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38 | Sodium fusion extract, obtained from aniline, on treatment with iron(II) sulphate and HβSOβ in presence of air gives a Prussian blue precipitate. The blue colour is due to the formation of | (A) Feβ[Fe(CN)β]β (B) Feβ[Fe(CN)β]β (C) Feβ[Fe(CN)β]β (D) Feβ[Fe(CN)β]β | A | 16 | no | chemistry |
39 | Which one of the following reagents is used in the above reaction? | (A) aq.NaOH + CHβCl (B) aq.NaOH + CHβClβ (C) aq.NaOH + CHClβ (D) aq.NaOH + CClβ | C | 16 | no | chemistry |
10 | The electrophile in this reaction is | (A) :CHCl (B) +CHClβ (C) :CClβ (D) -CClβ | C | 17 | no | chemistry |
41 | The structure of the intermediate I is | (A) [Structure A] (B) [Structure B] (C) [Structure C] (D) [Structure D] | B | 17 | yes | chemistry |
42 | Match the reactions in Column I with nature of the reactions/type of the products in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS. | Column I: (A) Oβ β Oβ + Oβ, (B) CrOβΒ²β» + HβΊ β, (C) MnOββ» +NOβ + HβΊ β, (D) NOβ + HβSOβ + FeΒ²βΊ β
Column II: (p) redox reaction, (q) one of the products has trigonal planar structure, (r) dimeric bridged tetrahedral metal ion, (s) disproportionation | (A, p), (B, r), (C, r), (D, s) | 18 | yes | chemistry |
43 | Match the compounds/ions in Column I with their properties/reactions in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS. | Column I: (A) CβHβ
CHO, (B) CHβCβ‘CH, (C) CNβ», (D) Iβ»
Column II: (p) gives precipitate with 2,4-dinitrophenylhydrazine, (q) gives precipitate with AgNOβ, (r) is a nucleophile, (s) is involved in cyanohydrin formation | (A, p), (B, q), (C, r), (D, s) | 18 | yes | chemistry |
44 | Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS. | (A) simple cubic and face-centred cubic, (B) cubic and rhombohedral, (C) cubic and tetragonal, (D) hexagonal and monoclinic, (p) have these cell parameters a =b=c and Ξ± = Ξ² = Ξ³, (q) are two crystal systems, (r) have only two crystallographic angles of 90Β°, (s) belong to same crystal system | p: A, D; q: B; r: C; s: D | 19 | yes | chemistry |
45 | Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are | (A) (4/3, 3), (B) (3, 2/3), (C) (3, 4/3), (D) (4/3, 2/3) | C | 19 | no | mathematics |
46 | If |z|=1 and z β Β±1, then all the values of z/(1-z^2) lie on | (A) a line not passing through the origin
(B) |z|=β2
(C) the x-axis
(D) the y-axis | D | 20 | no | mathematics |
47 | Let E^c denote the complement of an event E. Let E, F, G be pairwise independent events with P(G)>0 and P(E β© F β© G)=0. Then P[E^c β© F^c | G] equals | (A) P(E^c)+ P(F^c)
(B) P(E^c)- P(F^c)
(C) P(E^c)- P(F)
(D) P(E)- P(F^c) | C | 20 | no | mathematics |
48 | (d^2x)/(dy^2) equals | (A) (d^2y/dx^2)^-1
(B) -(d^2y/dx^2)^-1(dy/dx)^-3
(C) (d^2y/dx^2)(dy/dx)^2
(D) -(d^2y/dx^2)(dy/dx)^3 | D | 20 | no | mathematics |
49 | The differential equation dy/dx = β(1-y^2)/y determines a family of circles with | (A) variable radii and a fixed centre at (0, 1) (B) variable radii and a fixed centre at (0, -1) (C) fixed radius 1 and variable centres along the x-axis (D) fixed radius 1 and variable centres along the y-axis | C | 21 | yes | mathematics |
50 | Let a, b, c be unit vectors such that a + b + c = 0. Which one of the following is correct? | (A) a Γ b = b Γ c = c Γ a = 0 (B) a Γ b = b Γ c = c Γ a β 0 (C) a Γ b = b Γ c = a Γ c β 0 (D) a Γ b, b Γ c, c Γ a are mutually perpendicular | B | 21 | no | mathematics |
51 | Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB = 2 CD . Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is | (A) 3 (B) 2 (C) 3/2 (D) 1 | B | 21 | no | mathematics |
52 | Let f(x) = (x)/(1 + x^n)^(n) for n >= 2 and g(x) = (f β f β ... β f) (x). Then [x^(-2)g(x) dx] equals | (A) (1)/((n(n-1))(1 + nx^n)^(1/n) + K), (B) (1)/(n-1)(1 + nx^n)^(-1/n) + K, (C) (1)/((n(n+1))(1 + nx^n)^(1/n) + K), (D) (1)/(n+1)(1 + nx^n)^(1/n) + K | A | 22 | no | mathematics |
53 | The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is | (A) 360, (B) 192, (C) 96, (D) 48 | C | 22 | no | mathematics |
54 | Consider the planes 3x - 6y - 2z = 15 and 2x + y - 2z = 5. STATEMENT-1 : The parametric equations of the line of intersection of the given planes are x = 3 + 14t, y = 1 + 2t, z = 15t. because STATEMENT-2 : The vector 14i + 2j + 15k is parallel to the line of intersection of given planes. | (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 | 22 | no | mathematics |
55 | STATEMENT-1 : The curve y = -x^2/2 + x + 1 is symmetric with respect to the line x = 1. because STATEMENT-2 : A parabola is symmetric about its axis. | (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 | 23 | no | mathematics |
56 | Let f(x) = 2 + cos x for all real x. STATEMENT-1 : For each real t, there exists a point c in [t, t + Ο] such that f'(c) = 0. because STATEMENT-2 : f(t) = f(t + 2Ο) for each real t. | (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 | 23 | no | mathematics |
57 | Lines L1: y - x = 0 and L2: 2x + y = 0 intersect the line L3: y + 2 = 0 at P and Q, respectively. The bisector of the acute angle between L1 and L2 intersects L3 at R. STATEMENT-1: The ratio PR: RQ equals 2β2: β5. because STATEMENT-2: In any triangle, bisector of an angle divides the triangle into two similar triangles. | (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 | 24 | no | mathematics |
58 | Which one of the following statements is correct? (A) G1 > G2 > G3 > ... (B) G1 < G2 < G3 < ... (C) G2 = G1 = G3 = ... (D) G1 < G3 < G5 < ... and G2 > G4 > G6 > ... | (A) G1 > G2 > G3 > ... (B) G1 < G2 < G3 < ... (C) G2 = G1 = G3 = ... (D) G1 < G3 < G5 < ... and G2 > G4 > G6 > ... | C | 24 | no | mathematics |
59 | Which one of the following statements is correct? (A) A1 > A2 > A3 > ... (B) A1 < A2 < A3 < ... (C) A1 > A3 > A5 > ... and A2 < A4 < A6 < ... (D) A1 < A3 < A5 < ... and A2 > A4 > A6 > ... | (A) A1 > A2 > A3 > ... (B) A1 < A2 < A3 < ... (C) A1 > A3 > A5 > ... and A2 < A4 < A6 < ... (D) A1 < A3 < A5 < ... and A2 > A4 > A6 > ... | A | 24 | no | mathematics |
60 | Which one of the following statements is correct? | (A) Hβ > Hβ > Hβ > β―
(B) Hβ < Hβ < Hβ < β―
(C) Hβ > Hβ > Hβ > β― and Hβ < Hβ < Hβ < β―
(D) Hβ < Hβ < Hβ
< β― and Hβ > Hβ > Hβ > β― | B | 25 | no | physics |
61 | The line y = x meets y = ke^x for k β€ 0 at | (A) no point
(B) one point
(C) two points
(D) more than two points | B | 25 | no | mathematics |
62 | The positive value of k for which ke^x - x = 0 has only one root is | (A) 1/e
(B) 1
(C) e
(D) logβ
2 | A | 25 | no | mathematics |
63 | For k > 0, the set of all values of k for which ke^x - x = 0 has two distinct roots is | (A) (0, 1/e)
(B) (1/e, 1)
(C) (1/e, β)
(D) (0, 1) | A | 25 | no | mathematics |
64 | Let f(x) = (x^2 - 6x + 5) / (x^3 - 5x + 6). Match the expressions/statements in Column I with expressions/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) If -1 < x < 1, then f(x) satisfies (B) If 1 < x < 2, then f(x) satisfies (C) If 3 < x < 5, then f(x) satisfies (D) If x > 5, then f(x) satisfies
Column II: (p) 0 < f(x) < 1 (q) f(x) < 0 (r) f(x) > 0 (s) f(x) < 1 | p: not selected, q: A, r: C and D, s: A and D | 26 | yes | mathematics |
65 | Let (x, y) be such that sinβ»ΒΉ(a x) + cosβ»ΒΉ(y) + cosβ»ΒΉ(b x y) = Ο/2. Match the statements 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) If a = 1 and b = 0, then (x, y), (B) If a = 1 and b = 1, then (x, y), (C) If a = 1 and b = 2, then (x, y), (D) If a = 2 and b = 2, then (x, y)
Column II: (p) lies on the circle xΒ² + yΒ² = 1, (q) lies on (xΒ² - 1)(yΒ² - 1) = 0, (r) lies on y = x, (s) lies on (4xΒ² - 1)(yΒ² - 1) = 0 | p, q, r, s | 27 | no | mathematics |
66 | Match the statements in Column I with the properties in Column II and indicate your answer by darkening the appropriate bubbles in the 4 Γ 4 matrix given in the ORS. | (A) Two intersecting circles, (B) Two mutually external circles, (C) Two circles, one strictly inside the other, (D) Two branches of a hyperbola, (p) have a common tangent, (q) have a common normal, (r) do not have a common tangent, (s) do not have a common normal | A: pq, B: pq, C: rs, D: rs | 28 | yes | mathematics |
1 | Consider the two curves C1 : y^2 = 4x, C2 : x^2 + y^2 - 6x + 1 = 0. Then, | (A) C1 and C2 touch each other only at one point, (B) C1 and C2 touch each other exactly at two points, (C) C1 and C2 intersect (but do not touch) at exactly two points, (D) C1 and C2 neither intersect nor touch each other | B | 1 | no | mathematics |
2 | If 0 < x < 1, then sqrt(1 + x^2) ( [x cos (cot^-1 x) + sin (cot^-1 x)]^2 - 1 )^2 = | (A) x/sqrt(1+x^2), (B) x, (C) x*sqrt(1+x^2), (D) sqrt(1+x^2) | C | 1 | no | mathematics |
3 | The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors Γ’, bΜ, Δ such that Γ’.bΜ = bΜ.Δ = Δ.Γ’ = 1/2. Then, the volume of the parallelopiped is | (A) 1/sqrt(2), (B) 1/2sqrt(2), (C) sqrt(3)/2, (D) 1/sqrt(3) | A | 1 | no | mathematics |
4 | Let a and b be non-zero real numbers. Then, the equation (a x^2 + b y^2 + c) (x^2 - 5 x y + 6 y^2) = 0 represents | (A) four straight lines, when c = 0 and a, b are of the same sign, (B) two straight lines and a circle, when a = b, and c is of sign opposite to that of a, (C) two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a, (D) a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a | B | 1 | no | mathematics |
5 | Let g(x) = (x-1)^n/(log cos^m (x-1)), 0<x<2, m and n are integers, mβ 0, n>0, and let p be the left hand derivative of |x-1| at x=1. If lim g(x)=p, then | (A) n=1, m=1 (B) n=1, m=-1 (C) n=2, m=2 (D) n>2, m=n | C | 2 | no | mathematics |
6 | The total number of local maxima and local minima of the function f(x)={(2+x)^3, -3<xβ€-1; x^2/3, -1<x<2} | (A) 0 (B) 1 (C) 2 (D) 3 | C | 2 | no | mathematics |
7 | A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then | (A) 1/PS + 1/ST < 2/βQSΓSR (B) 1/PS + 1/ST > 2/βQSΓSR (C) 1/PS + 1/ST < 4/QR (D) 1/PS + 1/ST > 4/QR | B, D | 2 | yes | mathematics |
8 | Let P(x1, y1) and Q(x2, y2), y1 < 0, y2 < 0, be the end points of the latus rectum of the ellipse x^2 + 4y^2 = 4. The equations of parabolas with latus rectum PQ are | (A) x^2 + 2β3 y = 3 + β3, (B) x^2 - 2β3 y = 3 + β3, (C) x^2 + 2β3 y = 3 - β3, (D) x^2 - 2β3 y = 3 - β3 | C | 3 | no | mathematics |
9 | Let S_n = Ξ£(n/(n^2 + kn + k^2)) and T_n = Ξ£((n-1)/(n^2 + kn + k^2)), for n = 1, 2, 3, .... Then, | (A) S_n < Ο/3β3, (B) S_n > Ο/3β3, (C) T_n < Ο/3β3, (D) T_n > Ο/3β3 | A,D | 3 | no | mathematics |
10 | Let f(x) be a non-constant twice differentiable function defined on (-β, β) such that f(x) = f(1 - x) and f''(1/4) = 0. Then, | (A) f''(x) vanishes at least twice on [0, 1], (B) f'(1/2) = 0, (C) β«(1/2)(-1/2) f(x + 1/2) sin x dx = 0, (D) β«(1/2)(0) f(t) e^sin Οt dt = β«(1/2)(0) f(1 - t) e^sin Οt dt | A,B,C,D | 3 | no | mathematics |
11 | Let f and g be real valued functions defined on interval (- 1, 1) such that g''(x) is continuous, g(0) β 0, g'(0) = 0, g''(0) β 0, and f(x) = g(x)sin x. STATEMENT-1 : lim [g(x) cot x - g(0) cosec x] = f''(0) . and STATEMENT-2 : f'(0) = g(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 | 4 | no | mathematics |
12 | Consider three planes P1 :x - y + z = 1 P2 : x + y - z = -1 P3 :x - 3y + 3z = 2. Let L1, L2, L3 be the lines of intersection of the planes P2 and P3, P3 and P1, and P1 and P2, respectively. STATEMENT-1 : At least two of the lines L1, L2 and L3 are non-parallel. and STATEMENT-2 : The three planes do not have a common point. | (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 | 4 | no | mathematics |
13 | Consider the system of equations x - 2y + 3z = -1 -x + y - 2z = k x - 3y + 4z = 1 STATEMENT-1 : The system of equations has no solution for k β 3 and STATEMENT-2 : The determinant | 1 3 -1| |-1 -2 k| β 0, for k β 3. |1 4 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 | A | 5 | no | mathematics |
14 | Consider the system of equations ax + b y = 0 , c x + d y = 0 , where a, b, c, d Ο΅ {0, 1} . STATEMENT-1 : The probability that the system of equations has a unique solution is 3/8 . and STATEMENT-2 : The probability that the system of equations has a solution is 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 | B | 5 | no | mathematics |
15 | The equation of circle C is | (A) (x - 2β3)^2 + (y - 1)^2 = 1, (B) (x - 2β3)^2 + (y + 1/2)^2 = 1, (C) (x - β3)^2 + (y + 1)^2 = 1, (D) (x - β3)^2 + (y - 1)^2 = 1 | D | 6 | yes | mathematics |
16 | Points E and F are given by | (A) (β3/2 , 2), (β3, 0), (B) (β3/2 , 1/2), (β3, 0), (C) (β3/2 , 2), (β3/2 , 1/2), (D) (3/2, β3/2), (β3/2 , 1/2) | A | 6 | yes | mathematics |
17 | Equations of the sides QR , RP are | (A) y = -2/β3 x + 1, y = -2/β3 x - 1, (B) y = 1/β3 x, y = 0, (C) y = β3/2 x + 1, y = -β3/2 x - 1, (D) y = β3 x, y = 0 | D | 6 | yes | mathematics |
18 | If f (-10β2) = 2β2 , then f''(-10β2) = | (A) 4β2/7*32, (B) -4β2/7*32, (C) 4β2/7*3, (D) -4β2/7*3 | B | 6 | no | mathematics |
19 | The area of the region bounded by the curve y = f(x), the x-axis, and the lines x = a and x = b, where -β < a < b < -2, is | (A) β«β^b [x / (3((f(x))Β² - 1))] dx + b f(b) - a f(a), (B) -β«β^b [x / (3((f(x))Β² - 1))] dx + b f(b) - a f(a), (C) β«β^b [x / (3((f(x))Β² - 1))] dx - b f(b) + a f(a), (D) -β«β^b [x / (3((f(x))Β² - 1))] dx - b f(b) + a f(a) | A | 7 | no | mathematics |
20 | β«ββ^1 g'(x) dx = | (A) 2g(-1), (B) 0, (C) -2g(1), (D) 2g(1) | D | 7 | no | mathematics |
21 | The number of elements in the set A β© B β© C is | (A) 0, (B) 1, (C) 2, (D) β | B | 7 | no | mathematics |
22 | Let z be any point in A β© B β© C. Then, |z + 1 - i|Β² + |z - 5 - i|Β² lies between | (A) 25 and 29, (B) 30 and 34, (C) 35 and 39, (D) 40 and 44 | C | 7 | no | mathematics |
23 | Let z be any point in Aβ©Bβ©C and let w be any point satisfying |w-2-Ξ΅|<3 Then, |z|-|w|+3 lies between | (A) -6 and 3, (B) -3 and 6, (C) -6 and 6, (D) -3 and 9 | B | 8 | no | mathematics |
24 | Students I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of oscillations. The observations are shown in the table. Least count for length = 0.1 cm Least count for time = 0.1 s [Table with data for Student, Length of the pendulum (cm), Number of oscillations (n), Total time for (n) oscillations (s), Time period (s)] If E1, EII and EIII are the percentage errors in g, i.e., (Ξg/gΓ100) for students I, II and III, respectively, | (A) EI = 0, (B) EI is minimum, (C) EI = EII, (D) EII is maximum | B | 8 | no | physics |
25 | Figure shows three resistor configurations R1, R2 and R3 connected to 3 V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then | (A) P1 > P2 > P3, (B) P1 > P3 > P2, (C) P2 > P1 > P3, (D) P3 > P2 > P1 | C | 9 | yes | physics |
26 | Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube? | (A) Wavelength of characteristic X-rays decreases when the atomic number of the target increases, (B) Cut-off wavelength of the continuous X-rays depends on the atomic number of the target, (C) Intensity of the characteristic X-rays depends on the electrical power given to the X-ray tube, (D) Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube | B | 9 | no | physics |
27 | Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is 60Β°). In the position of minimum deviation, the angle of refraction will be | (A) 30Β° for both the colours, (B) greater for the violet colour, (C) greater for the red colour, (D) equal but not 30Β° for both the colours | A | 9 | no | physics |
28 | An ideal gas is expanding such that PV^Ξ³ = constant. The coefficient of volume expansion of the gas is | (A) 1/T (B) 2/T (C) 3/T (D) 4/T | C | 10 | no | physics |
29 | A spherically symmetric gravitational system of particles has a mass density Ο=Ο0 for rβ€R, 0 for r>R where Ο0 is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed V as a function of distance r (0<r<β) from the centre of the system is represented by | (A) (B) (C) (D) | C | 10 | yes | physics |
30 | Two balls, having linear momenta pβ1=piβ and pβ2=βpiβ, undergo a collision in free space. There is no external force acting on the balls. Let p'β1 and p'β2 be their final momenta. The following option(s) is(are) NOT ALLOWED for any non-zero value of p, a1, a2, b1, b2, c1 and c2 : | (A) p'β1=a1iβ+b1jβ+c1kβ p'β2=a2iβ+b2jβ (B) p'β1=c1kβ p'β2=c2kβ (C) p'β1=a1iβ+b1jβ+c1kβ p'β2=a2iβ+b2jββc1kβ (D) p'β1=a1iβ+b1jβ p'β2=a2iβ+b1jβ | A,D | 10 | no | physics |
31 | Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot to choose the correct choice(s) given below. | (A) Fusion of two nuclei with mass numbers lying in the range of 1 < A < 50 will release energy, (B) Fusion of two nuclei with mass numbers lying in the range of 51 < A < 100 will release energy, (C) Fission of a nucleus lying in the mass range of 100 < A < 200 will release energy when broken into two equal fragments, (D) Fission of a nucleus lying in the mass range of 200 < A < 260 will release energy when broken into two equal fragments | C,D | 11 | yes | physics |
32 | A particle of mass m and charge q, moving with velocity V enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field B, perpendicular to the plane of the paper. The length of the Region II is l. Choose the correct choice(s). | (A) The particle enters Region III only if its velocity V > q*B/m, (B) The particle enters Region III only if its velocity V < q*B/m, (C) Path length of the particle in Region II is maximum when velocity V = q*B/m, (D) Time spent in Region II is same for any velocity V as long as the particle returns to Region I | B,C | 11 | yes | physics |
33 | In a Young's double slit experiment, the separation between the two slits is d and the wavelength of the light is Ξ». The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice(s). | (A) If d = Ξ», the screen will contain only one maximum
(B) If Ξ» < d < 2Ξ», at least one more maximum (besides the central maximum) will be observed on the screen
(C) If the intensity of light falling on slit 1 is reduced so that it becomes equal to that of slit 2, the intensities of the observed dark and bright fringes will increase
(D) If the intensity of light falling on slit 2 is increased so that it becomes equal to that of slit 1, the intensities of the observed dark and bright fringes will increase | B | 12 | no | physics |
34 | STATEMENT-1
In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.
and
STATEMENT-2
Resistance of a metal increases with increase in temperature. | (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 | 12 | no | physics |
35 | STATEMENT-1
An astronaut in an orbiting space station above the Earth experiences weightlessness.
and
STATEMENT-2
An object moving around the Earth under the influence of Earth's gravitational force is in a state of 'free-fall'. | (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 | 12 | no | physics |
36 | STATEMENT-1
Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.
and
STATEMENT-2
By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline. | (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 | 13 | no | physics |
37 | STATEMENT-1
The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.
and
STATEMENT-2
In any steady flow of an incompressible fluid, the volume flow rate of the fluid 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 | A | 13 | no | physics |
38 | As the bubble moves upwards, besides the buoyancy force the following forces are acting on it | (A) Only the force of gravity
(B) The force due to gravity and the force due to the pressure of the liquid
(C) The force due to gravity, the force due to the pressure of the liquid and the force due to viscosity of the liquid
(D) The force due to gravity and the force due to viscosity of the liquid | D | 14 | yes | physics |
39 | When the gas bubble is at a height y from the bottom, its temperature is | (A) T0 ( P0 + Ο β
g β
H ) ^ (2/5) / ( P0 + Οi β
g β
y )
(B) T0 ( P0 + Ο β
g β
(H - y) ) ^ (2/5) / ( P0 + Ο β
g β
H )
(C) T0 ( P0 + Ο β
g β
H ) ^ (3/5) / ( P0 + Οi β
g β
y )
(D) T0 ( P0 + Ο β
g β
(H - y) ) ^ (3/5) / ( P0 + Ο β
g β
H ) | B | 14 | yes | physics |
40 | The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant) | (A) Ο β R g Tβ [(Pβ + Ο β g H )Β²ββ
] / [(Pβ + Ο β g y)ΒΉββ
], (B) [Ο β R g Tβ] / [(Pβ + Ο β g H )Β²ββ
[(Pβ + Ο β g (H - y))Β³ββ
]], (C) Ο β R g Tβ [(Pβ + Ο β g H )Β³ββ
] / [(Pβ + Ο β g y)β΅ββ], (D) [Ο β R g Tβ] / [(Pβ + Ο β g H )Β³ββ
[(Pβ + Ο β g (H - y))Β²ββ
]] | B | 15 | no | physics |
41 | The quantum number n of the state finally populated in HeβΊ ions is | (A) 2, (B) 3, (C) 4, (D) 5 | C | 15 | no | physics |
42 | The wavelength of light emitted in the visible region by HeβΊ ions after collisions with H atoms is | (A) 6.5 x 10β»β· m, (B) 5.6 x 10β»β· m, (C) 4.8 x 10β»β· m, (D) 4.0 x 10β»β· m | C | 15 | no | physics |
43 | The ratio of the kinetic energy of the n = 2 electron for the H atom to that of HeβΊ ion is | (A) 1/4, (B) 1/2, (C) 1, (D) 2 | A | 15 | no | physics |
44 | The speed of the block at point B immediately after it strikes the second incline is | (A) β60 m/s, (B) β45 m/s, (C) β30 m/s, (D) β15 m/s | B | 16 | yes | physics |
45 | The speed of the block at point C, immediately before it leaves the second incline is | (A) β120 m/s, (B) β105 m/s, (C) β90 m/s, (D) β75 m/s | B | 16 | yes | physics |
46 | If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is | (A) β30 m/s, (B) β15 m/s, (C) 0, (D) -β15 m/s | C | 16 | yes | physics |
47 | Hyperconjugation involves overlap of the following orbitals | (A) Ο-Ο, (B) Ο-p, (C) p-p, (D) Ο-Ο | B | 16 | no | chemistry |
48 | The major product of the following reaction is | (A) (B) (C) (D) | A | 17 | yes | chemistry |
49 | Aqueous solution of Na2S2O3 on reaction with Cl2 gives | (A) Na2S4O6 (B) NaHSO4 (C) NaCl (D) NaOH | B | 17 | no | chemistry |
50 | Native silver metal forms a water soluble complex with a dilute aqueous solution of NaCN in the presence of | (A) nitrogen (B) oxygen (C) carbon dioxide (D) argon | B | 17 | no | chemistry |
51 | Under the same reaction conditions, initial concentration of 1.386 mol dm^3 of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics, respectively. Ratio (k1/k0) of the rate constants for first order (k1) and zero order (k0) of the reactions is | (A) 0.5 mol^-1 dm^3 (B) 1.0 mol dm^-3 (C) 1.5 mol dm^-3 (D) 2.0 mol^-1 dm^3 | A | 17 | no | chemistry |
52 | 2.5 mL of 2/5 M weak monoacidic base (Kb = 1 x 10^-12 at 25Β°C) is titrated with 2/15 M HCl in water at 25Β°C. The concentration of H+ at equivalence point is (Kw = 1 x 10^-14 at 25Β°C) | (A) 3.7 x 10^-13 M, (B) 3.2 x 10^-7 M, (C) 3.2 x 10^-2 M, (D) 2.7 x 10^-2 M | D | 18 | no | chemistry |
53 | The correct statement(s) about the compound given below is (are) | (A) The compound is optically active, (B) The compound possesses centre of symmetry, (C) The compound possesses plane of symmetry, (D) The compound possesses axis of symmetry | A,D | 18 | yes | chemistry |
54 | The correct statement(s) concerning the structures E, F and G is (are) | (A) E, F and G are resonance structures, (B) E, F and E, G are tautomers, (C) F and G are geometrical isomers, (D) F and G are diastereomers | B,C,D | 18 | yes | chemistry |
55 | A solution of colourless salt H on boiling with excess NaOH produces a non-flammable gas. The gas evolution ceases after sometime. Upon addition of Zn dust to the same solution, the gas evolution restarts. The colourless salt(s) H is (are) | (A) NH4NO3, (B) NH4NO2, (C) NH4Cl, (D) (NH4)2SO4 | B | 19 | no | chemistry |
56 | A gas described by van der Waals equation (A) behaves similar to an ideal gas in the limit of large molar volumes (B) behaves similar to an ideal gas in the limit of large pressures (C) is characterised by van der Waals coefficients that are dependent on the identity of the gas but are independent of the temperature (D) has the pressure that is lower than the pressure exerted by the same gas behaving ideally | (A), (C) OR (A), (C), (D) | (A), (C) | 19 | no | chemistry |
57 | STATEMENT-1 : Bromobenzene upon reaction with Br2/Fe gives 1,4-dibromobenzene as the major product. and STATEMENT-2 : In bromobenzene, the inductive effect of the bromo group is more dominant than the mesomeric effect in directing the incoming electrophile. (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 | 19 | no | chemistry |
58 | STATEMENT-1 : PbβΊβΊ compounds are stronger oxidizing agents than SnβΊβΊ compounds. and STATEMENT-2 : The higher oxidation states for the group 14 elements are more stable for the heavier members of the group due to 'inert pair effect'. | (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 | 20 | no | chemistry |
59 | STATEMENT-1 : The plot of atomic number (y-axis) versus number of neutrons (x-axis) for stable nuclei shows a curvature towards x-axis from the line of 45Β° slope as the atomic number is increased. and STATEMENT-2 : Proton-proton electrostatic repulsions begin to overcome attractive forces involving protons and neutrons in heavier nuclides. | (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 | 20 | no | physics |
60 | STATEMENT-1 : For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero. and STATEMENT-2 : At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs 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 | D | 20 | no | chemistry |
61 | The structure of the product I is | (A) Me/\/\/\/\Br, (B) Me\/\/\/Br, (C) Me/\/\/\/Br, (D) Me\/\/Br | D | 21 | yes | chemistry |
62 | The structures of compounds J and K, respectively, are | (A) Me\/\/COOH and SOCl2, (B) Me/\/\/\/OH and SO2Cl2, (C) Me\/\/COOH and SOCl2, (D) Me\/\/COOH and CH3SO2Cl | A | 21 | yes | chemistry |
63 | The structure of product L is | (A) MeβCHO, (B) Me~CHO, (C) Me/\CHO, (D) Me~CHO | C | 22 | yes | chemistry |
64 | Among the following, the correct statement is (A) Phosphates have no biological significance in humans (B) Between nitrates and phosphates, phosphates are less abundant in earth's crust (C) Between nitrates and phosphates, nitrates are less abundant in earth's crust (D) Oxidation of nitrates is possible in soil | (A) Phosphates have no biological significance in humans, (B) Between nitrates and phosphates, phosphates are less abundant in earth's crust, (C) Between nitrates and phosphates, nitrates are less abundant in earth's crust, (D) Oxidation of nitrates is possible in soil | C | 22 | no | chemistry |
65 | Among the following, the correct statement is (A) Between NH3 and PH3, NH3 is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional (B) Between NH3 and PH3, PH3 is a better electron donor because the lone pair of electrons occupies sp3 orbital and is more directional (C) Between NH3 and PH3, NH3 is a better electron donor because the lone pair of electrons occupies sp3 orbital and is more directional (D) Between NH3 and PH3, PH3 is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional | (A) Between NH3 and PH3, NH3 is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional, (B) Between NH3 and PH3, PH3 is a better electron donor because the lone pair of electrons occupies sp3 orbital and is more directional, (C) Between NH3 and PH3, NH3 is a better electron donor because the lone pair of electrons occupies sp3 orbital and is more directional, (D) Between NH3 and PH3, PH3 is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional | C | 22 | no | chemistry |
66 | White phosphorus on reaction with NaOH gives PH3 as one of the products. This is a | (A) dimerization reaction, (B) disproportionation reaction, (C) condensation reaction, (D) precipitation reaction | B | 23 | no | chemistry |
67 | The freezing point of the solution M is | (A) 268.7 K, (B) 268.5 K, (C) 234.2 K, (D) 150.9 K | C | 23 | no | chemistry |
68 | The vapour pressure of the solution M is | (A) 39.3 mm Hg, (B) 36.0 mm Hg, (C) 29.5 mm Hg, (D) 28.8 mm Hg | B | 24 | no | chemistry |
69 | Water is added to the solution M such that the mole fraction of water in the solution becomes 0.9. The boiling point of this solution is | (A) 380.4 K, (B) 376.2 K, (C) 375.5 K, (D) 354.7 K | B | 24 | no | chemistry |
1 | A particle P starts from the point zβ = 1 + 2i, where i = β-1. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point zβ. From zβ the particle moves β2 units in the direction of the vector i + j and then it moves through an angle Ο/2 in anticlockwise direction on a circle with centre at origin, to reach a point zβ. The point zβ is given by | (A) 6 + 7i, (B) -7 + 6i, (C) 7 + 6i, (D) -6 + 7i | D | 1 | no | mathematics |
2 | Let the function g : (-β, β) β (Ο/2, Ο/2) be given by g(u) = 2tanβ»ΒΉ(eα΅) - Ο/2. Then, g is | (A) even and is strictly increasing in (0, β), (B) odd and is strictly decreasing in (-β, β), (C) odd and is strictly increasing in (-β, β), (D) neither even nor odd, but is strictly increasing in (-β, β) | C | 1 | no | mathematics |
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