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1 | 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 | (A) 3 Ω (B) 4 Ω (C) 5 Ω (D) 6 Ω | A | 1 | no | physics |
2 | 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, | (A) x < f (B) f < x < 2f (C) x = 2f (D) x > 2f | B | 1 | no | physics |
3 | 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 | (A) F/2m √(a^2 - x^2) (B) F/2m √(a^2 - x^2) (C) Fx/2ma (D) F/2m √(a^2 - x^2) * x | B | 1 | yes | physics |
4 | A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral. | (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 | A | 2 | no | physics |
5 | Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then, | (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 | D | 2 | no | physics |
6 | 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 | (A) 0
(B) 54 μC
(C) 27 μC
(D) 81 μC | C | 2 | yes | physics |
7 | 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 | (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 | C | 3 | no | physics |
8 | In the options given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is | (A) E(92U) > E(137I) + E(97Y) + 2E(n)
(B) E(92U) < E(137I) + E(97Y) + 2E(n)
(C) E(92U) < E(140Ba) + E(94Kr) + 2E(n)
(D) E(92U) = E(140Ba) + E(94Kr) + 2E(n) | A | 3 | no | chemistry |
9 | 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 | (A) 802 nm (B) 823 nm (C) 1882 nm (D) 1648 nm | B | 3 | no | physics |
10 | 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. | (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 | C | 4 | no | physics |
11 | 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. | (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 | B | 4 | no | physics |
12 | 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. | 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 | C | 5 | no | physics |
13 | 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. | 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 | B | 5 | no | physics |
14 | The ratio x1 / x2 is | (A) 2, (B) 1/2, (C) √2, (D) 1/√2 | C | 6 | no | mathematics |
15 | 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 | (A) 2Iω/3t, (B) 9Iω/2t, (C) 9Iω/4t, (D) 3Iω/2t | A | 6 | yes | physics |
16 | The loss of kinetic energy during the above process is | (A) Iω²/2, (B) Iω²/3, (C) Iω²/4, (D) Iω²/6 | B | 6 | no | physics |
17 | 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 | (A) Po, (B) Po/2, (C) Po/2 + Mg/πR²), (D) Po/2 - Mg/πR² | A | 6 | no | physics |
18 | 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 | (A) (2P₀πR⁴)/(πR²P₀ + Mg) (2L), (B) (P₀πR²-Mg)/(πR²P₀) (2L), (C) (P₀πR² + Mg)/(πR²P₀) (2L), (D) (P₀πR²)/(πR²P₀ - Mg) (2L) | D | 7 | no | physics |
19 | 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 | (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 | C | 7 | yes | physics |
20 | 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. | 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 | A:pq, B:qr, C:rr, D:ss | 8 | yes | physics |
21 | 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. | (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 | D, p, q; B, q, r; C, r; A, s | 9 | yes | physics |
22 | 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. | (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 | A(p,b,c), B(a,d), C(r), D(s) | 10 | no | physics |
23 | The species having bond order different from that in CO is | (A) NO-, (B) NO+, (C) CN-, (D) N2 | A | 10 | no | chemistry |
24 | Among the following, the paramagnetic compound is | (A) Na2O2, (B) O3, (C) N2O, (D) KO2 | D | 10 | no | chemistry |
25 | Extraction of zinc from zinc blende is achieved by | (A) electrolytic reduction, (B) roasting followed by reduction with carbon, (C) roasting followed by reduction with another metal, (D) roasting followed by self-reduction | B | 11 | no | chemistry |
26 | In the following reaction, conc. HNO3/conc. H2SO4 -> X the structure of the major product 'X' is | (A) Structure A, (B) Structure B, (C) Structure C, (D) Structure D | B | 11 | yes | chemistry |
27 | The reagent(s) for the following conversion, [image showing chemical conversion] | (A) alcoholic KOH, (B) alcoholic KOH followed by NaNH2, (C) aqueous KOH followed by NaNH2, (D) Zn/CH3OH | B | 12 | yes | chemistry |
28 | The number of structural isomers for C6H14 is | (A) 3, (B) 4, (C) 5, (D) 6 | C | 12 | no | chemistry |
29 | The percentage of p-character in the orbitals forming P–P bonds in P4 is | A) 25, B) 33, C) 50, D) 75 | D | 13 | no | chemistry |
30 | 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 | A) 0.5, B) 1, C) 2, D) 3 | A | 13 | no | chemistry |
31 | 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) | A) 5, B) 10, C) 95, D) 100 | B | 13 | no | chemistry |
32 | STATEMENT-1 : Boron always forms covalent bond. because STATEMENT-2 : The small size of B3+ favours formation of covalent bond. | (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 | A | 14 | no | chemistry |
33 | STATEMENT-1 : In water, orthoboric acid behaves as a weak monobasic acid. because STATEMENT-2 : In water, orthoboric acid acts as a proton donor. | (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 | C | 14 | no | chemistry |
34 | STATEMENT-1 : p-Hydroxybenzoic acid has a lower boiling point than o-hydroxybenzoic acid. because STATEMENT-2 : o-Hydroxybenzoic acid has intramolecular hydrogen bonding. | (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 | D | 15 | no | chemistry |
35 | 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. | (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 | B | 15 | no | chemistry |
36 | Argon is used in arc welding because of its | (A) low reactivity with metal
(B) ability to lower the melting point of metal
(C) flammability
(D) high calorific value | A | 16 | no | chemistry |
37 | The structure of XeO3 is | (A) linear (B) planar (C) pyramidal (D) T-shaped | C | 16 | no | chemistry |
38 | XeF4 and XeF6 are expected to be | (A) oxidizing (B) reducing (C) unreactive (D) strongly basic | A,B | 16 | no | chemistry |
39 | The total number of moles of chlorine gas evolved is | A) 0.5, B) 1.0, C) 2.0, D) 3.0 | B | 17 | no | chemistry |
40 | If the cathode is a Hg electrode, the maximum weight (g) of amalgam formed from this solution is | (A) 200 (B) 225 (C) 400 (D) 446 | D | 18 | no | chemistry |
41 | The total charge (coulombs) required for complete electrolysis is | (A) 24125, (B) 48250, (C) 96500, (D) 193000 | D | 19 | no | chemistry |
42 | 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. | 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 | A: pq, B: qr, C: rs, D: ps | 20 | yes | chemistry |
43 | 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. | 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 | A: p, s; B: q, q; C: r, r; D: s | 21 | yes | chemistry |
44 | 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. | 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 | A: p, s; B: q; C: r, r; D: s | 21 | yes | chemistry |
45 | 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 | (A) 2/9 (p - q)(2q - p) (B) 2/9 (q - p)(2p - q) (C) 2/9 (q - 2p)(2q - p) (D) 2/9 (2p - q)(2q - p) | D | 22 | no | mathematics |
46 | 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 | (A) 1/3x + 2x^2/3 (B) -1/x + 4x^2/3 (C) -1/x + 2/x^2 (D) 1/x | A | 22 | no | mathematics |
47 | 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 | (A) 1/2 (B) 1/3 (C) 2/5 (D) 1/5 | C | 22 | no | mathematics |
48 | 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)) | (A) on the left of x = c (B) on the right of x = c (C) at no point (D) at all points | A | 22 | no | mathematics |
49 | lim ∫ f(t) dt equals | (A) 8/π f(2), (B) 2/π f(2), (C) 2/π (1/2), (D) 4 f(2) | A | 23 | no | mathematics |
50 | 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 | (A) x^2 cosec^2 θ - y^2 sec^2 θ = 1, (B) x^2 sec^2 θ - y^2 cosec^2 θ = 1, (C) x^2 sin^2 θ - y^2 cos^2 θ = 1, (D) x^2 cos^2 θ - y^2 sin^2 θ = 1 | A | 23 | no | mathematics |
51 | 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 | (A) zero, (B) one, (C) two, (D) three | C | 23 | no | mathematics |
52 | 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 | (A) 3e^(i/4) + 4i, (B) (3 - 4i)e^(i/4), (C) (4 + 3i)e^(i/4), (D) (3 + 4i)e^(i/4) | D | 24 | no | mathematics |
53 | 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 | (A) zero, (B) one, (C) two, (D) four | C | 24 | no | mathematics |
54 | 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. | (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 | D | 24 | no | mathematics |
55 | 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 | A, B, C, D | A | 25 | no | mathematics |
56 | 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 | A, B, C, D | C | 25 | no | mathematics |
57 | 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 | 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 | D | 26 | no | mathematics |
58 | 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) | 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) | B | 26 | no | mathematics |
59 | T. is always | (A) an odd number, (B) an even number, (C) a prime number, (D) a composite number | D | 27 | no | mathematics |
60 | 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 - ... | (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 - ... | B | 27 | yes | mathematics |
61 | The ratio of the areas of the triangles PQS and PQR is | (A) 1 : √2, (B) 1 : 2, (C) 1 : 4, (D) 1 : 8 | C | 27 | yes | mathematics |
62 | The radius of the circumcircle of the triangle PRS is | (A) 5, (B) 3√3, (C) 3√2, (D) 2√3 | B | 27 | yes | mathematics |
63 | The radius of the incircle of the triangle PQR is | (A) 4, (B) 3, (C) 8/3, (D) 2 | (D) | 28 | no | mathematics |
64 | 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. | 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. | C-r, B-q, A-p, D-s | 28 | no | mathematics |
65 | 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. | 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) | A: pqr, B: qs, C: rs, D: pq | 29 | no | mathematics |
66 | 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. | A: [p, s], B: [s], C: [q], D: [r, s] | A: [s], B: [s], C: [q], D: [r] | 30 | yes | mathematics |
4 | A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of 3v^2/4g with respect to the initial position. The object is | (A) ring (B) solid sphere (C) hollow sphere (D) disc | D | 2 | yes | physics |
5 | Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is ρ, the surface tension of water is T and the atmospheric pressure is P0. Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude | (A) | 2P0 Rh + πR^2 ρgh - 2RT | (B) | 2P0 Rh + R ρgh^2 - 2RT | (C) | P0 πR^2 +R ρgh^2 - 2RT | (D) | P0 πR^2 + R ρgh^2 +2RT | | B | 2 | yes | physics |
6 | A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is | (A) zero everywhere, (B) non-zero and uniform, (C) non-uniform, (D) zero only at its center | B | 3 | yes | physics |
7 | Positive and negative point charges of equal magnitude are kept at (0, 0, a/2) and (0, 0, -a/2), respectively. The work done by the electric field when another positive point charge is moved from (-a, 0, 0) to (0, a, 0) is | (A) positive, (B) negative, (C) zero, (D) depends on the path connecting the initial and final positions | C | 3 | no | physics |
8 | A magnetic field B = B0j exists in the region. a < x < 2a and B = -B0j, in the region 2a < x < 3a, where B0 is a positive constant. A positive point charge moving with a velocity v = v0i, where v0 is a positive constant, enters the magnetic field at x = a. The trajectory of the charge in this region can be like, | (A) (B) (C) (D) | (A) | 4 | yes | physics |
9 | Electrons with de-Broglie wavelength λ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is | (A) λ0 = 2mc^2/h (B) λ0 = 2h/mc (C) λ0 = 2m^2c^523/h^2 (D) λ0 = λ | (A) | 4 | no | physics |
10 | STATEMENT-1
If there is no external torque on a body about its center of mass, then the velocity of the center of mass remains constant.
because
STATEMENT-2
The linear momentum of an isolated system remains constant. | (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 | D | 5 | no | physics |
11 | STATEMENT-1
A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.
because
STATEMENT-2
For every action there is an equal and opposite reaction. | (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 | B | 5 | no | physics |
12 | STATEMENT-1
A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure. The ring can float at a certain height above the coil.
because
STATEMENT-2
In the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the upward direction. | (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 | B | 6 | yes | physics |
13 | STATEMENT-1
The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume.
because
STATEMENT-2
The molecules of a gas collide with each other and the velocities of the molecules change due to the collision. | (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 | B | 6 | no | physics |
14 | The speed of sound of the whistle is | (A) 340 m/s for passengers in A and 310 m/s for passengers in B, (B) 360 m/s for passengers in A and 310 m/s for passengers in B, (C) 310 m/s for passengers in A and 360 m/s for passengers in B, (D) 340 m/s for passengers in both the trains | B | 7 | no | physics |
15 | The distribution of the sound intensity of the whistle as observed by the passengers in train A is best represented by | (A), (B), (C), (D) | A | 7 | yes | physics |
16 | The spread of frequency as observed by the passengers in train B is | (A) 310 Hz, (B) 330 Hz, (C) 350 Hz, (D) 290 Hz | A | 7 | no | physics |
17 | Light travels as a | (A) parallel beam in each medium, (B) convergent beam in each medium, (C) divergent beam in each medium, (D) divergent beam in one medium and convergent beam in the other medium | A | 7 | no | physics |
18 | The phases of the light wave at c, d, e and f are φc, φd, φe and φf respectively. It is given that φe ≠ φf. | (A) φc cannot be equal to φd, (B) φd can be equal to φc, (C) (φd - φf) is equal to (φc - φe), (D) (φd - φe) is not equal to (φf - φc) | C | 8 | no | physics |
19 | Speed of light is | (A) the same in medium-1 and medium-2, (B) larger in medium-1 than in medium-2, (C) larger in medium-2 than in medium-1, (D) different at b and d | B | 8 | no | physics |
20 | Column I describes some situations in which a small object moves. Column II describes some characteristics of these motions. Match the situations in Column I with the characteristics in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS. | A) The object moves on the x-axis under a conservative force in such a way that its "speed" and "position" satisfy v = c₁√(c₂ - x²), where c₁ and c₂ are positive constants. (B) The object moves on the x-axis in such a way that its velocity and its displacement from the origin satisfy v = -kx, where k is a positive constant. (C) The object is attached to one end of a mass-less spring of a given spring constant. The other end of the spring is attached to the ceiling of an elevator. Initially everything is at rest. The elevator starts going upwards with a constant acceleration a. The motion of the object is observed from the elevator during the period it maintains this acceleration. (D) The object is projected from the earth's surface vertically upwards with a speed 2√(GM/R), where, M is the mass of the earth and R is the radius of the earth. Neglect forces from objects other than the earth. | First option: p,c
Second option: d | 9 | yes | physics |
21 | Two wires each carrying a steady current I are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS. | (A) Point P is situated midway between the wires. (B) Point P is situated at the mid-point of the line joining the centers of the circular wires, which have same radii. (C) Point P is situated at the mid-point of the line joining the centers of the circular wires, which have same radii. (D) Point P is situated at the common center of the wires. | ACBCBDAD or ACBCBDDA | 10 | yes | physics |
22 | Column I gives some devices and Column II gives some processes on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS. | (A) Bimetallic strip, (B) Steam engine, (C) Incandescent lamp, (D) Electric fuse / (p) Radiation from a hot body, (q) Energy conversion, (r) Melting, (s) Thermal expansion of solids | A - 's, q' OR 's' alone, B - 'q', C - 'p, q' OR 'p' alone, D - 'q, r' OR 'r' alone | 11 | no | physics |
23 | Consider a titration of potassium dichromate solution with acidified Mohr's salt solution using diphenylamine as indicator. The number of moles of Mohr's salt required per mole of dichromate is | (A) 3, (B) 4, (C) 5, (D) 6 | D | 11 | no | chemistry |
24 | Among the following metal carbonyls, the C-O bond order is lowest in | (A) [Mn(CO)6]+, (B) [Fe(CO)5], (C) [Cr(CO)6], (D) [V(CO)6]– | D | 11 | no | chemistry |
25 | A solution of a metal ion when treated with KI gives a red precipitate which dissolves in excess KI to give a colourless solution. Moreover, the solution of metal ion on treatment with a solution of cobalt(II) thiocyanate gives rise to a deep blue crystalline precipitate. The metal ion is | (A) Pb2+, (B) Hg2+, (C) Cu2+, (D) Co2+ | B | 11 | no | chemistry |
26 | Cyclohexene on ozonolysis followed by reaction with zinc dust and water gives compound E. Compound E on further treatment with aqueous KOH yields compound F. Compound F is | (A) CHO, (B) CHO, (C) COOH, (D) CO2H, CO2H | A | 12 | yes | chemistry |
27 | The number of stereoisomers obtained by bromination of trans-2-butene is | (A) 1, (B) 2, (C) 3, (D) 4 | A | 12 | no | chemistry |
28 | Among the following, the least stable resonance structure is | (A) [Resonance structure A], (B) [Resonance structure B], (C) [Resonance structure C], (D) [Resonance structure D] | A | 12 | yes | chemistry |
29 | A positron is emitted from 2311Na. The ratio of the atomic mass and atomic number of the resulting nuclide is | A) 22/10, B) 22/11, C) 23/10, D) 23/12 | C | 13 | no | chemistry |
30 | For the process H2O(l) (1 bar, 373 K) → H2O(g) (1 bar, 373 K), the correct set of thermodynamic parameters is | A) ΔG = 0, ΔS = +ve, B) ΔG = 0, ΔS = -ve, C) ΔG = +ve, ΔS = 0, D) ΔG = -ve, ΔS = +ve | A | 13 | no | chemistry |
31 | Consider a reaction aG + bH → Products. When concentration of both the reactants G and H is doubled, the rate increases by eight times. However, when concentration of G is doubled keeping the concentration of H fixed, the rate is doubled. The overall order of the reaction is | A) 0, B) 1, C) 2, D) 3 | D | 13 | no | chemistry |
32 | STATEMENT-1 : Alkali metals dissolve in liquid ammonia to give blue solutions. because STATEMENT-2 : Alkali metals in liquid ammonia give solvated species of the type [M(NH3)x]+ (M = alkali metals). | (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 | B | 14 | no | chemistry |
33 | STATEMENT-1 : Glucose gives a reddish-brown precipitate with Fehling's solution. because STATEMENT-2 : Reaction of glucose with Fehling's solution gives CuO and gluconic acid. | (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 | C | 14 | no | chemistry |
34 | STATEMENT-1 : Molecules that are not superimposable on their mirror images are chiral. because STATEMENT-2 : All chiral molecules have chiral centres. | (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 | C | 15 | no | chemistry |
35 | STATEMENT-1 : Band gap in germanium is small. because STATEMENT-2 : The energy spread of each germanium atomic energy level is infinitesimally small. | (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 | B | 15 | no | physics |
36 | Among the following, identify the correct statement. | (A) Chloride ion is oxidised by O₂ (B) Fe²⁺ is oxidised by iodine (C) Iodide ion is oxidised by chlorine (D) Mn²⁺ is oxidised by chlorine | C | 16 | no | chemistry |
37 | While Fe³⁺ is stable, Mn³⁺ is not stable in acid solution because | (A) O₂ oxidises Mn²⁺ to Mn³⁺ (B) O₂ oxidises both Mn²⁺ to Mn³⁺ and Fe²⁺ to Fe³⁺ (C) Fe³⁺ oxidises H₂O to O₂ (D) Mn³⁺ oxidises H₂O to O₂ | D | 16 | no | chemistry |
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