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 |
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| 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 |