Kerala MCA entrance exam papers

I want to give the exam of entrance exam of Kerala MCA so I want to get the question papers of this exam so can you please help me out in getting the question papers?

The Kerala MCA entrance examination is conducted by the Commissioner for Entrance Examinations, Kerala.

Kerala MCA Entrance Exam Pattern
The paper is for duration of 2 hours

It consists of 150 Objective Type - Multiple Choice Questions (MCQs) covering the following areas

Mathematics: 20 questions
Statistics: 20 questions
Physics: 20 questions
Chemistry: 20 questions
General Knowledge: 20 questions
General English: 20 questions
Fundamentals of Computer Awareness: 30 questions

Kerala CEE MCA entrance exam question paper






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1. The set of all integers x such that |x – 3| < 2 is equal to
(a) {1, 2, 3, 4, 5} (b) {1, 2, 3, 4}
(c) {2, 3, 4} (d) {-4, -3, -2}

2. The Range of the function f(x) = x 2
2 x
−
− is
(a) R (b) R – {1}
(c) (-1) (d) R – {-1}

3. The value of (i)i
is
(a) ω (b) ω2

(c) e-π/2 (d) 2√2

4. ( )
( )
4
5
cos isin
icos sin
θ+ θ
θ+ θ is equal to
(a) cos isin − θ (b) cos9 isin9 θ− θ
(c) sin icos θ− θ (d) sin 9 icos9 θ− θ

5. The roots of the quadratic equation 2 ax bx c 0 + + = will be reciprocal to each other if
(a) a = 1/c (b) a = c
(c) b = ac (d) a = b

6. If α, β are the roots of 2 ax 2bx c 0 − += then 33 23 32 α β +α β +αβ is
(a) ( ) 2
3
c c 2b
a
+ (b) 3
3
bc
a
(c) 2
3
c
a (d) None of these

7. The sixth term of a HP is 1/61 and the 10th term is 1/105. The first term of the H.P. is
(a) 1/39 (b) 1/28
(c) 1/17 (d) 1/6

8. Let Sn denote the sum of first n terms of an A.P.. If S2n = 3Sn, then the ratio S3n / 5n is equal to
(a) 4 (b) 6
(c) 8 (d) 10

9. Solution of |3 – x| = x – 3 is
(a) x < 3 (b) x > 3
(c) x > 3 (d) x < 3

10. If the product of n positive numbers in 1, then their sum is
(a) a positive integer (b) divisible by n
(c) equal to 1 n n + (d) never less than n

11. A lady gives a dinner party to six quests. The number of ways in which they may be selected from
among ten friends, if two of the friends will not attend the party together is (a) 112 (b) 140
(c) 164 (d) None of these

12. For 1 ≤ r ≤ n, the value of n1 n2 r
rr r nCr C C _ _ _ C is − − + + ++
(a) r 1 nC + (b) n 1Cr
+
(c) n 1Cr 1
+
+ (d) None of them.

13. 2n 1 3n 1 2.4 3 + + + is divisible by
(a) 2 (b) 9
(c) 11 (d) 27

14. If Pn denotes the product of the binomial coefficients in the expansions of (1 + x)n
, the n 1
n
P
P
+ equals
(a) n !
n!
+ (b) n n
n!
(c) ( )n 1 n 1
n!
+
+ (d) ( )
( )
n 1
!
n 1
n 1
+
+
+

15. If x is very large and n is a negative integer or a proper fraction, then an approximate value of n
1 x
x
⎛ ⎞ + ⎜ ⎟ ⎝ ⎠ is
(a) x 1 n + (b) n 1 x +
(c) 1 1 x + (d) 1 n 1 x
⎛ ⎞ ⎜ ⎟ + ⎝ ⎠

16. If 4 log93 + 9 log24 = 10log x 83, (x ∈ R)
(a) 4 (b) 9
(c) 10 (d) None of these

17. The sum of the series 222
4 8 16 log log log _ _ _ _ −+ ∞to is
(a) e2
(b) loge2 + 1
(c) loge3 – 2 (d) 1 – loge2

18. tan 5x tan 3x tan2x is equal to
(a) tan5x tan3x tan 2x − − (b) sin5x sin3x sin 2x
cos5x cos3x cos2x
− −
− −
(c) 0 (d) None of these

19. If a = tan60
tan 420
and B = cot660
cot 780

(a) A = 2B (b) 1 A B
3 =
(c) A = B (d) 3A = 2B.

20. The value of 246 cos cos cos 777
πππ + + is
(a) 1 (b) -1
(c) 1/2 (d) -1/2

21. If 1 1 tan andsin , 7 10 α= β= where 0 , 2
π <αβ< , then 2β is equal to (a) 4
π − α (b) 3
4
π −α
(c) 8
π − α (d) 3
8 2
π π −

22. If sin cos 2 sin θ+ θ= θ , then
(a) 2 cosθ (b) − 2 sinθ
(c) − θ 2 cos (d) None of these

23. Value of 20 40
40 20
sin 20 cos 20
sin 20 cos 20
+
+ is
(a) 1 (b) 2
(c) ½ (d) None of these

24. Value of 60 40 20 32cos 20 48cos 20 18cos 20 1 −+− is
(a) 1
2 − (b) 1
2
(c) 3
2 (d) None of these

25. If sin cosec 2 θ+ θ= , then value of 3 3 sin cosec θ+ θ is
(a) 2 (b) 4
(c) 6 (d) 8

26. If 5 cosec cot 2 θ+ θ= , then the value of tanθ is
(a) 15
16 (b) 21
20
(c) 15
21 (d) 20
21

27. General value of x satisfying the equation 3sin x cos x 3 + = is given by
(a) n 6
π π ± (b) ( )n
n 1
4 3
π π π+− +
(c) n 3
π π ± (d) ( )n
n 1
3 6
π π π+− −

28. If length of the sides AB, BC and CA of a triangle are 8cm, 15 cm and 17 cm respectively, then
length of the angle bisector of ∠ABC is
(a) 120 2 cm 23 (b) 60 2 cm 23
(c) 30 2cm
23 (d) None of these

29. A man from the top of a 100 metre high tower sees a car moving towards the tower at an angle of
depression of 300
. After sometimes, the angle of depression becomes 600
. The distance (in metres)
traveled by the car during this time is
(a) 100 3 (b) 200 3
3
(c) 100 3
3 (d) 200 3

30. The shadow of a tower of height (1 3 + ) metre standing on the ground is found to be 2 metre
longer when the sun’s elevation is 300
, then when the sun’s elevation was
(a) 300
(b) 450

(c) 600 (d) 750


31. 1 5 cos cos 4
− ⎛ ⎞ π ⎜ ⎟ ⎝ ⎠is equal to
(a) 4 −π (b) 4
π
(c) 3
4
π (d) 5
4
π

32. If 1 1 x y cos cos 2 36
− − π + = , then value of 2 2 x xy y
4 9 2 3
− + is
(a) 3
4 (b) 1
2
(c) 1
4 (d) None of these

33. The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is
(a) 7/2 (b) 7/3
(c) 7/5 (d) 7/10

34. The straight lines x + y – 4 = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a traigle which is
(a) isosceles (b) right angled
(c) equilateral (d) None of these

35. Incentre of the triangle whose vertices are (6, 0) (0, 6) and (7, 7) is
(a) 9 9,
2 2
⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (b) 7 7,
2 2
⎛ ⎞ ⎜ ⎟ ⎝ ⎠
(c) 11 11 , 2 2
⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (d) None of these

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 3,
2 2
⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (b) 1 3
, 2 2
⎛ ⎞ −
⎜ ⎟ ⎝ ⎠
(c) 3 1 ,
2 2
⎛ ⎞ − ⎜ ⎟ ⎝ ⎠ (d) 1 3
, 2 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) ( ) 2 2 2ax 2by a b 4 0 + + ++=
(b) ( ) 2 2 2ax 2by a b 4 0 + − ++=
(c) ( ) 2 2 2ax 2by a b 4 0 − + ++=
(d) ( ) 2 2 2ax 2by a b 4 0 − − ++=

41. Centre of circle whose normals are 2 x 2xy 3x 6y 0 − −+= is
(a) 3 3,2
⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (b) 3,3
2
⎛ ⎞ ⎜ ⎟ ⎝ ⎠
(c) 3 3, 2
⎛ ⎞ ⎜ ⎟ −
⎝ ⎠ (d) 3 3, 2
⎛ ⎞ − ⎜ ⎟ −
⎝ ⎠

42. Centre of a circle is (2, 3). If the line x + y = 1 touches, its equation is
(a) 2 2 x y 4x 6y 4 0 + − − +=
(b) 2 2 x y 4x 6y 5 0 + − − +=
(c) 2 2 x y 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 1,
2 2
⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (b) 1 3,
2 2
⎛ ⎞ ⎜ ⎟ ⎝ ⎠
(c) 1 1,
2 2
⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (d) 1
2 1, 2
2
⎛ ⎞ ⎜ ⎟ − ⎝ ⎠

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) 1 1
tan
2
− ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (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 2a (b) 2 2a
(c) 2 4a (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 2 2 x y 1
49 4 + = is
(a) y x 45 = + (b) y x 53 = +
(c) 2 44
y x 11 11 = + (d) None of these
49. If the hyperbolas 222 xya − = and 2 xy c = are of equal size, then
(a) 2 2 c 2a = (b) c = 2a
(c) 2 2 2c a = (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) 1234 xxxx 0 = (b) 1234 yyyy 1=
(c) 1234 yyyy 0 = (d) 1234 xxxx 1 = −

51. If
ab0
0ab
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 111 0
abc
++= , then
1a 1 1
1 1b 1
1 1 1c
+
+
+
is equal to
(a) 0 (b) abc
(c) –abc (d) None of these

53. The determinant
() () 2 cos sin cos B
sin cos sin
cos sin cos
α+β − α+β
α αβ
−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 4n
n n
⎡ ⎤ −
⎢ ⎥ ⎣ ⎦ (b) 2n5n
n n
⎡ + − ⎤ ⎢ ⎥ ⎣ − ⎦

(c) ( )
( )
n n
n
3 4
1 1
⎡ ⎤ − ⎢ ⎥
⎢ ⎥ − ⎣ ⎦
(d) None of these

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

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

57. 3
3 x 4
1 cot x lim
2 cot x cot x →π
−
− − is
(a) 11
4 (b) 3
4
(c) 1
2 (d) None of these
58. 1
x 0
sin x limsec x
−
→
⎛ ⎞ ⎜ ⎟ = ⎝ ⎠
(a) 1 (b) 0
(c) 2
π (d) Does not exist

59. The function y 3x 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 ( ) ( )1
x cos x ,x 0 f x
K x0
⎧ ⎫ ⎪ ≠⎪ = ⎨ ⎬
⎪ ⎪ ⎩ ⎭ =
is continuous of x = 0 then value of k is
(a) 1 (b) -1
(c) 0 (d) e

63. 5 1 x dx
1 x
+ = + ∫
(a) 234 1x x x x c −+ − + + (b) 2345 xxxx x x 2345 − +−++
(c) ( )5
1x C + + (d) None of these

64. x x dx ∫
(a) 3 x
3 (b)
2 x x
3
(c)
2 x x
2 (d) None of these

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

66. ( ) 2
0
log tan x dx
π
∫
(a) 4
π (b) 2
π
(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.
2
2
0
x x dx ∫
(a) 5/3 (b) 7/3
(c) 8/3 (d) 4/3

69. 2
0
xsin x dx
1 cos x
π
+ ∫
(a) 2
8 π (b) 2
4 π
(c) 3
8 π (d) 4
8 π

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 4 32 y x 2x x 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
3 2
5 2 3 2
2
2 3 3
3
d y 4
dy dy dx x 1
dx dx d y
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 dy x. y 0 dx 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 ˆˆ ˆ ˆ ˆ ˆ a i j 2k and b i 3j 4k =+− =− +
r r
(a) 14 (b) 2 14
(c) 2 6 (d) 38

ANSWER KEYS
1. (c) 2. (c) 3. (c) 4. (d) 5. (b) 6. (a) 7. (d) 8. (b) 9. (d) 10. (d) 11. (b) 13. (c)16. (c) 17. (d) 18. (b) 19. (c) 20. (c) 21. (c) 22. (a) 23. (a) 24. (a) 25. (a) 26. (d) 27. (d) 28. (a) 29. (b) 30. (b) 31. (c) 32. (c) 33. (d) 34. (a) 35.(a)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)

__________________
Answered By StudyChaCha Member

I have applied for the Kerala MCA entrance examination and want to get the previous year question paper of it so can you please provide me this?