Mathematics Questions with solutions MCQs

1. The coordinates of the vertex of the parabola y = x2 – 2x + 3 is ______

A

(2, 4)

B

(1, 3)

C

(2, 3)

D

(1, 2)

Mathematics JSA 2021
Correct Answer : D
Explanation :

(1, 2)

Correct Answered :

Wrong Answered :

2. Which of the following includes all the elements of set B = {x : x is an integer, x2 ≤ 4}?

A

{–1, 0, 1, 2, 3}

B

{0, 1, 2, 3, 4}

C

{–2, –1, 0, –1}

D

{–2, –1, 0, 1, 2}

Mathematics JSA 2021
Correct Answer : D
Explanation :

{–2, –1, 0, 1, 2}

Correct Answered :

Wrong Answered :

3. If p + 2q + r = 7, p + 3r = 11 and 2p – 3q = 1, then what is the value of (p2 + q2 + r2 )?

A

11

B

9

C

14

D

10

Mathematics JSA 2021
Correct Answer : C
Explanation :

14

Correct Answered :

Wrong Answered :

4. If the equation of the base of an equilateral triangle is x + y – 6 = 0 and the coordinates of its opposite vertex is (1, 3), then what is the area of the triangle?

A

2/√3

B

1/√3

C

5/√3

D

4/√3

Mathematics JSA 2021
Correct Answer : A
Explanation :

2/√3

Correct Answered :

Wrong Answered :

5. For what value of K, the points (K, 2), (3, 5) and (9, 8) are collinear?

A

3

B

-3

C

-6

D

6

Mathematics JSA 2021
Correct Answer : B
Explanation :

-3

Correct Answered :

Wrong Answered :

6. Which of the following includes all the subsets of set {a, b}?

A

ϕ, {a}, {b}, {a, b}

B

ϕ, {a}, {b}

C

{a}, {b}, {a, b}

D

{a}, {b}

Mathematics JSA 2021
Correct Answer : A
Explanation :

ϕ, {a}, {b}, {a, b}

Correct Answered :

Wrong Answered :

7. If f(x) = [(x + 3)/(x2 + 1)], then what is the value of f`(1)?

A

–3/2

B

5/2

C

–5/2

D

3/2

Mathematics JSA 2021
Correct Answer : A
Explanation :

–3/2

Correct Answered :

Wrong Answered :

8. Which of the following is an example of equivalent set?

A

P = {3, 6, 9, 12, 15} and Q = {x : x = 3n and 1 ≤ x < 6}

B

P = {5, 25, 125, 625} and Q = {x : x = 5n and 1 ≤ x ≤ 3}

C

P = {a, b, c, d} and Q = {d, c, a, b, e}

D

P = {2, e, 4, 5, g} and Q = {g, 1, 2, 4, 5, 6}

Mathematics JSA 2021
Correct Answer : A
Explanation :

P = {3, 6, 9, 12, 15} and Q = {x : x = 3n and 1 ≤ x < 6}

Correct Answered :

Wrong Answered :

9. What is the distance between the points (4, 5) (7, 9)?

A

6

B

5

C

4

D

3

Mathematics JSA 2021
Correct Answer : B
Explanation :

5

Correct Answered :

Wrong Answered :

10. If f(x) = xn+2 and f`(1) = 14, then what is the value of n?

A

14

B

12

C

11

D

10

Mathematics JSA 2021
Correct Answer : B
Explanation :

12

Correct Answered :

Wrong Answered :

11. If P = {1, 2, 4, 5, 6}, then the number of subset of P is ______.

A

64

B

32

C

8

D

16

Mathematics JSA 2021
Correct Answer : B
Explanation :

32

Correct Answered :

Wrong Answered :

12. Differentiation of x3 + cosx + (1/x3 ) with respect to x is ______.

A

3x2 – sinx – (3/x4 )

B

3x2 – sinx + (2/x3 )

C

3x2 + sinx + (2/x3 )

D

3x2 + sinx – (2/x3 )

Mathematics JSA 2021
Correct Answer : A
Explanation :

3x2 – sinx – (3/x4 )

Correct Answered :

Wrong Answered :

13. In a school 40 percent of the students travels by bus, 30 percent travels by car and 5 percent travels by both bus and car. What percent of total students travel by bus or car?

A

65 percent

B

70 percent

C

60 percent

D

55 percent

Mathematics JSA 2021
Correct Answer : A
Explanation :

65 percent

Correct Answered :

Wrong Answered :

14. The radius of the circle having centre at (3, –4) and touching the line 3x + 4y – 8 = 0 is

A

3

B

2

C

4

D

5

Mathematics JSA 2021
Correct Answer : A
Explanation :

3

Correct Answered :

Wrong Answered :

15. If f(x) = 5x4 – 7 and f(0) = 5, then what is the anti-derivative of f(x)?

A

x4 – 7x + 2

B

x5 – 7x + 6

C

x4 – 7x + 5

D

x5 – 7x + 5

Mathematics JSA 2021
Correct Answer : D
Explanation :

x5 – 7x + 5

Correct Answered :

Wrong Answered :

16. If A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6}, then what is the value of A ∩ B?

A

{1, 2, 3, 4, 5, 6}

B

{2, 4, 6}

C

{2, 4}

D

ϕ

Mathematics JSA 2021
Correct Answer : B
Explanation :

{2, 4, 6}

Correct Answered :

Wrong Answered :

17. What is the length of latus-rectum of the parabola y2 = 16x?

A

16

B

12

C

20

D

8

Mathematics JSA 2021
Correct Answer : A
Explanation :

16

Correct Answered :

Wrong Answered :

18. Which of the following pairs of sets are equal?

A

A = {1, 2, 3, 4, 5, 6, 7, 8}, B = {x : x is a natural number and x < 8}

B

A = {3, 6, 9, 12}, B = {x : x = 3n and 1 ≤ n ≤ 4}

C

A = {2, 4, 6, 8}, B = {8, 6, 4, 1}

D

A = {a, e, i, o, v}, B = {e, a, u, i, o}

Mathematics JSA 2021
Correct Answer : B
Explanation :

A = {3, 6, 9, 12}, B = {x : x = 3n and 1 ≤ n ≤ 4}

Correct Answered :

Wrong Answered :

19. Differentiation of e-x with respect to x is ______.

A

-e-x

B

-ex

C

ex

D

e-x

Mathematics JSA 2021
Correct Answer : A
Explanation :

-e-x

Correct Answered :

Wrong Answered :

20. The roster form of the set P = {x : x is an integer and x2 – 81 = 0} is ______.

A

{49, –81}

B

{9, –9}

C

{81, –81}

D

{8, –8}

Mathematics JSA 2021
Correct Answer : B
Explanation :

{9, –9}

Correct Answered :

Wrong Answered :

21. The equation of the directrix of the parabola y2 = 4x + 4y is ______.

A

x + 6 = 0

B

x + 3 = 0

C

x + 5 = 0

D

x + 2 = 0

Mathematics JSA 2021
Correct Answer : D
Explanation :

x + 2 = 0

Correct Answered :

Wrong Answered :

22. If the circles x2+ y2 = K and x2 + y2 – 8x – 6y + 9 = 0 touches externally, then what is the value of K?

A

1

B

2

C

3

D

4

Mathematics JSA 2021
Correct Answer : A
Explanation :

1

Correct Answered :

Wrong Answered :

23. If P and Q are the two sets containing 3 and 6 elements respectively, then what can be the maximum number of elements in P ⋃ Q?

A

10

B

9

C

12

D

11

Mathematics JSA 2021
Correct Answer : B
Explanation :

9

Correct Answered :

Wrong Answered :

24. If the coordinates of the mid-points of the sides of a triangle are (1, 2), (2, 4) and (3, 5), then what is the value of coordinates of its centroid?

A

2, (11/3)

B

5, (11/6)

C

3, (11/4)

D

4, (9/4)

Mathematics JSA 2021
Correct Answer : A
Explanation :

2, (11/3)

Correct Answered :

Wrong Answered :

25. Differentiation of logtanx with respect to x is ___

A

2cosec2x

B

2sec2x

C

2sin2x

D

2cos2x

Mathematics JSA 2021
Correct Answer : A
Explanation :

2cosec2x

Correct Answered :

Wrong Answered :

26. What is the equation of the circle whose coordinates of centre is (2, 3) and radius is 4?

A

x2 + y2 – 4x – 6y – 3 = 0

B

x2 + y2 + 4x – 6y – 3 = 0

C

x2 + y2 – 4x + 6y + 3 = 0

D

x2 + y2 – 4x – 6y + 3 = 0

Mathematics JSA 2021
Correct Answer : A
Explanation :

x2 + y2 – 4x – 6y – 3 = 0

Correct Answered :

Wrong Answered :

27. A rod having length of √5 metre slides with its ends on two perpendicular lines. What is the locus of the mid-point of rod?

A

4x2 + 4y2 = √5

B

4x2 – 4y2 = 5

C

4x2 + 4y2 = 5

D

4x2 – 4y2 = √5

Mathematics JSA 2021
Correct Answer : C
Explanation :

4x2 + 4y2 = 5

Correct Answered :

Wrong Answered :

28. The roster form of the set of all letters in the word “MATHEMATICS” is ___

A

{M, A, T, H, E, M, A, T, C, S}

B

{M, A, T, H, E, I, S}

C

{M, A, T, E, H, I}

D

{M, A, T, H, E, I, C, S}

Mathematics JSA 2021
Correct Answer : D
Explanation :

{M, A, T, H, E, I, C, S}

Correct Answered :

Wrong Answered :

29. If A = {1, 2, 3, 4, 5, 6}, then which of the following statements is correct?

A

{1, 2, 3} ∈ A

B

{3, 4} ∈ A

C

{3, 4} ⊂ A

D

1 ⊂ A

Mathematics JSA 2021
Correct Answer : C
Explanation :

{3, 4} ⊂ A

Correct Answered :

Wrong Answered :

30. A circle of radius 2 units touches the coordinate axes in the first quadrant. What is the equation of its image in the line y = 0?

A

x2 + y2 – 4x + 4y + 4 = 0

B

x2 + y2 + 4x – 4y + 8 = 0

C

x2 + y2 + 4x + 4y + 8 = 0

D

x2 + y2 + 4x – 4y + 4 = 0

Mathematics JSA 2021
Correct Answer : A
Explanation :

x2 + y2 – 4x + 4y + 4 = 0

Correct Answered :

Wrong Answered :

31. Which of the following states that A = B?

A

A = {2, 7, 9} and B = {7, 9, 2}

B

A = {a, e, f} and B = {f, e}

C

A = {2, 4, 6, 8} and B = {4, 8}

D

A = {a, b, c, d, e} and B = {e, c, b, a}

Mathematics JSA 2021
Correct Answer : A
Explanation :

A = {2, 7, 9} and B = {7, 9, 2}

Correct Answered :

Wrong Answered :

32. Set builder form of the set {1, 8, 27, 64, 125} is ___

A

{x : x = n3 and 1 ≤ n ≤ 15}

B

{x : x = n3 and 1 ≤ n ≤ 5}

C

{x : x = 3n and 1 < n ≤ 15}

D

{x : x = 3n and 1 ≤ n ≤ 505}

Mathematics JSA 2021
Correct Answer : B
Explanation :

{x : x = n3 and 1 ≤ n ≤ 5}

Correct Answered :

Wrong Answered :

33. Differentiation of 4x + x5 + 31 with respect to x is ___

A

4x log2 + 5x5

B

5x log4 + 5x4

C

4x log4 + 5x4

D

4x log2 + 4x5

Mathematics JSA 2021
Correct Answer : C
Explanation :

4x log4 + 5x4

Correct Answered :

Wrong Answered :

34. What is the equation of the parabola whose focus is (2, 0) and the directrix is x + 5 = 0?

A

y2 = 21x – 14

B

y2 = 14x – 21

C

y2 = 14x + 21

D

y2 = 21x + 14

Mathematics JSA 2021
Correct Answer : C
Explanation :

y2 = 14x + 21

Correct Answered :

Wrong Answered :

35. If 5p – 7q + r = 11, 6p – 8q – r = 15 and 3p + 2q – 6r = 7, then what is the value of (p + q + r)?

A

–2

B

–3

C

zero

D

–1

Mathematics JSA 2021
Correct Answer : D
Explanation :

–1

Correct Answered :

Wrong Answered :

36. If y = x2sinx, then what is the value of (dy/dx) at x = π/2?

A

π

B

π/4

C

π/6

D

π/2

Mathematics JSA 2021
Correct Answer : A
Explanation :

π

Correct Answered :

Wrong Answered :

37. If the angle between two lines is π/4 and slope of one of the lines is 1/3, then what is the slope of the other line?

A

3

B

1

C

2

D

4

Mathematics JSA 2021
Correct Answer : C
Explanation :

2

Correct Answered :

Wrong Answered :

38. ϕ, {1}, {2}, {1, 2} are the subsets of ___

A

{1, 2}

B

{0, 1, 2}

C

{1}, {2}

D

{1, 3}

Mathematics JSA 2021
Correct Answer : A
Explanation :

{1, 2}

Correct Answered :

Wrong Answered :

39. Differentiation of cotx with respect to x is ___

A

–tan2x

B

tan2x

C

cosec2x

D

-cosec2x

Mathematics JSA 2021
Correct Answer : D
Explanation :

-cosec2x

Correct Answered :

Wrong Answered :

40. If y = ex cosx, then what is the value of (dy/dx) at x = 0?

A

zero

B

2

C

-1

D

1

Mathematics JSA 2021
Correct Answer : D
Explanation :

1

Correct Answered :

Wrong Answered :

41. Which of the following is a finite set?

A

The set of numbers which are multiple of 3

B

The set of even numbers

C

The set of whole number less than 1

D

The set of negative integers

Mathematics JSA 2021
Correct Answer : C
Explanation :

The set of whole number less than 1

Correct Answered :

Wrong Answered :

42. What is the value of the eccentricity of the ellipse 25x2 + 9y2 – 150x – 90y + 225 = 0?

A

2/5

B

3/4

C

3/5

D

4/5

Mathematics JSA 2021
Correct Answer : D
Explanation :

4/5

Correct Answered :

Wrong Answered :

43. Two vertices of a triangle are (3, 2) and (7, 4). If the centroid of the triangle is (8, 9), then what is the coordinates of the third vertex of that triangle?

A

(14, 21)

B

(21, 23)

C

(16, 19)

D

(15, 23)

Mathematics JSA 2021
Correct Answer : A
Explanation :

(14, 21)

Correct Answered :

Wrong Answered :

44. If A and B are two sets such that n(A)= 50, n(B) = 15 and n(A ∪ B) = 60, then what is the value of n(A ∩ B)?

A

5

B

15

C

8

D

10

Mathematics JSA 2021
Correct Answer : A
Explanation :

5

Correct Answered :

Wrong Answered :

45. What is the slope of the tangent to the curve f(x) = 2x5 + x3 – 2 at x = 1?

A

13

B

11

C

14

D

12

Mathematics JSA 2021
Correct Answer : A
Explanation :

f`(x) =10x4 + 3x2 So at x=1 f`(1)= 10 + 3 = 13

Correct Answered :

Wrong Answered :

46. Differentiation of sin(4x + 5) with respect to x is ___

A

4sin(4x + 5)

B

4cos(4x + 5)

C

5cos(4x + 5)

D

5sin(4x + 5)

Mathematics JSA 2021
Correct Answer : B
Explanation :

4cos(4x + 5)

Correct Answered :

Wrong Answered :

47. What is the equation of the line which is parallel to 2x – 3y + 10 = 0 and passes through the point (2, 3)?

A

2x – 3y + 5 = 0

B

2x + 3y + 10 = 0

C

2x – 3y + 10 = 0

D

2x + 3y + 5 = 0

Mathematics JSA 2021
Correct Answer : A
Explanation :

2x – 3y + 5 = 0

Correct Answered :

Wrong Answered :

48. Which of the following is correct form of De-Morgan`s Law?

A

(A ⋂ B )` = A` ∪ B`

B

(A ⋂ B)` = A` ⋂ B`

C

A ∪ B) = A ⋂ B

D

(A ⋂ B) = A` ⋂ B`

Mathematics JSA 2021
Correct Answer : A
Explanation :

(A ⋂ B )` = A` ∪ B`

Correct Answered :

Wrong Answered :

49. The length of the latus-rectum of the ellipse x2 + 4y2 + 2x + 16y + 13 = 0 is __

A

2

B

3

C

4

D

1

Mathematics JSA 2021
Correct Answer : D
Explanation :

1

Correct Answered :

Wrong Answered :

50. Which of the following is correct roaster form of set A = {x : x is an integer and –1 ≤ x < 3}?

A

A = {–1, 0, 1, 2}

B

A = {–1, 0, 1, 2, 3}

C

A = {0, 1, 2}

D

A = {0, 1, 2, 3}

Mathematics JSA 2021
Correct Answer : A
Explanation :

A = {–1, 0, 1, 2}

Correct Answered :

Wrong Answered :

51. The set builder form of the set A = {3, 9, 27, 81, 243} is ____

A

{x : x = 3n, n ∈ N and 1 < n < 5}

B

{x : x = 3n, n ∈ N and 1 < n ≤ 5}

C

{x : x = 3n, n ∈ N and 1 ≤ n ≤ 5}

D

{x : x = 3n, n ∈ N and 1 ≤ n < 5}

Mathematics JSA 2021
Correct Answer : C
Explanation :

{x : x = 3n, n ∈ N and 1 ≤ n ≤ 5}

Correct Answered :

Wrong Answered :

52. What is the equation of a line passing through (3, 5) and inclined at an angle of 135 degree with the positive direction of x-axis?

A

x + y = 8

B

x – y = –8

C

x + y = –8

D

x – y = 8

Mathematics JSA 2021
Correct Answer : A
Explanation :

x + y = 8

Correct Answered :

Wrong Answered :

53. If f(x) = kx3 + px + 10 and f`(3) = 15 and f`(1) = 10, then what is the value of (k + p)?

A

109/12

B

113/12

C

119/12

D

115/12

Mathematics JSA 2021
Correct Answer : D
Explanation :

115/12

Correct Answered :

Wrong Answered :

54. If f(x) = x2 – 8x + 7, then what is the value of f`(4) + 3f`(2)?

A

–18

B

–16

C

–12

D

–20

Mathematics JSA 2021
Correct Answer : C
Explanation :

–12

Correct Answered :

Wrong Answered :

55. Which of the following sets is finite?

A

Set of lines perpendicular to x-axis

B

The set of numbers which are multiple of 5

C

Set of letters in English alphabet

D

Set of lines parallel to x-axis

Mathematics JSA 2021
Correct Answer : C
Explanation :

Set of letters in English alphabet

Correct Answered :

Wrong Answered :

56. If a line passing through the points (k, 3k) and (2, 3) is perpendicular to the line 3x + 4y + 5 = 0, then what is the value of k?

A

4/5

B

2/5

C

3/5

D

1/5

Mathematics JSA 2021
Correct Answer : D
Explanation :

1/5

Correct Answered :

Wrong Answered :

57. Find the greatest number of three digits which is divisible by 12, 24, 32 and 30.

A

970

B

990

C

980

D

960

Mathematics DHOBI
Correct Answer : D
Explanation :

D

Correct Answered :

Wrong Answered :

58. Find the area of the square whose side is 235 cm. (In cm2

A

54225

B

56225

C

53225

D

55225

Mathematics DHOBI
Correct Answer : D
Explanation :

D

Correct Answered :

Wrong Answered :

59. Find the area of trapezium whose parallel sides are 24 cm and 20 cm long, and the distance between them is 17 cm. (In cm2 )

A

354

B

364

C

374

D

344

Mathematics DHOBI
Correct Answer : C
Explanation :

C

Correct Answered :

Wrong Answered :

60. What is the average of first five multiples of 13?

A

39

B

37

C

35

D

41

Mathematics DHOBI
Correct Answer : A
Explanation :

A

Correct Answered :

Wrong Answered :

61. The multiplicative inverse of -13 is p/13, then -p is equal to

A

1

B

0

C

-13

D

None of these

Mathematics JKPSI 2022 CBT
Correct Answer : A
Explanation :

1

Correct Answered :

Wrong Answered :

62. What is the value of p(t) = 2 + t + 2t2 - t3 for p(0)

A

1

B

2

C

3

D

5

Mathematics JKPSI 2022 CBT VERIFIED
Correct Answer : B
Explanation :

2

Correct Answered :

Wrong Answered :

63. How many pieces of length 125 can be cut from a rod 50 m long?

A

35

B

40

C

52

D

28

Mathematics JKPSI 2022 CBT
Correct Answer : B
Explanation :

Given:

length of rod = 50 m, length of each piece = 125 cm

Formula Used:

number of pieces of rod = length of rod/length of each piece

1 m = 100 cm

Calculation:

⇒ length of rod = 50 m = 5000 cm

⇒ number of pieces of rod = 5000/125 = 40  

∴ required number of pieces of rod = 40     

Correct Answered :

Wrong Answered :

64. Express 0.000532 is standard form

A

532 x 105

B

5.32 x 10-4

C

532 x x 10-3

D

0.532 x 102

Mathematics JKPSI 2022 CBT
Correct Answer : B
Explanation :

5.32 x 10<sup>-4</sup>

Correct Answered :

Wrong Answered :

65. The ratio of two sides of a parallelogram in 3:5 and its perimeter is 96 cim. Find the adjacent side of the parallelogram.

A

18 cm

B

20 cm

C

60 cm

D

45 cm

Mathematics JKPSI 2022 CBT VERIFIED
Correct Answer : A
Explanation :

18 cm

Correct Answered :

Wrong Answered :

66. if (1, -2) is a solution of the equation 2x -y = p, then find the value of p

A

4

B

0

C

2

D

1

Mathematics JKPSI 2022 CBT
Correct Answer : A
Explanation :

4

Correct Answered :

Wrong Answered :

67. Find the value of the polynomial 5x - 4x² + 3 at x = -1

A

8

B

-9

C

3

D

-6

Mathematics JKPSI 2022 CBT
Correct Answer : D
Explanation :

-6

Correct Answered :

Wrong Answered :

68. Express 231 in prime factors

A

3x7x11

B

21x11

C

33x4

D

3x4x11

Mathematics JKPSI 2022 CBT
Correct Answer : A
Explanation :

3x7x11

Correct Answered :

Wrong Answered :

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