2 + 1)

Q. 46 A curve passes through the point (1, π/6). Let the slope of the curve at each point (x, y) be y/x + sec(y/x), x > 0. Then the equation of the curve is

A. A

B. B

C. C

D. D

Q. 47 Choose the correct option:

A. 23/25

B. 25/23

C. 23/24

D. 24/23

Q. 48 For a> b> c> 0, the distance between (1, 1) and the point of intersection of the lines ax + by + c = 0 and bx + ay + c = 0 is less than 2√2 . Then

A. a + b – c > 0

B. a – b + c < 0

C. a – b + c > 0

D. a + b – c < 0

Q. 49 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 50 Let P̅R̅ = 3î + ĵ -2k̂ and S̅Q̅ = î – 3ĵ -4k̂ determine diagonals of a parallelogram PQRS and P̅T̅ = î + 2ĵ + 3k̂ be another vector. Then the volume of the parallelepiped determined by the vectors PT , PQ and PS is

A. 5

B. 20

C. 10

D. 30

Q. 51 Choose the correct option:

A. 1056

B. 1088

C. 1120

D. 1332

Q. 52 For 3 x 3 matrices M and N, which of the following statement(s) is (are) NOT correct ?

A. A

B. B

C. C

D. D

Q. 53 Let f (x) = x sin πx, x > 0 . Then for all natural numbers n, f'(x) vanishes at

A. a unique point in the interval (n, n + 1/2)

B. a unique point in the interval (n + 1/2, n + 1)

C. a unique point in the interval (n, n + 1)

D. two points in the interval (n, n + 1)

Q. 54 A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are

A. 24

B. 32

C. 45

D. 60

Q. 55 A line l passing through the origin is perpendicular to the lines Then, the coordinate(s) of the point(s) on l2, at a distance of √17 from the point of intersection of l and l₁ is (are)

A. (7/3, 7/3, 5/3)

B. (-1, -1, 0)

C. (1, 1, 1)

D. (7/9, 7/9, 8/9)

Q. 56 The coefficients of three consecutive terms of (1+x)ⁿ⁺⁵ are in the ratio 5: 10: 14. Then n =

Q. 57 A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the removed cards is k, then k – 20 =

Q. 58 Of the three independent events E₁, E₂, and E₃, the probability that only E₁ occurs is α, only E₂ occurs is β and only E₃ occurs is γ. Let the probability p that none of the events E₁, E₂ or E₃ occurs to satisfy the equations (α – 2β)p = αβ and (β – 3γ)p = 2βγ. All the given probabilities are assumed to lie in the interval (0, 1).

Q. 59 A vertical line passing through the point (h, 0) intersects the ellipse x²/4 + y²/3 = 1 at the points P and Q. Let the tangents to the ellipse at P and Q meet at the point R.

Q. 60 Consider the set of eight vectors (given in the image). Three non-coplanar vectors can be chosen from V in 2ᵖ ways. Then p is

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

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