# KVS PGT Mathematics 2014 Previous Year Paper with Answers

To crack the KVS PGT/ TGT/ PRT 2018 Exam, candidates must practice the previous year papers of the different subjects for which they are applying this year. It will help them in improving their speed of attempting maximum questions in minimum time with accuracy. So, in this article we have shared the KVS PGT Math Previous Year Paper alongwith their answers.

## KVS PGT Math Previous Year Paper with Answers

1. Dimension of a subspace W = { (x, y, z, t) : x + z + t = 0, y + z + t = 0 } of R4 is

(A) 4

(B) 3

(C) 1

(D) 2

2. If S = { (1, 1, 0), (2, 1, 3) } is a subset of R3 then which one of the following vectors of R3 is not in the linear span of S?

(A) (0, 0, 0)

(B) (3, 2, 3)

(C) (1, 2, 3)

(D) (4/3, 1, 1)

3. The set { e2x, e3x } for x ϵ R is

(A) L.I. over R

(B) L.D. over R

(C) L.I. over R\{0}

(D) none of these

4. Let T: R3 --> R2 be a linear transformation defined by T(x, y, z) = (x + y, x - z). Then dimension of null space of T is

(A) 1

(B) 2

(C) 0

(D) none of these

5. Let T: R2 --> R3 be a linear transformation defined by T(x, y) = (x + y, x y, y). Then Rank of T is

(A) 3

(B) 2

(C) 0

(D) none of these

6. If A and B are symmetric matrices of the same order, then (ABt – BAt) is

(A) symmetric

(B) null matrix

(C) skew symmetric

(D) none of these

7. If A is skew symmetric matrix, then A2 is a

(A) null matrix

(B) unitary matrix

(C) skew symmetric

(D) symmetric

(A) p – 2

(B) p – 1

(C) p

(D) none of these

10. At what point the line y = x + 1 is a tangent to the curve y2 = 4x ?

(A) (1, –2)

(B) (1, –2), (1, 2)

(C) (1, 2)

(D) none of these

11. The parametric equation of a parabola is x = t2 + 1, y = 2t + 1. The Cartesian equation of its directrix is

(A) y = 1

(B) x = 1

(C) y = 0

(D) x = 0

12. The slope of a line, which passes through the origin, and mid-point of the line segment joining the points P(0, – 4) and B(8, 0) is

13. The value of x for which the points (x, –1), (2, 1) and (4, 5) are collinear is

(A) – 1

(B) 2

(C) 1

(D) none of these

14. The distance between the directrices of the ellipse 9x2 + 4y2 = 36 is

15. The distance of the point (2, 3, 4) from the plane 3x – 6y + 2z + 11 = 0 is

(A) 1

(B) 21

(C) 10

(D) none of these

17. If f(x) = sin2 + 3 cos x – 5, then f(x) is

(A) an even function

(B) an odd function

(C) monotonic

(D) none of these

18. If g = {(1, 1), (2, 3), (3, 5), (4, 7)} is a function described by g(x) = ax + b, then what values should be assigned to a and b?

(A) 1, 1

(B) 1, -2

(C) 2, -1

(D) -2, -1

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33. The decimal number 1.23657657657657…… is equal to the rational number

(A) 123/99

(B) 1235/9990

(C) 123657/100000

(D) 123534/99900

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34. In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach both physics and mathematics. How many teach only physics?

(A) 12

(B) 8

(C) 16

(D) none of these

35. How many integers from 1 to 500 are divisible by at least one of 3, 5 and 7?

(A) 271

(B) 266

(C) 337

(D) none of these

44. If |z2 – 1|=|z|2 + 1, then z lies on

(A) circle

(B) Real axis

(C) Imaginary axis

(D) ellipse

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46. If |z + 4| = 3 then the maximum value of |z + 1|is

(A) 10

(B) 4

(C) 0

(D) 6

47. The average of the squares of the numbers 0, 1, 2, …, n is

48. Mean of five observations is 4 and their variance is 5.2. If three of them are 1, 2, 6 then other two are

(A) 2, 9

(B) 5, 6

(C) 2, 10

(D) 4, 7

49. In a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

(A) 20.5

(B) 25.5

(C) 24

(D) 22

50. Mean of 100 observations is 45. It was later found that two observations 19 and 31 were recorded incorrectly as 91 and 13, then the correct mean is

(A) 44.46

(B) 44

(C) 45

(D) none of these

52. The probability that in a family of 5 members, exactly two members have birthday on Sunday, is

53. A five digit number is formed by using the digits 1, 2, 3, 4, 5 in a random order without repetitions. Then the probability that the number is divisible by 4 is

(A) 3/5

(B) 18/5

(C) 1/5

(D) 6/5

54. A coin is tossed 3 times. The probability of getting head and tail alternatively is

(A) 1/4

(B) 1/8

(C) 1/2

(D) 3/8

55. Probability that in a year of 22nd century chosen at random has 53 Sundays, is

(A) 3/28

(B) 5/28

(C) 7/28

(D) none of these

65. The local maximum values of the function f(x) = 3 x 4 + 4 x 3 – 12 x 2 + 12 are

(A) 1

(B) 2

(C) – 2

(D) 0

(A) 3

(B) 1

(C) 2

(D) 5

67. The general solution of the differential equation (y + x3) dx + (x + 10y3) dy = 0 is

(A) 4xy + x4 + 10y4 = c

(B) 4xy + x4 + y4 = c

(C) 4xy + y4 = c

(D) none of these

68. Every homogeneous equation f(x, y, z) = 0 represents

(A) Sphere with centre at origin

(B) Cone with vertex at origin

(C) Cylinder

(D) None of these

69. The differential equation of all lines passing through the origin is

(A) 8

(B) 10

(C) 9

(D) none of these

71. If altitudes of a triangle are in AP then sides of the triangle are in

(A) GP

(B) AP

(C) HP

(D) AG

72. In an arithmetic progression sum of terms, equidistant from the beginning and the end is equal to the

(A) Last term

(B) First term

(C) Second term

(D) Sum of the first and last term

73. If log 2, log (2n – 1), log (2n + 3) are in AP, then n is equal to

(A) log2 5

(B) log3 5

(C) 5

(D) 25

74. Number of subsets of a finite set with n elements are

(A) 2n

(B) n!

(C) n2

(D) nn

75. If cos2 A + cos2 C = sin2 B then triangle ABC is

(A) equilateral

(B) right angled

(C) isosceles

(D) none of these

76. Let R = { (x, y) | x + 2y = 8 } be a relation on N, then domain of R is

(A) {1, 2, 3}

(B) {1, 2, 3, 4, 5, 6}

(C) {2, 4, 6}

(D) {1, 3, 5}

Q.No.

Ans.

Q.No.

Ans.

Q.No.

Ans.

Q.No.

Ans.

1

D

21

A

41

C

61

C

2

C

22

B

42

D

62

D

3

C

23

A

43

A

63

A

4

A

24

C

44

C

64

B

5

B

25

B

45

A

65

D

6

C

26

A

46

D

66

C

7

D

27

C

47

B

67

A

8

B

28

D

48

D

68

B

9

A

29

B

49

C

69

D

10

C

30

C

50

A

70

B

11

D

31

A

51

B

71

C

12

B

32

B

52

D

72

D

13

C

33

D

53

C

73

A

14

D

34

B

54

A

74

A

15

A

35

A

55

B

75

B

16

C

36

C

56

B

76

C

17

A

37

D

57

C

77

D

18

C

38

A

58

A

78

A

19

B

39

B

59

D

79

B

20

D

40

A

60

B

80

C

Practice makes the man perfect! The more you will practice, the more accuracy you will gain which will eventually lead you to a high score in the exam. Practice will help you in avoiding silly mistakes and making unnecessary guess works while attempting the Math Paper of KVS PGT 2018 Exam. Therefore, practicing previous year papers will help you in achieving accuracy and high score in KVS PGT/ TGT/ PRT 2018 Exam.