question:
In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength (λ) of incident light and the corresponding stopping potential (V0) are given below:

λ (μm)    V0 (Volt)
0.3         2.0
0.4         1.0
0.5         0.4

Given that c = 3 x 10^8 m s^-1 and e =1.6 x 10^-19 C , Planck's constant (in units of J s) found from such an experiment is

answer: B

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question_subject: physics


question: A uniform wooden stick of mass 1.6 kg and length l rests in an inclined manner on a smooth, vertical wall of height h (< l), such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of 30° with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio h/l and the frictional force f at the bottom of the stick are

answer: D

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question_subject: physics


question: A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load). The temperature of water fed into the device cannot exceed 30 °C and the entire stored 120 litres of water is initially cooled to 10 °C. The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is

answer: B

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question_subject: physics


question: A parallel beam of light is incident from air at an angle α on the side PQ of a right angled triangular prism of refractive index n = √2. Light undergoes total internal reflection in the prism at the face PR when α has a minimum value of 45°. The angle θ of the prism is

answer: A

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question_subject: physics


question: An infinite line charge of uniform electric charge density λ lies along the axis of an electrically conducting infinite cylindrical shell of radius R. At time t = 0, the space inside the cylinder is filled with a material of permittivity ε and electrical conductivity σ. The electrical conduction in the material follows Ohm's law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density j(t) at any point in the material?

response_choices: A, B, C, D

answer: C

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question_subject: physics


question: Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principal quantum number n , where n>>1. Which of the following statement(s) is(are) true?

response_choices:
(A) Relative change in the radii of two consecutive orbitals does not depend on Z
(B) Relative change in the radii of two consecutive orbitals varies as 1/n
(C) Relative change in the energy of two consecutive orbitals varies as 1/n^3
(D) Relative change in the angular momenta of two consecutive orbitals varies as 1/n

answer: (A), (B), and (D)

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question_subject: physics


question: Two loudspeakers M and N are located 20 m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car is initially at a point P, 1800 m away from the midpoint Q of the line MN and moves towards Q constantly at 60 km/hr along the perpendicular bisector of MN. It crosses Q and eventually reaches a point R, 1800 m away from Q. Let v(t) represent the beat frequency measured by a person sitting in the car at time t. Let vp, vq and vr be the beat frequencies measured at locations P, Q and R, respectively. The speed of sound in air is 330 m s^-1. Which of the following statement(s) is(are) true regarding the sound heard by the person?

response_choices: (A) vp = vr - 2 vq (B) The rate of change in beat frequency is maximum when the car passes through Q (C) The plot below represents schematically the variation of beat frequency with time [Plot image 1] (D) The plot below represents schematically the variation of beat frequency with time [Plot image 2]

answer: (A), (B), and (C)

image_available: yes

question_subject: physics


question: An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is(are) true?

response_choices: (A) The temperature distribution over the filament is uniform (B) The resistance over small sections of the filament decreases with time (C) The filament emits more light at higher band of frequencies before it breaks up (D) The filament consumes less electrical power towards the end of the life of the bulb

answer: (C) and (D)

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question_subject: physics


question: A plano-convex lens is made of a material of refractive index n. When a small object is placed 30 cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens, another faint image is observed at a distance of 10 cm away from the lens. Which of the following statement(s) is(are) true?

response_choices: (A) The refractive index of the lens is 2.5 (B) The radius of curvature of the convex surface is 45 cm (C) The faint image is erect and real (D) The focal length of the lens is 20 cm

answer: (A) and (D)

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question_subject: physics


question: A length-scale (l) depends on the permittivity (ε) of a dielectric material, Boltzmann constant (kB), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression(s) for l is(are) dimensionally correct?

response_choices: (A) l = √(nq²/εkBT), (B) l = √(εkBT/nq²), (C) l = √(q²/εn²/³kBT), (D) l = √(q²/εn¹/³kBT)

answer: (B) and (D)

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question_subject: physics


question: A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the 90° vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at a constant rate of 10 A s^-1. Which of the following statement(s) is(are) true?

response_choices: (A) The magnitude of induced emf in the wire is (μ0/π) volt, (B) If the loop is rotated at a constant angular speed about the wire, an additional emf of (μ0/π) volt is induced in the wire, (C) The induced current in the wire is in opposite direction to the current along the hypotenuse, (D) There is a repulsive force between the wire and the loop

answer: (A) and (D)

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question_subject: physics


question: The position vector r of a particle of mass m is given by the following equation: r(t)=αt^3 i + βt^2 j, where α=10/3 m s^-3, β=5 m s^-2 and m=0.1 kg. At t=1 s, which of the following statement(s) is(are) true about the particle?

response_choices:
(A) The velocity v is given by v=(10i + 10j) m s^-1
(B) The angular momentum L with respect to the origin is given by L=-(5/3)k N m s
(C) The force F is given by F=(i + 2j) N
(D) The torque τ with respect to the origin is given by τ=-(20/3)k N m

answer: (A), (B) and (D)

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question_subject: physics


question: A transparent slab of thickness d has a refractive index n(z) that increases with z. Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n1 and n2 (>n1), as shown in the figure. A ray of light is incident with angle θi from medium 1 and emerges in medium 2 with refraction angle θf with a lateral displacement l. Which of the following statement(s) is(are) true?

response_choices: (A) n1 sin θi = n2 sin θf (B) n1 sin θi = (n2 - n1) sin θf (C) l is independent of n2 (D) l is dependent on n(z)

answer: (A), (C) and (D)

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question_subject: physics


question: A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P) by the metal. The sensor has a scale that displays log₂(P/P₀), where P₀ is a constant. When the metal surface is at a temperature of 487 °C, the sensor shows a value 1. Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to 2767 °C?

answer: 9

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question_subject: physics


question: The isotope ¹³B having a mass 12.014 u undergoes β-decay to ¹²C. ¹²C has an excited state of the nucleus (¹²C*) at 4.041 MeV above its ground state. If ¹³B decays to ¹²C*, the maximum kinetic energy of the β-particle in units of MeV is (1 u = 931.5 MeV/c², where c is the speed of light in vacuum).

answer: 8 OR 9

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question_subject: physics


question: A hydrogen atom in its ground state is irradiated by light of wavelength 970 Å. Taking hc/e = 1.237 × 10^-5 eV m and the ground state energy of hydrogen atom as -13.6 eV, the number of lines present in the emission spectrum is

response_choices: No response choices provided.

answer: (5)

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question_subject: physics


question: Consider two solid spheres P and Q each of density 8 gm cm^-3 and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density 0.8 gm cm^-3 and viscosity η=3 poiseulles. Sphere Q is dropped into a liquid of density 1.6 gm cm^-3 and viscosity η=2 poiseulles. The ratio of the terminal velocities of P and Q is

response_choices: No response choices provided.

answer: (3)

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question_subject: physics


question: Two inductors L1 (inductance 1 mH, internal resistance 3 Ω) and L2 (inductance 2 mH, internal resistance 4 Ω), and a resistor R (resistance 12 Ω) are all connected in parallel across a 5 V battery. The circuit is switched on at time t = 0. The ratio of the maximum to the minimum current (Imax / Imin) drawn from the battery is

response_choices: No response choices provided.

answer: (8)

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question_subject: physics


question: P is the probability of finding the 1s electron of hydrogen atom in a spherical shell of infinitesimal thickness, dr, at a distance r from the nucleus. The volume of this shell is 4 πr^2 dr. The qualitative sketch of the dependence of P on r is

answer: (D)

image_available: yes

question_subject: chemistry


question: One mole of an ideal gas at 300 K in thermal contact with surroundings expands isothermally from 1.0 L to 2.0 L against a constant pressure of 3.0 atm. In this process, the change in entropy of surroundings (ΔSsur) in J K^-1 is

answer: C

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question_subject: chemistry


question: The increasing order of atomic radii of the following Group 13 elements is

response_choices: (A) Al < Ga < In < Tl    (B) Ga < Al < In < Tl    (C) Al < In < Ga < Tl    (D) Al < Ga < Tl < In

answer: B

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question_subject: chemistry


question: Among [Ni(CO)4], [NiCl4]^2-, [Co(NH3)6Cl3]Cl, Na3[CoF6], Na2O2 and CsO2, the total number of paramagnetic compounds is

answer: B

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question_subject: chemistry


question: On complete hydrogenation, natural rubber produces

response_choices: (A) ethylene-propylene copolymer    (B) vulcanised rubber    (C) polypropylene    (D) polybutylene

answer: A

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question_subject: chemistry


question: According to the Arrhenius equation, (A) a high activation energy usually implies a fast reaction. (B) rate constant increases with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy. (C) higher the magnitude of activation energy, stronger is the temperature dependence of the rate constant. (D) the pre-exponential factor is a measure of the rate at which collisions occur, irrespective of their energy.

answer: (B), (C) and (D)

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question_subject: chemistry


question: A plot of the number of neutrons (N) against the number of protons (P) of stable nuclei exhibits upward deviation from linearity for atomic number, Z > 20. For an unstable nucleus having N/P ratio less than 1, the possible mode(s) of decay is(are) (A) β⁻-decay (β emission) (B) orbital or K-electron capture (C) neutron emission (D) β⁺-decay (positron emission)

answer: (B) and (D)

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question_subject: physics


question: The crystalline form of borax has

response_choices:
(A) tetranuclear [B₄O₅(OH)₄]²⁻ unit
(B) all boron atoms in the same plane
(C) equal number of sp² and sp³ hybridized boron atoms
(D) one terminal hydroxide per boron atom

answer: (A), (C) and (D)

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question_subject: chemistry


question: The compound(s) with TWO lone pairs of electrons on the central atom is(are)

response_choices: (A) BrF₃	(B) ClF₃	(C) XeF₄	(D) SF₄

answer: (B) and (C)

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question_subject: chemistry


question: The reagent(s) that can selectively precipitate S²⁻ from a mixture of S²⁻ and SO₄²⁻ in aqueous solution is(are)

response_choices: (A) CuCl₂	(B) BaCl₂	(C) Pb(OOCCH₃)₂	(D) Na₂[Fe(CN)₅NO]

answer: (A) OR (A) and (C)

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question_subject: chemistry


question: Positive Tollen's test is observed for

response_choices:
(A) [Structure 1]

(B) [Structure 2]

(C) [Structure 3]

(D) [Structure 4]

answer: (A), (B) and (C)

image_available: yes

question_subject: chemistry


question: The product(s) of the following reaction sequence is(are)

answer: B

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question_subject: chemistry


question: The correct statement(s) about the following reaction sequence is(are)

response_choices: (A) R is steam volatile, (B) Q gives dark violet coloration with 1% aqueous FeCl3 solution, (C) S gives yellow precipitate with 2, 4-dinitrophenylhydrazine, (D) S gives dark violet coloration with 1% aqueous FeCl3 solution

answer: (B) and (C)

image_available: yes

question_subject: chemistry


question: The mole fraction of a solute in a solution is 0.1. At 298 K, molarity of this solution is the same as its molality. Density of this solution at 298 K is 2.0 g cm^-3. The ratio of the molecular weights of the solute and solvent, (MW_solute / MW_solvent), is

response_choices: A SINGLE DIGIT INTEGER ranging from 0 to 9

answer: 9

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question_subject: chemistry


question: The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases x times. The value of x is

response_choices: A SINGLE DIGIT INTEGER ranging from 0 to 9

answer: 4

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question_subject: physics


question: In neutral or faintly alkaline solution, 8 moles of permanganate anion quantitatively oxidize thiosulphate anions to produce X moles of a sulphur containing product. The magnitude of X is

answer: 6

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question_subject: chemistry


question: The number of geometric isomers possible for the complex [CoL₂Cl₂]⁻ (L = H₃NCH₂CH₂O⁻)

answer: 5

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question_subject: chemistry


question: In the following monobromination reaction, the number of possible chiral products is

answer: 5

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question_subject: chemistry


question: Let π/6 < θ < π/12. Suppose α1 and β1 are the roots of the equation x^2 - 2xsecθ +1 = 0 and α2 and β2 are the roots of the equation x^2 + 2xtanθ - 1 = 0. If α1 > β1 and α2 > β2, then α1 + β2 equals

response_choices: (A) 2(secθ - tanθ), (B) 2secθ, (C) -2tanθ, (D) 0

answer: (C)

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question_subject: mathematics


question: A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is

answer: (A)

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question_subject: mathematics


question: Let S ={(x ϵ (-π, π)): x ≠ 0, ±π/2}. The sum of all distinct solutions of the equation √3 secx + cosecx + 2(tanx - cotx) = 0 in the set S is equal to

answer: (C)

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question_subject: mathematics


question: A computer producing factory has only two plants T1 and T2. Plant T1 produces 20% and plant T2 produces 80% of the total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P(computer turns out to be defective given that it is produced in plant T1) = 10P(computer turns out to be defective given that it is produced in plant T2), where P(E) denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T2 is

answer: C

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question_subject: mathematics


question: The least value of a ∈ R  for which 4αx^2 + 1/x ≥ 1, for all x > 0, is

answer: C

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question_subject: mathematics


question: Consider a pyramid OPQRS located in the first octant (x ≥ 0, y ≥ 0, z ≥ 0) with O as origin, and OP and OR along the x-axis and the y-axis, respectively. The base OPQR of the pyramid is a square with OP = 3. The point S is directly above the mid-point T of diagonal OQ such that TS = 3. Then

response_choices:
(A)  the acute angle between OQ and OS is 2/3
(B)  the equation of the plane containing the triangle OQS is x - y = 0
(C)  the length of the perpendicular from P to the plane containing the triangle OQS is 3/√2
(D)  the perpendicular distance from O to the straight line containing RS is √15/2

answer: (B), (C) and (D)

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question_subject: mathematics


question: Let f : (0, ∞) → R be a differentiable function such that f'(x) = 2 - f(x)/x for all x ∈ (0, ∞) and f(1) = 1. Then

answer: (A)

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question_subject: mathematics


question: Let P = [3 -1 -2; 2 0 α; 3 -5 0], where α ∈ R . Suppose Q = [qij] is a matrix such that PQ = kI, where k ∈ R , k ≠ 0 and I is the identity matrix of order 3. If α23 = -k/8 and det(Q) = k^2/2, then

answer: (B) and (C)

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question_subject: mathematics


question: In a triangle XYZ, let x, y, z be the lengths of sides opposite to the angles X,Y,Z, respectively, and 2s = x + y + z. If x/4 = y/3 = z/2 and area of incircle of the triangle XYZ is 8π/3, then

response_choices:
(A) area of the triangle XYZ is 6√6
(B) the radius of circumcircle of the triangle XYZ is 35/6 √6
(C) sinX/sinY sinZ/sinY = 4/35
(D) sin²(X+Y)/2 = 3/5

answer: (A), (C) and (D)

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question_subject: mathematics


question: A solution curve of the differential equation (x² +xy + 4x + 2y + 4)dy/dx - y² = 0 , x > 0, passes through the point (1,3). Then the solution curve

response_choices:
(A) intersects y = x + 2 exactly at one point
(B) intersects y = x + 2 exactly at two points
(C) intersects y = (x + 2)²
(D) does NOT intersect y = (x + 3)²

answer: (A) and (D)

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question_subject: mathematics


question: Let f : R→R, g : R→R and h : R→R be differentiable functions such that f(x) = x^3 + 3x + 2, g(f(x)) = x and h(g(g(x))) = x for all x ∈ R. Then

answer: (B) and (C)

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question_subject: mathematics


question: The circle C1 : x^2 + y^2 = 3, with centre at O, intersects the parabola x^2 = 2y at the point P in the first quadrant. Let the tangent to the circle C1 at P touches other two circles C2 and C3 at R2 and R3, respectively. Suppose C2 and C3 have equal radii 2√3 and centres Q2 and Q3, respectively. If Q2 and Q3 lie on the y-axis, then

response_choices: (A) Q2Q3 = 12, (B) R2R3 = 4√6, (C) area of the triangle OR2R3 is 6√2, (D) area of the triangle PQ2Q3 is 4√2

answer: (A), (B) and (C)

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question_subject: mathematics


question: Let RS be the diameter of the circle x^2 + y^2 = 1, where S is the point (1, 0). Let P be a variable point (other than R and S) on the circle and tangents to the circle at S and P meet at the point Q. The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. Then the locus of E passes through the point(s)

answer: (A) and (C)

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question_subject: mathematics


question: The total number of distinct x ∈ R for which [2x 4x^2 1+8x^3] = 10 is [3x 9x^2 1+27x^3]

response_choices: No multiple choice options provided

answer: 2

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question_subject: mathematics


question: Let m be the smallest positive integer such that the coefficient of x^3 in the expansion of (1+x)^2 + (1+x)^3 + ... + (1+x)^(3+mx)^m is (3n+1) ^(n/3) for some positive integer n. Then the value of n is

response_choices: No multiple choice options provided

answer: 5

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question_subject: mathematics


question: The total number of distinct x ∈ [0,1] for which \int_{0}^{1} \frac{t^2}{1+t^4} dt = 2x - 1 is

answer: (1)

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question_subject: mathematics


question: Let α, β ∈ ℝ be such that lim \frac{x^2sin(βx)}{x→0 αx - sinx} = 1. Then 6(α + β) equals

answer: (7)

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question_subject: mathematics


question: Let z = (-1 + √3i)/2, where i = √-1, and r, s ∈ {1, 2, 3}. Let P = [(-z)^r  z^s; z^s  z^r] and I be the identity matrix of order 2. Then the total number of ordered pairs (r, s) for which P^2 = -I is

answer: (1)

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question_subject: mathematics