question: 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.

response_choices: A), B), C) and D)

answer: B

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question_subject: physics


question: 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

response_choices: (A)always radially outwards. (B)always radially inwards. (C)radially outwards initially and radially inwards later. (D)radially inwards initially and radially outwards later.

answer: D

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question_subject: physics


question: 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

answer: C

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question_subject: physics


question: 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

answer: C

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question_subject: physics


question: 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

answer: C

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question_subject: physics


question: 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

answer: (A)

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question_subject: physics


question: 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

answer: (A)

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question_subject: physics


question: 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

answer: (B)

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question_subject: physics


question: 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)

answer: B

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question_subject: physics


question: 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)

response_choices: 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)

answer: D

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question_subject: physics


question: 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

answer: D

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question_subject: physics


question: 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

answer: D

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question_subject: physics


question: If the piston is pushed at a speed of 5 mms^-1, the air comes out of the nozzle with a speed of

answer: (C)

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question_subject: physics


question: 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

response_choices: (A) ρa/ρℓ, (B)√ρaρℓ, (C) ρℓ/ρa, (D)ρℓ

answer: (A)

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question_subject: physics


question: 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

response_choices:
(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

answer: C

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question_subject: physics


question: 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)

response_choices: (A) μ₀I²a²/a	(B) μ₀I²a²/2a	(C) √3μ₀I²a²/a	(D) √3μ₀I²a²/2a

answer: B

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question_subject: physics


question: 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.

answer: A

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question_subject: physics


question: 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.

answer: B

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question_subject: physics


question: 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.

answer: D

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question_subject: physics


question: 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.

answer: C

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question_subject: physics


question: The acidic hydrolysis of ether (X) shown below is fastest when

response_choices: 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.

answer: C

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question_subject: chemistry


question: Isomers of hexane, based on their branching, can be divided into three distinct classes as shown in the figure.

response_choices: (A) I > II > III, (B) III > II > I, (C) II > III > I, (D) III > I > II

answer: B

image_available: yes

question_subject: chemistry


question: The major product in the following reaction is

response_choices: A, B, C, D

answer: D

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question_subject: chemistry


question: Hydrogen peroxide in its reaction with KIO4 and NH4OH respectively, is acting as a

response_choices: A) reducing agent, oxidising agent, B) reducing agent, reducing agent, C) oxidising agent, oxidising agent, D) oxidising agent, reducing agent

answer: A

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question_subject: chemistry


question: The product formed in the reaction of SOCl2 with white phosphorous is

response_choices: (A) PCl3, (B) SO2Cl2, (C) SCl2, (D) POCl3

answer: A

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question_subject: chemistry


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

answer: C

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question_subject: chemistry


question: For the identification of β-naphthol using dye test, it is necessary to use

response_choices: (A) dichloromethane solution of β-naphthol. (B) acidic solution of β-naphthol. (C) neutral solution of β-naphthol. (D) alkaline solution of β-naphthol.

answer: D

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question_subject: chemistry


question: 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

answer: B

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question_subject: chemistry


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

response_choices: (A) ΔSsystem > 0 and ΔSsurroundings > 0 (B) ΔSsystem > 0 and ΔSsurroundings < 0 (C) ΔSsystem < 0 and ΔSsurroundings > 0 (D) ΔSsystem < 0 and ΔSsurroundings < 0

answer: B

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question_subject: chemistry


question: Assuming 2s-2p mixing is NOT operative, the paramagnetic species among the following is

answer: C

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question_subject: chemistry


question: The product X is

response_choices: (A) H3CO CH2 H, (B) H CH3CO, (C) CH3CH2OH, (D) CH3CHO

answer: C

image_available: yes

question_subject: chemistry


question: The product Y is

response_choices: (A) BrCH2CH3, (B) Br(CH2)4Br, (C) BrCH2CH2OH, (D) CH3CH(Br)CH3

answer: C

image_available: yes

question_subject: chemistry


question: The correct statement with respect to product Y is

response_choices:
(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.

answer: C

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question_subject: chemistry


question: M1, Q and R, respectively are

response_choices:
(A) Zn2+, KCN and HCl
(B) Ni2+, HCl and KCN
(C) Cd2+, KCN and HCl
(D) Co2+, HCl, and KCN

answer: B

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question_subject: chemistry


question: Reagent S is

response_choices: (A) K4[Fe(CN)6] (B) Na3HPO4 (C) K2CrO4 (D) KOH

answer: D

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question_subject: chemistry


question: The value of d in cm (shown in the figure), as estimated from Graham's law, is

answer: C

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question_subject: chemistry


question: The experimental value of d is found to be smaller than the estimate obtained using Graham's law. This is due to

response_choices: (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.

answer: D

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question_subject: chemistry


question: 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.

response_choices: Options (A), (B), (C) and (D)

answer: (A)

image_available: yes

question_subject: chemistry


question: 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.

answer: C

image_available: yes

question_subject: chemistry


question: 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]

response_choices: 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

answer: (B)

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question_subject: chemistry


question: 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.

answer: C

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question_subject: chemistry


question: 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

answer: B

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question_subject: mathematics


question: The following integral from 1 to pi/2 of (2 cosec x)^17 dx is equal to

response_choices: 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

answer: A

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question_subject: mathematics


question: Coefficient of x^11 in the expansion of (1 + x^2)^4 (1 + x^5)^7 (1 + x^4)^12 is

answer: C

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question_subject: mathematics


question: 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

answer: B

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question_subject: mathematics


question: 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

answer: D

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question_subject: mathematics


question: For x ∈ (0, π), the equation sin x + 2 sin 2x − sin 3x = 3 has

response_choices: (A) infinitely many solutions, (B) three solutions, (C) one solution, (D) no solution

answer: D

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question_subject: mathematics


question: 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

answer: B

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question_subject: mathematics


question: 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

answer: C

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question_subject: mathematics


question: 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

answer: A

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question_subject: mathematics


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

response_choices: (A) only purely imaginary roots, (B) all real roots, (C) two real and two purely imaginary roots, (D) neither real nor purely imaginary roots

answer: D

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question_subject: mathematics


question: The value of r is

answer: D

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question_subject: mathematics


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

answer: B

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question_subject: mathematics


question: The value of g(1/2) is

answer: A

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question_subject: mathematics


question: The value of g'(1/2) is

answer: D

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question_subject: mathematics


question: The probability that x1 + x2 + x3 is odd, is

answer: B

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question_subject: mathematics


question: The probability that x1, x2, x3 are in an arithmetic progression, is

answer: C

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question_subject: mathematics


question: Let zk = cos(2kπ/10) + i sin(2kπ/10); k = 1, 2, ..., 9.

response_choices: List I: P. For each zk there exists a zj such that zk × zj, Q. There exists a k ∈ {1,2,...,9} such that z1 × z ̸=, zk has no solution z in the set of complex numbers., R. |1-z1|/|1-z2|...|1-z9|/10 equals, S. 1 - Σ9k=1 cos(2kπ/10) equals

answer: (C) 1 2 3 4

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question_subject: mathematics


question: P. The number of polynomials f(x) with non-negative integer coefficients of degree ≤ 2, satisfying f(0) = 0 and ∫01 f(x)dx = 1, is, Q. The number of points in the interval [−√13, √13] at which sin(x2) + cos(x2) attains its maximum value, is, R. ∫-12 (1+x2) dx equals (∫12 1 (1-x)2 cos 2x log (1+x) dx), S. (∫02 cos 2x log (1+x/1-x) dx) equals

answer: (D) 2 3 1 4

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question_subject: mathematics


question: Let y(x) = cos(3 cos^-1 x), x ∈ [-1,1], x ≠ ±√(5/2). Then (1/y(x))(x^2 - (d^2y(x)/dx^2 + x (dy(x)/dx)) equals

answer: A

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question_subject: mathematics


question: Let f1: ℝ → ℝ, f2: [0, ∞) → ℝ, f3: ℝ → ℝ and f4: ℝ → [0, ∞) be defined by f1(x) = {|x| if x < 0, e^x if x ≥ 0}; f2(x) = x^2; f3(x) = {sin x if x < 0, x if x ≥ 0} and f4(x) = {f2(f1(x)) if x < 0, f2(f1(x)) - 1 if x ≥ 0}. List II P. f4 is Q. f1 is R. f2◦f1 is S. f2 is

answer: D

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question_subject: mathematics