question: Extra pure N2 can be obtained by heating

response_choices: (A) NH3 with CuO, (B) NH4NO3, (C) (NH4)2Cr2O7, (D) Ba(N3)2

answer: D

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question_subject: chemistry


question: Geometrical shapes of the complexes formed by the reaction of Ni2+ with Cl-, CN- and H2O, respectively, are

response_choices: (A) octahedral, tetrahedral and square planar, (B) tetrahedral, square planar and octahedral, (C) square planar, tetrahedral and octahedral, (D) octahedral, square planar and octahedral

answer: B

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question_subject: chemistry


question: Bombardment of aluminum by α-particle leads to its artificial disintegration in two ways, (i) and (ii) as shown. Products X, Y and Z respectively are,

response_choices: (A) proton, neutron, positron, (B) neutron, positron, proton, (C) proton, positron, neutron, (D) positron, proton, neutron

answer: A

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question_subject: chemistry


question: Dissolving 120 g of urea (mol. wt. 60) in 1000 g of water gave a solution of density 1.15 g/mL. The molarity of the solution is

answer: C

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question_subject: chemistry


question: AgNO3 (aq.) was added to an aqueous KCl solution gradually and the conductivity of the solution was measured. The plot of conductance (Λ) versus the volume of AgNO3 is

answer: S

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question_subject: chemistry


question: Among the following compounds, the most acidic is

response_choices: (A) p-nitrophenol, (B) p-hydroxybenzoic acid, (C) o-hydroxybenzoic acid, (D) p-toluic acid

answer: C

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question_subject: chemistry


question: The major product of the following reaction is

answer: A

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question_subject: chemistry


question: Extraction of metal from the ore cassiterite involves

response_choices: (A) carbon reduction of an oxide ore, (B) self-reduction of a sulphide ore, (C) removal of copper impurity, (D) removal of iron impurity

answer: AD

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question_subject: chemistry


question: The correct statement(s) pertaining to the adsorption of a gas on a solid surface is (are)

response_choices: (A) Adsorption is always exothermic. (B) Physisorption may transform into chemisorption at high temperature. (C) Physisorption increases with increasing temperature but chemisorption decreases with increasing temperature. (D) Chemisorption is more exothermic than physisorption, however it is very slow due to higher energy of activation.

answer: ABD

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question_subject: chemistry


question: According to kinetic theory of gases

response_choices: (A) collisions are always elastic. (B) heavier molecules transfer more momentum to the wall of the container. (C) only a small number of molecules have very high velocity. (D) between collisions, the molecules move in straight lines with constant velocities.

answer: ACD

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question_subject: chemistry


question: Amongst the given options, the compound(s) in which all the atoms are in one plane in all the possible conformations (if any), is (are)

response_choices: (A) H2C=C-CH2 (B) H-C≡C-CH2 (C) H2C=C=O (D) H2C=C-CH2

answer: BC

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question_subject: chemistry


question: The metal rod M is

response_choices: (A) Fe (B) Cu (C) Ni (D) Co

answer: B

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question_subject: chemistry


question: The compound N is

answer: A

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question_subject: chemistry


question: The final solution contains

answer: C

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question_subject: chemistry


question: The structure of compound P is

response_choices: (A) CH3CH2CH2CH2—C≡C—H, (B) H3CH2C—C≡C—CH2CH3, (C) H3C—C—C≡C—CH3, (D) H3C—C—C≡C—H

answer: D

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question_subject: chemistry


question: The structure of the compound Q is

response_choices: (A) H3C—OH—C—CH2CH3, (B) H3C—C—C—CH3, (C) H3C—OH—CH2CHCH3, (D) CH3CH2CH2CHCH2CH3

answer: B

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question_subject: chemistry


question: The difference in the oxidation numbers of the two types of sulphur atoms in Na₂S₂O₆ is

answer: 5

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question_subject: chemistry


question: Reaction of Br₂ with Na₂CO₃ in aqueous solution gives sodium bromide and sodium bromate with evolution of CO₂ gas. The number of sodium bromide molecules involved in the balanced chemical equation is

answer: 5

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question_subject: chemistry


question: The maximum number of electrons that can have principal quantum number, n = 3, and spin quantum number, m_s = –1/2, is

answer: 9

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question_subject: chemistry


question: The work function (Φ) of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metal is

answer: 4

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question_subject: chemistry


question: To an evacuated vessel with movable piston under external pressure of 1 atm., 0.1 mol of He and 1.0 mol of an unknown compound (vapour pressure 0.68 atm. at 0 °C) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at 0 °C is close to

answer: 7

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question_subject: chemistry


question: The total number of alkenes possible by dehydrobromination of 3-bromo-3-cyclopentyihexane using alcoholic KOH is

answer: 5

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question_subject: chemistry


question: A decapeptide (Mol. Wt. 796) on complete hydrolysis gives glycine (Mol. Wt. 75), alanine and phenylalanine. Glycine contributes 47.0 % to the total weight of the hydrolysed products. The number of glycine units present in the decapeptide is

answer: 6

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question_subject: chemistry


question: A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall building which reflects the sound waves. The speed of sound in air is 320 m/s. The frequency of the siren heard by the car driver is

answer: A

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question_subject: physics


question: 5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T₁, the work done in the process is

answer: A

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question_subject: physics


question: Consider an electric field E = E₀ x, where E₀ is a constant. The flux through the shaded area (as shown in the figure) due to this field is

response_choices: (A) 2E₀a² (B) √(2E₀a²) (C) E₀a² (D) (E₀a²/√2)

answer: C

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question_subject: physics


question: The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 Å. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is

answer: A

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question_subject: physics


question: A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) is

answer: D

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question_subject: physics


question: A meter bridge is set-up as shown, to determine an unknown resistance 'X' using a standard 10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of 'X' is

answer: B

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question_subject: physics


question: A 2 μF capacitor is charged as shown in figure. The percentage of its stored energy dissipated after the switch S is turned to position 2 is

answer: D

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question_subject: physics


question: A spherical metal shell A of radius RA and a solid metal sphere B of radius RB (< RA) are kept far apart and each is given charge '+Q'. Now they are connected by a thin metal wire. Then

response_choices: (A) Einside = 0, (B) QA > QB, (C) σA = RB/RA * σB, (D) Eout surface A < Eout surface B

answer: ABCD

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question_subject: physics


question: An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?

response_choices: (A) They will never come out of the magnetic field region, (B) They will come out travelling along parallel paths, (C) They will come out at the same time, (D) They will come out at different times.

answer: BC, BD, BCD

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question_subject: physics


question: A composite block is made of slabs A, B, C, D and E of different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat 'Q' flows only from left to right through the blocks. Then in steady state

response_choices:
A) heat flow through A and E slabs are same.
B) heat flow through slab E is maximum.
C) temperature difference across slab E is smallest.
D) heat flow through C = heat flow through B + heat flow through D.

answer: D

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question_subject: physics


question: A metal rod of length 'L' and mass 'm' is pivoted at one end. A thin disk of mass 'M' and radius 'R' (< L) is attached at its center to the free end of the rod. Consider two ways the disc is attached: (case A) The disc is not free to rotate about its center and (case B) the disc is free to rotate about its center. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is (are) true?

response_choices:
A) Restoring torque in case A = Restoring torque in case B
B) Restoring torque in case A < Restoring torque in case B
C) Angular frequency for case A > Angular frequency for case B.
D) Angular frequency for case A < Angular frequency for case B.

answer: D

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question_subject: physics


question: Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed.

response_choices: No response choices provided

answer: No answer provided

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question_subject: physics


question: For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis.

response_choices: No response choices provided

answer: No answer provided

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question_subject: physics


question: For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure.

response_choices: No response choices provided

answer: No answer provided

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question_subject: physics


question: The phase space diagram for a ball thrown vertically up from ground is

response_choices: A, B, C, D

answer: D

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question_subject: physics


question: The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and E1 and E2 are the total mechanical energies respectively. Then

answer: C

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question_subject: physics


question: Consider the spring-mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is

answer: B

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question_subject: physics


question: Taking the electronic charge as 'e' and the permittivity as '\epsilon_0', use dimensional analysis to determine the correct expression for \omega_p.

response_choices: (A) \sqrt{Ne/m\epsilon_0}, (B) \sqrt{m\epsilon_0/Ne}, (C) \sqrt{Ne^2/m\epsilon_0}, (D) \sqrt{m\epsilon_0/Ne^2}

answer: C

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question_subject: physics


question: Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons N = 4 × 10^27 m^-3. Take \epsilon_0 = 10^-11 and m = 10^-30, where these quantities are in proper SI units.

answer: B

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question_subject: physics


question: A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. The stick applies a force of 2 N on the ring and rolls it without slipping with an acceleration of 0.3 m/s². The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is (P/10). The value of P is

answer: 4

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question_subject: physics


question: A block is moving on an inclined plane making an angle 45° with the horizontal and the coefficient of friction is μ. The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N = 10 μ, then N is

answer: 5

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question_subject: physics


question: Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side 'a '. The surface tension of the soap film is γ. The system of charges and planar film are in equilibrium, and α = k [a^2/γ]^(1/N), where 'k' is a constant. Then N is

answer: 3

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question_subject: physics


question: Steel wire of length 'L' at 40°C is suspended from the ceiling and then a mass 'm' is hung from its free end. The wire is cooled down from 40°C to 30°C to regain its original length 'L'. The coefficient of linear thermal expansion of the steel is 10^(-5) /°C, Young's modulus of steel is 10^11 N/m^2 and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of 'm' in kg is nearly

answer: 3

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question_subject: physics


question: The activity of a freshly prepared radioactive sample is 10^10 disintegrations per second, whose mean life is 10^9 s. The mass of an atom of this radioisotope is 10^(-23) kg. The mass (in mg) of the radioactive sample is

answer: 1

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question_subject: physics


question: A long circular tube of length 10 m and radius 0.3 m carries a current I along its curved surface as shown. A wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as I = I0 cos (300 t) where I0 is constant. If the magnetic moment of the loop is N d0 I0 sin (300 t), then 'N' is

response_choices: (No response choices provided)

answer: 6

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question_subject: physics


question: Four solid spheres each of diameter √5 cm and mass 0.5 kg are placed with their centers at the corners of a square of side 4cm. The moment of inertia of the system about the diagonal of the square is N × 10^-4 kg-m^2, then N is

response_choices: (No response choices provided)

answer: 9

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question_subject: physics


question: Let (x0, y0) be the solution of the following equations (2x)^(ln2) = (3y)^(ln3), 3^(ln x) = 2^(ln y). Then x0 is

answer: C

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question_subject: mathematics


question: The value of ∫(^(3)_(0.5)) (1/sin x^2 + sin (ln 6 - x^2)) dx is

answer: A

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question_subject: mathematics


question: Let a⃗=i⃗+j⃗+k⃗, b⃗=i⃗−j⃗+k⃗ and c⃗=i⃗−j⃗−k⃗ be three vectors. A vector v⃗ in the plane of a⃗ and b⃗, whose projection on c⃗ is 1/√3, is given by

response_choices: A) i⃗−3j⃗+3k⃗, B) −3i⃗−3j⃗−k⃗, C) 3i⃗−j⃗+3k⃗, D) i⃗+3j⃗−3k⃗

answer: C

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question_subject: mathematics


question: Let P={θ: sin θ−cos θ=√2 cos θ} and Q={θ: sin θ+cos θ=√2 sin θ} be two sets. Then

response_choices: A) P⊂Q and Q−P≠∅, B) Q⊄P, C) P⊄Q, D) P=Q

answer: D

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question_subject: mathematics


question: Let the straight line x=b divide the area enclosed by y=(1−x)², y=0, and x=0 into two parts R₁ (0≤x≤b) and R₂ (b≤x≤1) such that R₁−R₂=1/4. Then b equals

answer: B

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question_subject: mathematics


question: Let α and β be the roots of x^2 - 6x - 2 = 0, with α > β. If a_n = α^n - β^n for n≥1, then the value of (a_0 - 2a_1)/2a_0 is

answer: C

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question_subject: mathematics


question: A straight line L through the point (3,-2) is inclined at an angle 60° to the line √3x + y = 1. If L also intersects the x-axis, then the equation of L is

answer: B

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question_subject: mathematics


question: The vector(s) which is/are coplanar with vectors \vec{i} + \vec{j} + 2\vec{k} and \vec{i} + 2\vec{j} + \vec{k}, and perpendicular to the vector \vec{i} + \vec{j} + \vec{k} is/are

answer: AD

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question_subject: mathematics


question: Let M and N be two 3x3 non-singular skew-symmetric matrices such that MN = NM . If P^T denotes the transpose of P, then M^2N^2 (M^TN)^-1 (MN^-1)^T is equal to

answer: MARKS TO ALL

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question_subject: mathematics


question: Let the eccentricity of the hyperbola x^2/a^2 - y^2/b^2 = 1 be reciprocal to that of the ellipse x^2 + 4y^2 = 4 . If the hyperbola passes through a focus of the ellipse, then

response_choices: (A) the equation of the hyperbola is x^2/3 - y^2/2 = 1, (B) a focus of the hyperbola is (2, 0), (C) the eccentricity of the hyperbola is \sqrt{5}/3, (D) the equation of the hyperbola is x^2 - 3y^2 = 3

answer: BD

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question_subject: mathematics


question: Let f : R → R be a function such that f(x + y) = f(x) + f(y), ∀x, y ∈ R. If f(x) is differentiable at x = 0, then

response_choices: (A) f(x) is differentiable only in a finite interval containing zero, (B) f(x) is continuous ∀x ∈ R, (C) f'(x) is constant ∀x ∈ R, (D) f(x) is differentiable except at finitely many points

answer: BC,BCD

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question_subject: mathematics


question: If the point P(a, b, c), with reference to (E), lies on the plane 2x + y + z = 1, then the value of 7a + b + c is

answer: D

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question_subject: mathematics


question: Let ω be a solution of x^3 - 1 = 0 with Im(ω) > 0. If a = 2 with b and c satisfying (E), then the value of (3/ω^4) + (1/ω^6) + (3/ω^5) is equal to

answer: A

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question_subject: mathematics


question: Let b = 6, with a and c satisfying (E). If α and β are the roots of the quadratic equation ax^2 + bx + c = 0, then Σ[(1/α)^n + (1/β)^n] is

answer: B

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question_subject: mathematics


question: The probability of the drawn ball from U2 being white is

answer: B

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question_subject: mathematics


question: Given that the drawn ball from U2 is white, the probability that head appeared on the coin is

answer: D

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question_subject: mathematics


question: Consider the parabola y² = 8x. Let A₁ be the area of the triangle formed by the end points of its latus rectum and the point P(1, 2) on the parabola, and A₂ be the area of the triangle formed by drawing tangents at P and at the end points of the latus rectum. Then A₁/A₂ is

answer: 2

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question_subject: mathematics


question: Let a₁, a₂, a₃, ..., a₁₀₀ be an arithmetic progression with a₁ = 3 and S₅ = Σⁿᵖ=¹ aᵖ , 1 ≤ p ≤ 100. For any integer n with 1 ≤ n ≤ 20, let m = 5n. If S_m/S₅ does not depend on n, then a₅ is

answer: 3, 9, 3 & 9 BOTH

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question_subject: mathematics


question: The positive integer value of n > 3 satisfying the equation 1/[sin(π/n)] = 1/[sin(2π/n)] + 1/[sin(3π/n)] is

answer: 7

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question_subject: mathematics


question: Let f : [1, ∞) → [2, ∞) be a differentiable function such that f(1) = 2. If ∫(6/1) f(t) dt = 3x f(x) - x5 for all x ≥ 1, then the value of f(2) is

answer: MARKS TO ALL

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question_subject: mathematics


question: If z is any complex number satisfying |z - 3 - 2i| ≤ 2, then the minimum value of |2z - 6 + 5i| is

answer: 5

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question_subject: mathematics


question: The minimum value of the sum of real numbers a^-5, a^-4, 3a^-3, 1, a8 and a^10 with a > 0 is

answer: 8

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question_subject: mathematics


question: Let f(θ) = sin(tan^-1((sin θ)/√(cos 2θ))), where -π/4 < θ < π/4. Then the value of d/d(tan θ)(f(θ)) is

answer: 1

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question_subject: mathematics