(Paper) E Litmus Fresher Job Interview Placement Paper part - 2 : 26-jul-2011

e litmus

Job Interview Placement Paper

36. The area bounded by the curves y = |x| − 1 and y = − |x| + 1 is
(a) 1 (b) 2
(c) 2 2 (d) 4

37. The coordinates of foot of the perpendicular drawn from the point (2, 4) on the line x + y = 1 are
(a) 1 , 32 2
(b) 1, 32 2−
(c) 3 , 12 2 −
(d) 1, 32 2− −

38. Three lines 3x + 4y + 6 = 0, 2x + 3y + 2 2 = 0 and 4x + 7y + 8 = 0 are
(a) Parallel (b) Sides of a triangles
(c) Concurrent (d) None of these

39. Angle between the pair of straight lines x2 – xy – 6y2 – 2x + 11y – 3 = 0 is
(a) 450, 1350
(b) tan-1 2, π = tan-1 2
(c) tan-1 3, π = tan-1 3
(d) None of these

40. If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then locus of its centre is
(a) 2ax + 2by + (a2 + b2 + 4) = 0
(b) 2ax + 2by − (a2 + b2 + 4) = 0
(c) 2ax − 2by + (a2 + b2 + 4) = 0
(d) 2ax − 2by − (a2 + b2 + 4) = 0

41. Centre of circle whose normals are x2 − 2xy − 3x + 6y = 0 is
(a) 3, 32
(b) 3 ,32
(c) 3, 32−
(d) 3, 32−−
42. Centre of a circle is (2, 3). If the line x + y = 1 touches, its equation is
(a) x2 + y2 − 4x − 6y + 4 = 0
(b) x2 + y2 − 4x − 6y + 5 = 0
(c) x2 + y2 − 4x − 6y − 5 = 0
(d) None of these

43. The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x2 + y2 = 9 is
(a) 3 , 12 2
(b) 1 , 32 2
(c) 1 , 12 2
(d) 12 1, 22−

44. The line y = mx + 1 is a tangent to the parabola y2 = 4x if
(a) m = 1 (b) m = 2
(c) m = 3 (d) m = 4

45. The angle between the tangents drawn from the origin to the parabola y2 = 4a (x – a) is
(a) 900 (b) 300
(c) tan 1 12−(d) 450

46. The area of the triangle formed by the tangent and the normal to the parabola y2 = 4ax, both drawn at the same end of the latus rectum and the axis of the parabola is
(a) 2 2 a2 (b) 2a2
(c) 4a2 (d) None of these

47. The eccentricity of the eclipse 16x2 + 7y2 = 112 is
(a) 4/3 (b) 7/16
(c) 3/ 17 (d) 3/4

48. A common tangent to the circle x2 + y2 = 16 and an ellipse x2 y2 149 4+ = is
(a) y = x + 4 5 (b) y = x + 53
(c) y 2 x 4 4
11 11
= + (d) None of these

49. If the hyperbolas x2 − y2 = a2 and xy = c2 are of equal size, then
(a) c2 = 2a2 (b) c = 2a
(c) 2c2 = a2 (d) none of these

50. If a circle cuts rectangles hyperbola xy = 1 in the point (xi, yi), i = 1, 2, 3, 4 then
(a) 1 2 3 4 x x x x = 0 (b) 1 2 3 4 y y y y =1
(c) 1 2 3 4 y y y y = 0 (d) 1 2 3 4 x x x x = −1

51. If a b 0 0 a b  b 0 a = 0 then
(a) a is a cube root of 1 (b) b is a cube root of 1
(c) a/b is a cube root of 1 (d) a/b is a cube roots of -1

52. If 1 1 1 0 a b c + + = , then 1 a 1 11 1 b 11 1 1 c + + + is equal to
(a) 0 (b) abc
(c) –abc (d) None of these

53. The determinant cos( ) sin( ) cos2 Bsin cos sincos sin cosα + β − α + βα α β− α α β is independent of
(a) α (b) β
(c) α and β (D) Neither α nor β

54. If 3 4 A 1 1−= −, the value of An
(a) 3n 4nn n−
(b) 2 n 5 nn n + − −
(c)( )( )n nn3 41 1−−
(d) None of these

55. The domain of the function ( ) 2 f x 1x 3x 2=− +is
(a) (−∞,1)(2,∞) (b) (−∞,1]∪[2,∞)
(c) [−∞,1)(2,∞] (d) (1, 2)

56. Range of function ( 2 )4sin x 1x 1π ++is
(a) 0 (b) {0}
(c) [-1, 1] (d) (0, 1)

57. 3 x 3 4lim 1 cot x→π 2 cot x cot x − − −is
(a) 114 (b) 34
(c) 12 (d) None of these

58. 1x 0 limsec sin x x − → =
(a) 1 (b) 0
(c) 2
π (d) Does not exist

59. The function y = 3 x − x −1 is continuous
(a) x < 0 (b) x > 1
(c) no point (d) None of these

60. The function ( ) 0,x is irrational is f x 1,x is rational =
(a) continuous at x = 1 (b) discontinuous only at 0
(c) discontinuous only at 0, 1
(d) discontinuous everywhere

61. Let f : R → R be a function defined by f(x) = max. {x, x3}. The set of all points where f(x) is not differentiable is
(a) {-1, 1} (b) {-1, 0}
(c) {0, 1} (d) {-1, 0, 1}

62. If the function ( ) ( )1cos x x ,x 0 f xK x 0 ≠ = = is continuous of x = 0 then value of k is
(a) 1 (b) -1
(c) 0 (d) e

63.1 x5dx1 x+=+ ∫
(a) 1− x + x2 − x3 + x4 + c
(b)x2 x3 x4 x5 x x 2 3 4 5− + − + +
(c) ( )5 1+ x + C
(d) None of these

64. ∫ x x dx
(a)x33
(b)x2 x3
(c)x2 x2
(d) None of these

65. 11x 2dx x 2 −+=+ ∫
(a) 1 (b) 2
(c) 0 (d) -1

66. ( )20 log tan x dx π ∫
(a) 4π (b) 2π
(c) 0 (d) 1

67. If a < 0 < b, then  b a x dx x ∫
(a) a – b (b) b – a
(c) a + b (d) –a – b

68.220∫ x x dx
(a) 5/3 (b) 7/3
(c) 8/3 (d) 4/3

69. 20xsin x dx1 cos xπ+ ∫
(a) 28π
(b) 24π
(c) 38π
(d) 48π

70. The area bounded by curve y = 4x – x2 and x – axis is
(a) 30 sq. units.7
(b) 31 sq. units.7
(c) 32 sq. units.3
(d) 34 sq. units.3

71. The area bounded by the curves y = |x| - 1 and y = -|x| + 1 is
(a) 1 (b) 2
(c) 2 2 (d) 4

72. The area bounded by the curves y = x4 − 2x3 + x2 − 3 , the x-axis and the two ordinates corresponding to the points of minimum of this Function is
(a) 91/15 (b) 91/30
(c) 19/30 (d) None of these

73. Degree of the differential equation 2 3 2 5 2 3 2 2 3 3 3 4 d y d y dx d y x 1dx d y dx  dx + + = − , then
(a) m = 3, n = 3 (b) m = 3, n = 2
(c) m = 3, n = 5 (d) m = 3, n = 1

74. A solution of the differential equation 2 dy x. dy y 0dx dx − + = is
(a) y = 2 (b) y = 2x
(c) 4y = x2 + c (d) y = 2x2 – 4

75. The area (in square units) of the parallelogram whose diagonals are a = ˆi + ˆj− 2kˆ and b = ˆi − 3ˆj+ 4kˆr r
(a) 14 (b) 2 14
(c) 2 6 (d) 38

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ANSWER KEYS : 36. (b) 37. (b) 38. (c) 39. (d) 40. (b) 41. (a) 42. (b) 43. (d) 44. (a) 45. (a) 46. (c) 47. (d) 48. (d) 49. (c) 50. (b) 51. (d) 52. (b) 53. (a) 54. (d) 55. (a) 56. (b) 57. (b) 58. (d) 59. (d) 60. (d) 61. (d) 62. (a) 63. (b) 64. (b) 65. (b) 66. (c) 67. (c) 68. (c) 69. (a) 70. (c) 71. (b) 72. (b) 73. (d) 74. (c) 75. (a)

Company Name: e litmus
No of Rounds:
Aptitude Test
Exam/Interview Date: 26-Jul-2011
Location : Delhi