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 |
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| 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 |