CET – MATHEMATICS – 2013
VERSION CODE: C – 2
1. If sin – 1 a is the acute angle between the curves x2 + y2 = 4x and x2 + y2 = 8 at (2, 2), then a = ___________ (4) 23 (1) 1 (2) 0 (3)
Ans: (3)
2. The maximum area of a rectangle that can be inscribed in a circle of radius 2 units is _______
(1) 8π sq. units (2) 4 sq. units (3) 5 sq. units (4) 8 sq. units
Ans: (4)
3. If the length of the sub-tangent at any point to the curve xyn = a is proportional to the abscissa, then ‘n’ is ______
(1) any non-zero real number (2) 2
(3) -2 (4) 1
Ans: (1)
4. ∫+−xsinxcos1n1ndx, n ≠ 0 is _________ (1) nxcotn (2) 1nxcot1n−−− (3) nxcotn− (4) xcot
Ans: (3)
5. ∫+−3x)1x(e)1x(dx = _________ (1) e (2) 2x)1x(e+ (3) 3x)1x(e+ (4) )1x(e.xx+
Ans: (2) 6. If I1 = . sin x dx and I2 = . cos x dx, then which one of the following is true? ∫π2/0x
(1) I1 = I2 (2) I1 + I2 = 0 (3) I1 = 2π.I2 (4) I1 + I2 = 2π
Ans: (4)
7. The value of ∫−21x|x|dx is __________
(1) 0 (2) 1 (3) 2 (4) 3
Ans: (2)
8. ∫
π+0444xsinxcosxcosdx =
(1) 4π (2) 2π (3) 8π (4) π
Ans: (2) 9. The area bounded by the curve y = sin ⎜⎛, x-axis and lines x = 0 and x = 3π is _____
(1) 9 (2) 0 (3) 6 (4) 3
Ans: (3)
10. The general solution of the differential equation 22yx1−.dx = y . dx + x . dy is ______
(1) sin (xy) = x + c (2) sin – 1 (xy) + x = c
(3) sin (x + c) = xy (4) sin (xy) + x = c
Ans: (3)
11. If ‘m’ and ‘n’ are the order and degree of the differential equation
(y||)5 + 4 . |||3||y)y( + y||| = sin x, then
(1) m = 3, n = 5 (2) m = 3, n = 1 (3) m = 3, n = 3 (4) m = 3, n = 2
Ans: (4) 12. If (, then sin-1 A + tan-1 B + sec-1 C = __________ (1) 2π (2) 6π (3) 0 (4) 5
Ans: (4)
13. The sum of the series, +++322.5.432.4.322.3.21 ………… to an terms is _______ (1) 2 (2) 12n21n−++ (3) 22n21n+++ (4) 22n21n−++
Ans: (2)
14. If the roots of the equation x3 + ax2 + bx + c = 0 are in A.P., then 2a3 – 9ab = _______
(1) 9c (2) 18c (3) 27c (4) -27c
Ans: (4)
15. If the value of Co + 2 . C1 + 3 . C2 + ………… + (n + 1) . Cn = 576, then n is _______
(1) 7 (2) 5 (3) 6 (4) 9
Ans: (1)
16. The inverse of the proposition (p ∧ ~ q) → r is ____
(1) (~r) → (~p) ∨ q (2) (~p) ∨ q → (~r) (3) r → p ∧ (~q) (4) (~p) ∨ (~q) → r
Ans: (2)
17. The range of the function f (x) = sin [x], -4π < x < 4π where [x] denotes the greatest integer ≤ x, is ______
(1) {0} (2) {0, -1} (3) {0, ± sin 1} (4) {0, -sin 1}
Ans: (4)
18. If the line 6x – 7y + 8 + λ (3x – y + 5) = 0 is parallel to y – axis, then λ = ______
(1) -7 (2) -2 (3) 7 (4) 2
Ans: (1)
19. The angle between the lines sin2α . y2 – 2xy . cos2 α + (cos2 α - 1) x2 = 0 is _____
(1) 90o (2) α (3) 2α (4) 2α
Ans: (1)
20. The minimum area of the triangle formed by the variable line 3 cos θ . x + 4 sin θ . y = 12 and the co-ordinate axes is ______ (1) 144 (2) 25 (3) 449 (4) 12
Ans: (4)
21. log (sin 1o) . log (sin 2o) . log (sin 3o) ……… log (sin 179o)
(1) is positive (2) is negative
(3) lies between 1 and 180 d) is zero
Ans: (4) 22. If sin x – sin y = and cos x – cos y = 1, then tan (x + y) =
(1) 83 (2) -83 (3) 34 (4) -34
Ans: (3)
23. In a triangle ABC, if aAcos = bBcos = cCcos and a = 2, then its area is ……….. (1) 23 (2) 3 (3) 23 (4) 43
Ans: (2) 24. = ………….
(1) loge 3 (2) 0 (3) log3 e (4) 1
Ans: (3) 25. Let f (x) = ⎨⎧ then f is ……………
(1) continuous everywhere (2) discontinuous everywhere
(3) continuous only at x = 0 (4) continuous at all rational numbers
Ans: (3)
26. In a regular graph of 15 vertices the sum of the degree of the vertices is 60. Then the degree of each vertex is ………..
(1) 5 (2) 3 (3) 4 (4) 2
Ans: (4)
27. The remainder when, 1010 . (1010 + 1) (1010 + 2) is divided by 6 is …………
(1) 2 (2) 4 (3) 0 (4) 6
Ans: (3)
28. A value of x satisfying 150x ≡ 35 (Mod 31) is …………
(1) 14 (2) 22 (3) 24 (4) 12
Ans: (3)
29. The smallest positive divisor greater than 1 of a composite number ‘a’ is ………….. (1) < 2 (2) = a (3) > a (4) ≤ a
Ans: (4)
30. If A and B are square matrices of order ‘n’ such that A2 – B2 = (A – B) (A + B), then which of the following will be true?
(1) Either of A or B is zero matrix (2) A = B
(3) AB = BA (4) Either of A or B is an identify matrix
Ans: (3)
31. If A = and |A⎥⎦⎤⎢⎣⎡αα223| = 125, then α = ……………….
(1) ± 1 (2) ± 2 (3) ± 3 (4) ± 5
Ans: (3) 32. If A = 1 and B = x11x, then dxdA = ……………
(1) 3B + 1 (2) 3B (3) -3B (4) 1 – 3B
Ans: (2)
33. If the determinant of the adjoint of a (real) matrix of order 3 is 25, then the determinant of the inverse of the matrix is
(1) 0.2 (2) ± 5 (3) 56251 (4) ± 0.2
Ans: (4)
34. If the matrix = A + B, where A is symmetric and B is skew symmetric, then B = …. ⎥⎦⎤⎢⎣⎡−1532 (1) ⎢⎡ (2) ⎥⎢⎡ (3) ⎢⎡ (4) ⎥⎦⎤⎢⎣⎡−0110
Ans: (4)
35. In a group (G, ∗), for some element ‘a’ of G, if a2 = e, where e is the identify element, then (1) a = a – 1 (2) a = e (3) a = (4) a = e
Ans: (1)
36. In the group (Z, ∗), if a ∗ b = a + b – n ∀ a, b ∈ Z, where n is a fixed integer, then the inverse of (-n) is ………..
(1) n (2) –n (3) -3n (4) 3n
Ans: (4)
37. If = (1, 2, 3), = (2, -1, 1), = (3, 2, 1) and x ( x ) = α + β x γ, then →a→b→c→a→b→c→a→b→c
(1) α = 1, β = 10, γ = 3 (2) α = 0, β = 10, γ = -3
(3) α + β + γ = 8 (4) α = β = γ = 0
Ans: (2)
38. If ⊥ and ( + ) ⊥ ( + m), then m = →a→b→a→b→a→b
(1) -1 (2) 1 (3) |b||a|2→→− (4) 0
Ans: (3) 39. If , , are unit vectors such that + + = , then . + . + . = … →a→b→c→a→b→c→0→a→b→b→c→a
(1) 23 (2) -23 (3) 32 (4) 21
Ans: (2)
40. If is vector perpendicular to both and , then →a→b→c
(1) . ( x ) = 0 (2) x ( x ) = →a→b→c→a→b→c→0 (3) x ( + ) = (4) + ( + ) = →a→b→0→a→b→c→0
Ans: (2)
41. A tangent is drawn to the circle 2x2 + 2y2 – 3x + 4y = 0 at point ‘A’ and it meets the line
x + y = 3 at B (2, 1), then AB = ……….
1) 10 2) 2 3) 22 4) 0
Ans: (2)
42. The area of the circle having its centre at (3, 4) and touching the line 5x + 12y – 11 = 0 is …….
1) 16 π sq. units 2) 4 πsq. units 3) 12 π sq. units 4) 25 π sq. units
Ans: (1)
43. The number of real circles cutting orthogonally the circle x2 + y2 + 2x – 2y + 7 = 0 is ……
1) 0 2) 1 3) 2 4) infinitely many
Ans: (1)
44. The length of the chord of the circle x2 + y2 + 3x + 2y – 8 = 0 intercepted by the y-axis is
1) 3 2) 8 3) 9 4) 6
Ans: (4)
45. A ≡ (cos θ, sin θ), B ≡ (sin θ, - cos θ) are two points. The locus of the centroid of ΔOAB, where ‘O” is the origin is …………
1) x2 + y2 = 3 2) 9x2 + 9y2 = 2 3) 2x2 + 2y2 = 9 4) 3x2 + 3y2 = 2
Ans: (2)
46. The sum of the squares of the eccentricities of the conics 4x2 + 3y3 = 1 and 4x2 - 3y2 = 1 is ………. 1) 2 2) 37 3) 7 4) 3
Ans: (1) 47. The equation of the tangent to the parabola y2 = 4x inclined at an angle of to the +ve direction of x-axis is ………..
1) x + y – 4 = 0 2) x – y + 4 = 0 3) x – y – 1 = 0 4) x – y + 1 = 0
Ans: (4)
48. If the distance between the foci and the distance between the directrices of the hyperbola 22ax - 22by = 1 are in the ratio 3 : 2, then a : b is ………….
1) 2 + 1 2) 1 : 2 3) 3: 2 4) 2 : 1
Ans: (1)
49. If the area of the auxillary circle of the ellipse 22ax + 22by = 1 (a > b) is twice the area of the ellipse, then the eccentricity of the ellipse is ………….. 1) 31 2) 21 3) 21 4)
Ans: (4) 50. cos ⎢⎡ = …………
1) 51 2) 562− 3) - 51 4) 56
Ans: (2)
51. The value of tan-1 ⎟⎟⎠⎞⎜⎜⎝⎛yx - tan-1 ⎟⎟⎠⎞⎜⎜⎝⎛+−yxyx, x, y > 0 is 1) π 2) - 4π 3) 2π 4) - 2π
Ans: (1) 52. The general solution of sin x – cos x = , for any integer ‘n’ is ………..
1) 2nπ + 43π 2) nπ 3) (2n + 1)π 4) 2nπ
Ans: (1)
53. The modulus and amplitude of 2)i1(1i21−−+ are ……..
1) 2 and 6π 2) 1 and 4π 3) 1 and 0 4) 1 and 3π
Ans: (3)
54. If 2x = - 1 + 3I, then the value of (1 + x2 + x)6 – (1 – x + x2)6 = …………
1) 32 2) 64 3) – 64 4) 0
Ans: (4)
55. If x + y = tan-1 y and 22dxyd = f (y) dxdy, then f (y) = …………. 1) 3y2− 2) 2 3) y1 4) y1−
Ans: (2) 56. f (x) =
Then which of the following is true?
1) f (x) is not differentiable at x = a. 2) f (x) is discontinuous at x = a.
3) f (x) is continuous for all x < a. 4) f (x) is differentiable for all x ≥ a.
Ans: (1) 57. Let f (x) = cos-1 . Then f’ (0.5) = …………
1) 0.5 2) 1 3) 0 4) – 1
Ans: (2)
58. If f (x) is a function such that f” (x) + f (x) = 0 and g (x) = [f (x)]2 + [f’ (x)]2 and g (3) = 8, then g (8) = ……..
1) 0 2) 3 3) 5 4) 8
Ans: (4)
59. If f (x) = f’ (x) = f” (x) + f”’ (x) + ……… and f (0) = 1, then f (x) = …………. a) e 2) ex 3) e2x 4) e4x
Ans: (1)
60. The function f (x) = 3x + x3 decreases in the interval
1) (-3, 3) 2) (-∞, 3) 3) (3, ∞) 4) (-9, 9)
Ans: (1)
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