question: A resistance of 2 Ω is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2 Ω, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is

answer: A

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question_subject: physics


question: In an experiment to determine the focal length (f) of a concave mirror by the u-v method, a student places the object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then,

answer: B

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question_subject: physics


question: Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance 'a' from the center P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes 2x, is

answer: B

image_available: yes

question_subject: physics


question: A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.

response_choices:
(A) A potential difference appears between the two cylinders when a charge density is given to the inner cylinder
(B) A potential difference appears between the two cylinders when a charge density is given to the outer cylinder
(C) No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders
(D) No potential difference appears between the two cylinders when same charge density is given to both the cylinders

answer: A

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question_subject: physics


question: Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,

response_choices:
(A) negative and distributed uniformly over the surface of the sphere
(B) negative and appears only at the point on the sphere closest to the point charge
(C) negative and distributed non-uniformly over the entire surface of the sphere
(D) zero

answer: D

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question_subject: physics


question: A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is

answer: C

image_available: yes

question_subject: physics


question: A ray of light traveling in water is incident on its surface open to air. The angle of incidence is θ, which is less than the critical angle. Then there will be

response_choices:
(A) only a reflected ray and no refracted ray
(B) only a refracted ray and no reflected ray
(C) a reflected ray and a refracted ray and the angle between them would be less than 180°– 2θ
(D) a reflected ray and a refracted ray and the angle between them would be greater than 180°– 2θ

answer: C

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question_subject: physics


question: In the options given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is

answer: A

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question_subject: chemistry


question: The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

answer: B

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question_subject: physics


question:
STATEMENT-1
A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30° with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.

because

STATEMENT-2
The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

response_choices:
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True

answer: C

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question_subject: physics


question:
STATEMENT-1
In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.

because

STATEMENT-2
In an elastic collision, the linear momentum of the system is conserved.

response_choices:
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True

answer: B

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question_subject: physics


question: The formula connecting u, v and f for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature. because STATEMENT-2 Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

response_choices: A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 C) Statement-1 is True, Statement-2 is False D) Statement-1 is False, Statement-2 is True

answer: C

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question_subject: physics


question: STATEMENT-1 If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic X-rays do not change. because STATEMENT-2 When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy.

response_choices: A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 C) Statement-1 is True, Statement-2 is False D) Statement-1 is False, Statement-2 is True

answer: B

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question_subject: physics


question: The ratio x1 / x2 is

answer: C

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question_subject: mathematics


question: When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is

answer: A

image_available: yes

question_subject: physics


question: The loss of kinetic energy during the above process is

answer: B

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question_subject: physics


question: The piston is now pulled out slowly and held at a distance 2L from the top. The pressure in the cylinder between its top and the piston will then be

response_choices: (A) Po, (B) Po/2, (C) Po/2 + Mg/πR²), (D) Po/2 - Mg/πR²

answer: A

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question_subject: physics


question: While the piston is at a distance 2L from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is

response_choices: (A) (2P₀πR⁴)/(πR²P₀ + Mg) (2L), (B) (P₀πR²-Mg)/(πR²P₀) (2L), (C) (P₀πR² + Mg)/(πR²P₀) (2L), (D) (P₀πR²)/(πR²P₀ - Mg) (2L)

answer: D

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question_subject: physics


question: The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is ρ. In equilibrium, the height H of the water column in the cylinder satisfies

response_choices: (A) ρg(L₀ - H)² + P₀(L₀ - H) + L₀P₀ = 0, (B) ρg(L₀ - H)² - P₀(L₀ - H) - L₀P₀ = 0, (C) ρg(L₀ - H)² + P₀(L₀ - H) - L₀P₀ = 0, (D) ρg(L₀ - H)² - P₀(L₀ - H) + L₀P₀ = 0

answer: C

image_available: yes

question_subject: physics


question: Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.

response_choices:
Column I: (A) GMeMe, G - universal gravitational constant, Me - mass of the earth, Ms - mass of the Sun
(B) 3RT/M, R - universal gas constant, T - absolute temperature, M - molar mass
(C) F^2/q^2B^2, F - force, q - charge, B - magnetic field
(D) GMe/Re, G - universal gravitational constant, Me - mass of the earth, Re - radius of the earth

Column II: (p) (volt) (coulomb) (metre)
(q) (kilogram) (metre)^3 (second)^-2
(r) (metre)^2 (second)^-2
(s) (farad) (volt)^2 (kg)^-1

answer: A:pq, B:qr, C:rr, D:ss

image_available: yes

question_subject: physics


question: Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4x4 matrix given in the ORS.

response_choices: (A) A charged capacitor is connected to the ends of the wire, (B) The wire is moved perpendicular to its length with a constant velocity in a uniform magnetic field perpendicular to the plane of motion, (C) The wire is placed in a constant electric field that has a direction along the length of the wire, (D) A battery of constant emf is connected to the ends of the wire, (p) A constant current flows through the wire, (q) Thermal energy is generated in the wire, (r) A constant potential difference develops between the ends of the wire, (s) Charges of constant magnitude appear at the ends of the wire

answer: D, p, q; B, q, r; C, r; A, s

image_available: yes

question_subject: physics


question: Some laws / processes are given in Column I. Match these with the physical phenomena given in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.

response_choices: (A) Transition between two atomic energy levels, (B) Electron emission from a material, (C) Mosley's law, (D) Change of photon energy into kinetic energy of electrons, (p) Characteristic X-rays, (q) Photoelectric effect, (r) Hydrogen spectrum, (s) β-decay

answer: A(p,b,c), B(a,d), C(r), D(s)

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question_subject: physics


question: The species having bond order different from that in CO is

answer: A

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question_subject: chemistry


question: Among the following, the paramagnetic compound is

answer: D

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question_subject: chemistry


question: Extraction of zinc from zinc blende is achieved by

response_choices: (A) electrolytic reduction, (B) roasting followed by reduction with carbon, (C) roasting followed by reduction with another metal, (D) roasting followed by self-reduction

answer: B

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question_subject: chemistry


question: In the following reaction, conc. HNO3/conc. H2SO4 -> X the structure of the major product 'X' is

response_choices: (A) Structure A, (B) Structure B, (C) Structure C, (D) Structure D

answer: B

image_available: yes

question_subject: chemistry


question: The reagent(s) for the following conversion, [image showing chemical conversion]

response_choices: (A) alcoholic KOH, (B) alcoholic KOH followed by NaNH2, (C) aqueous KOH followed by NaNH2, (D) Zn/CH3OH

answer: B

image_available: yes

question_subject: chemistry


question: The number of structural isomers for C6H14 is

answer: C

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question_subject: chemistry


question: The percentage of p-character in the orbitals forming P–P bonds in P4 is

answer: D

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question_subject: chemistry


question: When 20 g of naphthoic acid (C11H8O2) is dissolved in 50 g of benzene (Kf = 1.72 K kg mol^-1), a freezing point depression of 2 K is observed. The van't Hoff factor (i) is

answer: A

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question_subject: chemistry


question: The value of log10K for a reaction A ⇌ B is (Given : ΔrH°298K = −54.07 kJ mol^-1, ΔrS°298K = 10 JK^-1 mol^-1 and R = 8.314 JK^-1 mol^-1, 2.303 × 8.314 × 298 = 5705)

answer: B

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question_subject: chemistry


question: STATEMENT-1 : Boron always forms covalent bond. because STATEMENT-2 : The small size of B3+ favours formation of covalent bond.

response_choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

answer: A

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question_subject: chemistry


question: STATEMENT-1 : In water, orthoboric acid behaves as a weak monobasic acid. because STATEMENT-2 : In water, orthoboric acid acts as a proton donor.

response_choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

answer: C

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question_subject: chemistry


question: STATEMENT-1 : p-Hydroxybenzoic acid has a lower boiling point than o-hydroxybenzoic acid. because STATEMENT-2 : o-Hydroxybenzoic acid has intramolecular hydrogen bonding.

response_choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

answer: D

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question_subject: chemistry


question: STATEMENT-1 : Micelles are formed by surfactant molecules above the critical micellar concentration (CMC). because STATEMENT-2 : The conductivity of a solution having surfactant molecules decreases sharply at the CMC.

response_choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

answer: B

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question_subject: chemistry


question: Argon is used in arc welding because of its

response_choices:
(A) low reactivity with metal
(B) ability to lower the melting point of metal
(C) flammability
(D) high calorific value

answer: A

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question_subject: chemistry


question: The structure of XeO3 is

response_choices: (A) linear	(B) planar	(C) pyramidal	(D) T-shaped

answer: C

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question_subject: chemistry


question: XeF4 and XeF6 are expected to be

response_choices: (A) oxidizing	(B) reducing	(C) unreactive	(D) strongly basic

answer: A,B

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question_subject: chemistry


question: The total number of moles of chlorine gas evolved is

answer: B

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question_subject: chemistry


question: If the cathode is a Hg electrode, the maximum weight (g) of amalgam formed from this solution is

answer: D

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question_subject: chemistry


question: The total charge (coulombs) required for complete electrolysis is

answer: D

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question_subject: chemistry


question: Match the complexes in Column I with their properties listed in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.

response_choices:
Column I: (A) [Co(NH3)4(H2O)2]Cl2, (B) [Pt(NH3)2Cl2], (C) [Co(H2O)6]Cl]Cl, (D) [Ni(H2O)6]Cl2
 Column II: (p) geometrical isomers, (q) paramagnetic, (r) diamagnetic, (s) metal ion with +2 oxidation state

answer: A: pq, B: qr, C: rs, D: ps

image_available: yes

question_subject: chemistry


question: Match the chemical substances in Column I with type of polymers/type of bonds in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.

response_choices:
Column I: (A) cellulose, (B) nylon-6, 6, (C) protein, (D) sucrose
 Column II: (p) natural polymer, (q) synthetic polymer, (r) amide linkage, (s) glycoside linkage

answer: A: p, s; B: q, q; C: r, r; D: s

image_available: yes

question_subject: chemistry


question: Match gases under specified conditions listed in Column I with their properties/laws in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.

response_choices:
Column I: (A) hydrogen gas (P = 200 atm, T = 273 K), (B) hydrogen gas (P = 0, T= 273 K), (C) CO2 (P = 1 atm, T = 273 K), (D) real gas with very large molar volume
 Column II: (p) compressibility factor ≠ 1, (q) attractive forces are dominant, (r) PV = nRT, (s) P(V-nb)=nRT

answer: A: p, s; B: q; C: r, r; D: s

image_available: yes

question_subject: chemistry


question: Let α, β be the roots of the equation x^2 - px + r = 0 and α/2, 2β be the roots of the equation x^2 - qx + r = 0. Then the value of r is

answer: D

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question_subject: mathematics


question: Let f(x) be differentiable on the interval (0, ∞) such that f(1) = 1, and lim (t^2 f(t) - x^2 f(x) / t^2 - x^2) = 1 for each x > 0. Then f(x) is

answer: A

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question_subject: mathematics


question: One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

answer: C

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question_subject: mathematics


question: The tangent to the curve y = e^x drawn at the point (c, e^c) intersects the line joining the points (c -1, e^(c-1)) and (c + 1, e^(c+1))

response_choices: (A) on the left of x = c (B) on the right of x = c (C) at no point (D) at all points

answer: A

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question_subject: mathematics


question: lim ∫ f(t) dt equals

answer: A

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question_subject: mathematics


question: A hyperbola, having the transverse axis of length 2 sin θ, is confocal with the ellipse 3x^2 + 4y^2 = 12. Then its equation is

answer: A

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question_subject: mathematics


question: The number of distinct real values of λ, for which the vectors - λ^2 i + j + k, i - λ^2 j + k and i + j - λ^2 k are coplanar, is

response_choices: (A) zero, (B) one, (C) two, (D) three

answer: C

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question_subject: mathematics


question: A man walks a distance of 3 units from the origin towards the north-east (N 45°E) direction. From there, he walks a distance of 4 units towards the north-west (N 45°W) direction to reach a point P. Then the position of P in the Argand plane is

answer: D

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question_subject: mathematics


question: The number of solutions of the pair of equations 2sin^2 θ - cos 2θ = 0, 2cos^2 θ - 3sin θ = 0 in the interval [0,2π] is

response_choices: (A) zero, (B) one, (C) two, (D) four

answer: C

image_available: no

question_subject: mathematics


question: Let H1, H2, ..., Hn be mutually exclusive and exhaustive events with P(Hi) > 0, i = 1, 2, ..., n. Let E be any other event with 0 < P(E) < 1. STATEMENT-1 : P(Hi | E) > P(E | Hi). P(Hi) for i = 1, 2, ..., n. because STATEMENT-2 : ΣP(Hi) = 1.

response_choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1, (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1, (C) Statement-1 is True, Statement-2 is False, (D) Statement-1 is False, Statement-2 is True

answer: D

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question_subject: mathematics


question: Tangents are drawn from the point (17, 7) to the circle x^2 + y^2 = 169 . STATEMENT-1 : The tangents are mutually perpendicular. because STATEMENT-2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x^2 + y^2 = 338 . (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

response_choices: A, B, C, D

answer: A

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question_subject: mathematics


question: Let the vectors PQ , QR , RS , ST , TU and UP represent the sides of a regular hexagon. STATEMENT-1 : PQ × (RS + ST) ≠ 0 . because STATEMENT-2 : PQ × RS = 0 and PQ × ST ≠ 0 . (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

response_choices: A, B, C, D

answer: C

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question_subject: mathematics


question: Let F(x) be an indefinite integral of sin^2 x. STATEMENT-1 : The function F(x) satisfies F(x + π) = F(x) for all real x. because STATEMENT-2 : sin^2(x + π) = sin^2 x for all real x. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

response_choices: A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1, B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1, C) Statement-1 is True, Statement-2 is False, D) Statement-1 is False, Statement-2 is True

answer: D

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question_subject: mathematics


question: Let Vr denote the sum of the first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is (2r - 1). Let Tr = Vr+1 - Vr - 2 and Qr = Tr+1 - Tr for r = 1, 2,... The sum V1 + V2 + ... + Vn is (A) 1/12 n(n + 1)(3n^2 - n + 1) (B) 1/12 n(n + 1)(3n^2 + n + 2) (C) 1/2 n(2n^2 - n + 1) (D) 1/3 (2n^3 - 2n + 3)

answer: B

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question_subject: mathematics


question: T. is always

response_choices: (A) an odd number, (B) an even number, (C) a prime number, (D) a composite number

answer: D

image_available: no

question_subject: mathematics


question: Which one of the following is a correct statement? (A) Q1, Q2, Q3,... are in A.P. with common difference 5 (B) Q1, Q2, Q3,... are in A.P. with common difference 6 (C) Q1, Q2, Q3,... are in A.P. with common difference 11 (D) Q1 - Q2 = Q3 - ...

response_choices: (A) Q1, Q2, Q3,... are in A.P. with common difference 5, (B) Q1, Q2, Q3,... are in A.P. with common difference 6, (C) Q1, Q2, Q3,... are in A.P. with common difference 11, (D) Q1 - Q2 = Q3 - ...

answer: B

image_available: yes

question_subject: mathematics


question: The ratio of the areas of the triangles PQS and PQR is

answer: C

image_available: yes

question_subject: mathematics


question: The radius of the circumcircle of the triangle PRS is

answer: B

image_available: yes

question_subject: mathematics


question: The radius of the incircle of the triangle PQR is

answer: (D)

image_available: no

question_subject: mathematics


question: Consider the following linear equations ax + by + cz = 0 bx + cy + az = 0 cx + ay + bz = 0 Match the conditions/expressions in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.

response_choices: Column I: (A) a + b + c ≠ 0 and a^2 + b^2 + c^2 = ab + bc + ca (B) a + b + c = 0 and a^2 + b^2 + c^2 ≠ ab + bc + ca (C) a + b + c ≠ 0 and a^2 + b^2 + c^2 ≠ ab + bc + ca (D) a + b + c = 0 and a^2 + b^2 + c^2 = ab + bc + ca Column II: (p) the equations represent planes meeting only at a single point. (q) the equations represent the line x = y = z. (r) the equations represent identical planes. (s) the equations represent the whole of the three dimensional space.

answer: C-r, B-q, A-p, D-s

image_available: no

question_subject: mathematics


question: Match the functions in Column I with the properties in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.

response_choices:
Column I: (A) x⌊x⌋, (B) √x, (C) x+⌊x⌋, (D) ⌊x-1⌋+⌊x+1⌋
 Column II: (p) continuous in (-1, 1), (q) differentiable in (-1, 1), (r) strictly increasing in (-1, 1), (s) not differentiable at least at one point in (-1, 1)

answer: A: pqr, B: qs, C: rs, D: pq

image_available: no

question_subject: mathematics


question: Match the integrals in Column I with the values in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.

answer: A: [s], B: [s], C: [q], D: [r]

image_available: yes

question_subject: mathematics