id int64 1 84 | question stringlengths 11 1.17k | response_choices stringlengths 0 901 | answer stringclasses 330 values | page_number int64 1 40 | image_available stringclasses 2 values | question_subject stringclasses 3 values |
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9 | A transparent thin film of uniform thickness and refractive index n₁= 1.4 is coated on the convex spherical surface of radius Rat 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 | (A) and (C) | 5 | yes | physics |
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 = 2R2 = R3, (D) 2V1 = V2 and 2R1 = R2 = R3 | (A), (B) and (D) | 6 | yes | physics |
11 | Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30° and 60° with respect to the horizontal respectively as shown in figure. The speed of A is 100√3 ms⁻¹. At time t = 0 s, an observer in A finds B at a distance of 500 m. 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 | No response choices provided. | 5 | 7 | yes | physics |
12 | During Searle's experiment, zero of the Vernier scale lies between 3.20 × 10⁻² m and 3.25 × 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 × 10⁻² m and 3.25 × 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 × 10⁻⁷ m². The least count of the Vernier scale is 1.0 × 10⁻⁵ m. The maximum percentage error in the Young's modulus of the wire is | No response choices provided. | 4 | 7 | no | physics |
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 | No response choices provided | 2 | 8 | yes | physics |
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 in the same plane 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 | No response choices provided | 3 | 8 | no | physics |
15 | To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density ρ of the fog, intensity (power/area) S of the light from the signal and its frequency f. The engineer finds that disproportionatos^1/n . The value of n is | No response choices provided | 3 | 8 | no | physics |
16 | A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990 Ω resistance, it can be converted into a voltmeter of range 0 - 30 V. If connected to a 249/2Ω resistance, it becomes an ammeter of range 0 - 1.5 A. The value ofn is | No response choices provided | 5 | 8 | no | physics |
17 | Consider an elliptically shaped rail PQ in the vertical plane with OP = 3 m and OQ = 4 m. A block of mass 1 kg 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 × 10)Joules. The value of n is (take acceleration due to gravity = 10 ms^-2) | No response choices provided | 5 | 9 | yes | physics |
18 | A rocket is moving in a gravity free space with a constant acceleration of 2 ms^-2 along +x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in +x direction with a speed of 0.3 ms^-1 relative to the rocket. At the same time, another ball is thrown in –x direction with a speed of 0.2 ms^-1 from its right end relative to the rocket. The time in seconds when the two balls hit each other is | No response choices provided | 2 OR 8 | 9 | yes | physics |
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 ms^-1 with respect to the ground. The rotational speed of the platform inrads^-1 after the balls leave the platform is | Answer: 4 | 4 | 10 | yes | physics |
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 Waf = 200 J, Wib = 50 J and Wbf = 100 J respectively. The heat supplied to the system along the path iaf, ib and bf are Qiaf, Qib and Qbf respectively. If the internal energy of the system in the state b is Ub = 200 J and Qiaf = 500 J, the ratio Qbf /Qib is | Answer : 2 | 2 | 10 | yes | physics |
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 | (A), (C) and (D) | 11 | no | chemistry |
22 | he reactivity of compound Z with different halogens under appropriate conditions is given below:, 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 | (A), (B) and (C) | 11 | yes | chemistry |
23 | In the reaction shown below, the major product(s) formed is/are | A, B, C, D | A | 12 | yes | chemistry |
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) P2V2' = P1V1' | (A), (B) and (C) | 13 | yes | physics |
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. | (A), (B) and (D) | 14 | no | chemistry |
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. | (A) and (C) or only (A) | 14 | no | chemistry |
27 | Upon heating with Cu₂S, the reagent(s) that give copper metal is/are | (A) CuFeS₂ (B) CuO (C) Cu₂O (D) CuSO₄ | (B), (C) and (D) | 14 | no | chemistry |
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. | (B) and (D) | 15 | no | chemistry |
29 | For the reaction: I⁻ + ClO₃⁻ + H₂SO₄ → Cl⁻ + HSO₄⁻ + 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. | (A), (B) and (D) OR (A) and (D)* | 15 | no | chemistry |
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 | (A), (B) and (C) | 15 | no | chemistry |
31 | Consider all possible isomeric 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 | 5 | 16 | no | chemistry | |
32 | A list of species having the formula XZ4 is given below. XeF4, SF4, SiF4, BF4, BrF4, [Cu(NH3)4]2+, [FeCI4]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 | 4 | 16 | no | chemistry | |
33 | Among PbS, CuS, HgS, MnS, Ag2S, NiS, CoS, Bi2S3 and SnS2, the total number of BLACK coloured sulfides is | 6 OR 7 | 16 | no | chemistry | |
34 | The total number(s) of stable conformers with non-zero dipole moment for the following compound is (are) | 3 | 16 | yes | chemistry | |
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 | 4 | 18 | no | chemistry | |
40 | MX2 dissociates into M²⁺ and X⁻ ions in an aqueous solution, with a degree of dissociation (α) 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 | 2 | 18 | no | chemistry | |
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 | (A), (B) | 19 | no | mathematics |
42 | For every pair of continuous functions f, g: [0, 1] → R such that
max {f(x): x ∈ [0, 1]} = max {g(x): x ∈ [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] | (A), (D) | 19 | no | mathematics |
43 | Let f : (0, ∞) → ℝ be given by f(x) = ∫(x/2)^x e^(-(t+1)/t) dt/t | (A) f(x) is monotonically increasing on (1, ∞)
(B) f(x) is monotonically decreasing on (0, 1)
(C) f(x) + f(1/t) = 0, for all x ∈ (0, ∞)
(D) f(2^x) is an odd function of x on ℝ | (A), (C), (D) | 20 | no | mathematics |
44 | Let a ∈ ℝ and let f : ℝ → ℝ be given by f(x) = x^5 - 5x + a. | (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 if -4 < a < 4 | (B), (D) | 20 | no | mathematics |
45 | Let f: [a, b] → [1, ∞) be a continuous function and let g: ℝ → ℝ be defined as (see image for mathematical expression) | (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 | (A), (C) | 21 | yes | mathematics |
46 | Let f: (−π/2, π/2) → ℝ be given by f(x) = (log(sec x + tan x))³. Then (see image for options) | (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 | (A), (B) and (C) | 21 | no | mathematics |
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 ∠QPR is a right angle, then the possible value(s) of λ is(are) | (A) √2, (B) 1, (C) −1, (D) −√2 | (C) | 22 | no | mathematics |
48 | Let 𝑥⃗, 𝑦⃗ and 𝑧⃗ be three vectors each of magnitude √2 and the angle between each pair of them is π/4. If 𝑎⃗ is a nonzero vector perpendicular to 𝑥⃗ and 𝑦⃗ × 𝑧⃗ and 𝑏⃗ is a nonzero vector perpendicular to 𝑦⃗ and 𝑧⃗ × 𝑥⃗, then | (A) 𝑏⃗ = (𝑏⃗ · 𝑧⃗)(𝑧⃗ − 𝑥⃗), (B) 𝑎⃗ = (𝑎⃗ · 𝑦⃗)(𝑦⃗ − 𝑧⃗), (C) 𝑎⃗ · 𝑏⃗ = −(𝑎⃗ · 𝑦⃗)(𝑏⃗ · 𝑧⃗), (D) 𝑎⃗ = (𝑎⃗ · 𝑦⃗)(𝑧⃗ − 𝑦⃗) | (A), (B) and (C) | 22 | no | mathematics |
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) | (B), (C) | 22 | no | mathematics |
50 | Let M be a 2 × 2 symmetric matrix with integer entries. Then M is invertible if | (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 | (C), (D) | 23 | no | mathematics |
51 | Let a, b, c be positive integers such that ˢ√c 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 | 4 | 23 | no | mathematics | |
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 | 5 | 23 | no | mathematics | |
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 | 7 | 23 | no | mathematics | |
54 | Let f: R → R and g: R → R be respectively given by f(x) = |x| + 1 and g(x) = x^2 + 1. Define h: R → R by h(x) = { max {f(x), g(x)} if x ≤ 0, min {f(x), g(x)} if x > 0. The number of points at which h(x) is not differentiable is | 3 | 24 | no | mathematics | |
55 | The value of ∫[1/0] 4x^3 (d^2(1-x^2)^5/dx^2) dx is | 2 | 24 | no | mathematics | |
56 | The slope of the tangent to the curve (y - x^5)^2 = x(1 + x^2)^2 at the point (1, 3) is | 8 | 24 | no | mathematics | |
57 | The largest value of the nonnegative integer a for which lim[x→1] {(-ax + sin(x - 1) + a)^(1-x)/(x + sin(x - 1) - 1)} = 1/4 is | 0 (zero) | 24 | no | mathematics | |
58 | Let f: [0, 4π] → [0, π] be defined by f(x) = cos⁻¹(cos x). The number of points x ∈ [0, 4π] satisfying the equation f(x) = (10 - x)/10 | 3 | 25 | no | mathematics | |
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 | 6 | 25 | no | mathematics | |
60 | Let a⃗, b⃗, and c⃗ be three non-coplanar unit vectors such that the angle between every pair of them is π/3. If a⃗ × b⃗ + b⃗ × c⃗ = pa⃗ + qb⃗ + rc⃗, where p, q and r are scalars, then the value of (p²+2q²+r²)/q² is | 4 | 25 | no | mathematics | |
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 sketches describes the variation of its kinetic energy K with timet most appropriately? The figures are only illustrative and not to the scale. | A), B), C) and D) | B | 1 | yes | physics |
2 | A wire, whichpasses 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. | D | 2 | yes | physics |
3 | During an experiment with ametre 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 is1 mm. The unknown resistance is | (A)60 ± 0.15Ω (B)135 ± 0.56Ω (C)60 ± 0.25Ω (D)135 ± 0.23Ω | C | 2 | yes | physics |
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 | C | 3 | yes | physics |
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 the top of the block. The refractive index of the liquid is | (A) 1.21, (B) 1.30, (C) 1.36, (D) 1.42 | C | 3 | yes | physics |
6 | Parallel rays of light of intensity I = 912 W/m^-2 are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant σ = 5.7 × 10^-8W/m^-2 K^-4 and assume that the energy exchange with the surroundingsis 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 | (A) | 4 | no | physics |
7 | A metal surface is illuminated by light of two different wavelengths 248nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths areu1 and u2,respectively. If the ratio u1: u2 = 2: 1and hc = 1240 eV nm, the work function of the metal is nearly | (A) 3.7 eV, (B) 3.2 eV, (C) 2.8 eV, (D) 2.5eV | (A) | 4 | no | physics |
8 | If λCu is the wavelength of Kα X-ray line of copper (atomic number 29) and λMo is the wavelength of the Kα X-ray line of molybdenum (atomic number 42), then the ratio λCu/λMo is close to | (A) 1.99, (B) 2.14, (C) 0.50, (D) 0.48 | (B) | 4 | no | physics |
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=5R 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 10^6m and the acceleration due to gravity on Earth is 10 ms^-2) | A) 96 N, B) 108 N, C) 120 N, D) 150 N | B | 5 | no | physics |
10 | A glass capillary tube is of 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 ρ, and its contact angle with glass is θ, the value of h will be (g is the acceleration due to gravity) | A) 2S/bρg cos(θ − α), B) 2S/bρg cos(θ + α), C) 2S/bρg cos(θ − α/2), D) 2S/bρg cos(θ + α/2) | D | 5 | yes | physics |
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 | D | 6 | yes | physics |
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) −100R | D | 6 | yes | physics |
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)5 ms^-1 | (C) | 7 | yes | physics |
14 | If the density of air is ρa and that of the liquid ρℓ , then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to | (A) ρa/ρℓ, (B)√ρaρℓ, (C) ρℓ/ρa, (D)ρℓ | (A) | 7 | yes | physics |
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 | C | 8 | yes | physics |
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 currents in the wires are in the opposite directions, the torque on the loop at its new position will be (assume that the net field due to the wires is constant over the loop) | (A) μ₀I²a²/a (B) μ₀I²a²/2a (C) √3μ₀I²a²/a (D) √3μ₀I²a²/2a | B | 8 | yes | physics |
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 with List II and select the correct answer using the code given below the lists. | 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 | A | 9 | yes | physics |
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 using the code given below the lists. | (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 | B | 10 | yes | physics |
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 block m2 and the plane are equal to μ = 0.3. In List II expressions for the friction on block m2 are given. Match the correct expression of the friction in List II with the angles given in List I, and choose the correct option. The acceleration due to gravity is denoted by g. | 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 | D | 11 | yes | physics |
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 using the code given below the list. | 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 | C | 12 | no | physics |
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. | C | 13 | yes | chemistry |
22 | Isomers of hexane, based on their branching, can be divided into three distinct classes as shown in the figure. | (A) I > II > III, (B) III > II > I, (C) II > III > I, (D) III > I > II | B | 14 | yes | chemistry |
23 | The major product in the following reaction is | A, B, C, D | D | 15 | yes | chemistry |
24 | Hydrogen peroxide in its reaction with KIO4 and NH4OH 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 | A | 15 | no | chemistry |
25 | The product formed in the reaction of SOCl2 with white phosphorous is | (A) PCl3, (B) SO2Cl2, (C) SCl2, (D) POCl3 | A | 16 | no | chemistry |
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 | C | 16 | yes | chemistry |
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. | D | 17 | no | chemistry |
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 is | (A) 4 (B) 3 (C) 2 (D) 1 | B | 17 | no | chemistry |
29 | For the process H₂O (l) → H₂O (g) at T = 100°C and 1 atmosphere pressure, the correct choice is | (A) ΔSsystem > 0 and ΔSsurroundings > 0 (B) ΔSsystem > 0 and ΔSsurroundings < 0 (C) ΔSsystem < 0 and ΔSsurroundings > 0 (D) ΔSsystem < 0 and ΔSsurroundings < 0 | B | 17 | no | chemistry |
30 | Assuming 2s-2p mixing is NOT operative, the paramagnetic species among the following is | (A) Be2, (B) B2, (C) C2, (D) N2 | C | 18 | no | chemistry |
31 | The product X is | (A) H3CO CH2 H, (B) H CH3CO, (C) CH3CH2OH, (D) CH3CHO | C | 19 | yes | chemistry |
32 | The product Y is | (A) BrCH2CH3, (B) Br(CH2)4Br, (C) BrCH2CH2OH, (D) CH3CH(Br)CH3 | C | 19 | yes | chemistry |
32 | The correct statement with respect to product Y is | (A) It gives a positive Tollens test and is a functional isomer of X.
(B) It gives a 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. | C | 20 | yes | chemistry |
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 | B | 21 | yes | chemistry |
34 | Reagent S is | (A) K4[Fe(CN)6] (B) Na3HPO4 (C) K2CrO4 (D) KOH | D | 22 | no | chemistry |
35 | The value of d in cm (shown in the figure), as estimated from Graham's law, is | (A) 8
(B) 12
(C) 16
(D) 20 | C | 23 | yes | chemistry |
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. | D | 24 | no | chemistry |
37 | Different possible thermal decomposition pathways for peroxyesters are shown below. Match each pathway from List I with an appropriate structure from List II and select the correct answer using the code given below the lists. | Options (A), (B), (C) and (D) | (A) | 25 | yes | chemistry |
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 using the code given below the lists. | (A) 1 4 2 3, (B) 3 1 4 2, (C) 3 4 2 1, (D) 4 1 3 2 | C | 26 | yes | chemistry |
39 | Match each coordination compound in List-I with an appropriate pair of characteristics from List-II and select the correct answer using the code given below the lists. [en = H2NCH2CH2NH2; atomic numbers: Ti = 22; Cr = 24; Co = 27; Pt = 78] | List-I: P. [Cr(NH3)4Cl2]Cl, Q. [Ti(H2O)6Cl](NO3)2, R. [Pt(en)(NH3)Cl]NO3, S. [Co(NH3)4(NO3)2]NO3 | List-II: 1. Paramagnetic and exhibits ionisation isomerism, 2. Diamagnetic and exhibits cis-trans isomerism, 3. Paramagnetic and exhibits cis-trans isomerism, 4. Diamagnetic and exhibits ionisation isomerism | Codes: (A) 4 3 2 1, (B) 3 2 1 4, (C) 2 1 4 3, (D) 1 4 3 2 | (B) | 27 | no | chemistry |
40 | Match the orbital overlap figures shown in List-I with the description given in List-II and select the correct answer using the code given below the lists. | 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 | C | 28 | yes | chemistry |
41 | The function y = f (x) is the solution of the differential equation dy/dx = xy/(x^2 - 1) = (x^4 + 2x)/sqrt(1 - x^2) in (-1, 1) satisfying f (0) = 0. Then the integral from -sqrt(3)/2 to sqrt(3)/2 of f (x) dx is | A) pi - sqrt(3)/2, B) pi - sqrt(3)/4, C) pi - sqrt(3)/4, D) pi - sqrt(3)/2 | B | 29 | no | mathematics |
42 | The following integral from 1 to pi/2 of (2 cosec x)^17 dx is equal to | A) Integral from 0 to log(1+sqrt(2)) of 2(e^u + e^(-u))^16 du, B) Integral from 0 to log(1+sqrt(2)) of (e^u + e^(-u))^17 du, C) Integral from 0 to log(1+sqrt(2)) of (e^u - e^(-u))^17 du, D) Integral from 0 to log(1+sqrt(2)) of 2(e^u - e^(-u))^16 du | A | 29 | no | mathematics |
43 | Coefficient of x^11 in the expansion of (1 + x^2)^4 (1 + x^5)^7 (1 + x^4)^12 is | (A) 1051, (B) 1106, (C) 1113, (D) 1120 | C | 30 | no | mathematics |
44 | Let f : [0, 2] -> ℝ be a function which is continuous on [0, 2] and is differentiable on (0, 2) with f'(0) = 1. Let F(x) = ∫₀ˣ f(√t) dt for x ∈ [0, 2]. If F'(x) = f'(x) for all x ∈ (0, 2), then F(2) equals | (A) e² - 1, (B) e⁴ - 1, (C) e - 1, (D) e⁵ | B | 30 | yes | mathematics |
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 | D | 30 | no | mathematics |
46 | For x ∈ (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 | D | 31 | no | mathematics |
47 | In a triangle the sum of two sides is x and the product of the same two sides is y. If x² − c² = y, where c is the third side of the triangle, then the ratio of the in-radius to the circum-radius of the triangle is | (A) 3y/2(x+c), (B) 3y/2(x+c), (C) 3y/4(x+c), (D) 3y/4(x+c) | B | 31 | no | mathematics |
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 | C | 31 | no | mathematics |
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 | A | 32 | no | mathematics |
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 | D | 32 | no | mathematics |
51 | The value of r is | (A) -1/4, (B) (2+i)/4, (C) 1/4, (D) (2-1)/4 | D | 33 | no | mathematics |
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