Top 50 MCQs for CBSE Class 12 Maths Half Yearly Exam 2025 with Answer Key

Preparing for your CBSE Class 12 Maths Half Yearly Exam 2025 can feel like a big challenge, but with the right resources, you can definitely succeed. This article offers a comprehensive set of 50 Multiple Choice Questions (MCQs) specifically designed to help you ace your upcoming exam. These questions cover key concepts and important topics from the CBSE Class 12 Maths syllabus, ensuring you get a thorough review.
By practicing these carefully selected MCQs, you'll not only strengthen your understanding of core mathematical principles but also become more familiar with the exam pattern. This targeted practice will boost your confidence and improve your problem-solving skills, ultimately helping you score better in your CBSE Class 12 Maths Half Yearly Exam. Get ready to solidify your knowledge and achieve excellent results!

CBSE Class Mathematics 2025-26: Course Structure

Check: CBSE Class 12 Maths Sample Paper 2025-26

Top 50 MCQs for CBSE Class 12 Maths Half Yearly Exam 2025

Here are 50 Multiple Choice Questions (MCQs) for CBSE Class 12 Maths Half Yearly Exam

1. If f(x) = |x|, for x < 0, f(x) is equal to:

   (A) x

   (B) -x

   (C) 0

   (D) 1

   Correct Answer: (B) -x

2. The principal value of inverse sine of (-1/2) is:

   (A) pi/6

   (B) -pi/6

   (C) pi/3

   (D) -pi/3

   Correct Answer: (B) -pi/6

3. A matrix having 6 elements can have how many possible orders?

   (A) 2

   (B) 3

   (C) 4

   (D) 6

   Correct Answer: (C) 4

4. If matrix A = [2 1; 3 4] and matrix B = [1 0; 2 1], then A + B is:

   (A) [3 1; 5 5]

   (B) [3 1; 1 3]

   (C) [3 0; 6 4]

   (D) [1 1; 1 3]

   Correct Answer: (A) [3 1; 5 5]

5. The value of the determinant of an upper triangular matrix with diagonal elements 1, 2, 3 is:

   (A) 1

   (B) 2

   (C) 3

   (D) 6

   Correct Answer: (D) 6

6. If y = sin(x squared), then dy/dx is:

   (A) cos(x squared)

   (B) -cos(x squared)

   (C) 2x cos(x squared)

   (D) -2x cos(x squared)

   Correct Answer: (C) 2x cos(x squared)

7. For a function to be continuous at a point 'a', the limit of f(x) as x approaches 'a' must be equal to:

   (A) f(a)

   (B) 0

   (C) infinity

   (D) Not defined

   Correct Answer: (A) f(a)

8. The rate of change of the circumference of a circle with respect to its radius r is:

   (A) pi

   (B) 2pi

   (C) 2r

   (D) pi*r squared

   Correct Answer: (B) 2pi

9. The derivative of inverse tan(x) is:

   (A) 1 / (1 - x squared)

   (B) 1 / (1 + x squared)

   (C) tan x

   (D) cot x

   Correct Answer: (B) 1 / (1 + x squared)

10. Integral of sec squared(x) dx is:

    (A) tan x + C

    (B) cot x + C

    (C) sec x + C

    (D) sin x + C

    Correct Answer: (A) tan x + C

11. The order of the differential equation (dy/dx) + y = sin x is:

    (A) 0

    (B) 1

    (C) 2

    (D) Not defined

    Correct Answer: (B) 1

12. If y = e to the power x, then dy/dx is:

    (A) x * e to the power x-1

    (B) e to the power x

    (C) log x

    (D) 1 / x

    Correct Answer: (B) e to the power x

13. The function f(x) = x squared has a local minimum at x =:

    (A) 1

    (B) -1

    (C) 0

    (D) 2

    Correct Answer: (C) 0

14. Definite integral of 1 / (1 + x squared) from 0 to 1 is:

    (A) pi/2

    (B) pi/4

    (C) 0

    (D) 1

    Correct Answer: (B) pi/4

15. The area under the curve y = x from x = 0 to x = 1 is:

    (A) 1 unit squared

    (B) 0.5 unit squared

    (C) 2 unit squared

    (D) 0 unit squared

    Correct Answer: (B) 0.5 unit squared

16. If matrix A = [1 0; 0 1], then A inverse is:

    (A) [1 0; 0 1]

    (B) [0 1; 1 0]

    (C) [-1 0; 0 -1]

    (D) [0 0; 0 0]

    Correct Answer: (A) [1 0; 0 1]

17. A relation R on set A is called reflexive if:

    (A) (a, a) is in R for all a in A

    (B) (a, b) is in R implies (b, a) is in R

    (C) (a, b) and (b, c) are in R implies (a, c) is in R

    (D) R is empty

    Correct Answer: (A) (a, a) is in R for all a in A

18. If y = log(x), then dy/dx is:

    (A) x

    (B) 1/x

    (C) e to the power x

    (D) log x

    Correct Answer: (B) 1/x

19. Integral of 1 dx is:

    (A) 0

    (B) x + C

    (C) 1

    (D) x squared / 2 + C

    Correct Answer: (B) x + C

20. The general solution of dy/dx = 1 is:

    (A) y = x

    (B) y = x + C

    (C) y = 1

    (D) y = 0

    Correct Answer: (B) y = x + C

21. The derivative of sin inverse(x) is:

    (A) 1 / (sqrt(1 - x squared))

    (B) -1 / (sqrt(1 - x squared))

    (C) cos inverse(x)

    (D) tan inverse(x)

    Correct Answer: (A) 1 / (sqrt(1 - x squared))

22. The slope of the tangent to the curve y = x squared at x = 2 is:

    (A) 2

    (B) 4

    (C) 0

    (D) -2

    Correct Answer: (B) 4

23. If the rows of a determinant are identical, its value is:

    (A) 1

    (B) -1

    (C) 0

    (D) Undefined

    Correct Answer: (C) 0

24. A matrix is called a symmetric matrix if:

    (A) A = Transpose of A

    (B) A = - Transpose of A

    (C) All elements are zero

    (D) It is a square matrix

    Correct Answer: (A) A = Transpose of A

25. Integral of e to the power x dx is:

    (A) e to the power x

    (B) e to the power x + C

    (C) x * e to the power x-1

    (D) log x + C

    Correct Answer: (B) e to the power x + C

26. The area under the curve y = cos x from x = 0 to x = pi/2 is:

    (A) 0

    (B) 1

    (C) -1

    (D) pi/2

    Correct Answer: (B) 1

27. The general solution of dy/dx = sin x is:

    (A) y = cos x + C

    (B) y = -cos x + C

    (C) y = sin x + C

    (D) y = -sin x + C

    Correct Answer: (B) y = -cos x + C

28. The domain of sin inverse(x) is:

    (A) (-1, 1)

    (B) [-1, 1]

    (C) [0, 1]

    (D) (-infinity, infinity)

    Correct Answer: (B) [-1, 1]

29. If y = log(sin x), then dy/dx is:

    (A) cos x

    (B) -cos x

    (C) cot x

    (D) -cot x

    Correct Answer: (C) cot x

30. The slope of the normal to the curve y = x squared at x = 1 is:

    (A) 2

    (B) -1/2

    (C) 1/2

    (D) -2

    Correct Answer: (B) -1/2

31. If a relation R is reflexive and symmetric, it is always:

    (A) Transitive

    (B) An equivalence relation

    (C) Neither transitive nor equivalence

    (D) Identity relation

    Correct Answer: (C) Neither transitive nor equivalence

32. If A is an invertible matrix of order 2, then det(A inverse) is:

    (A) det(A)

    (B) 1 / det(A)

    (C) 0

    (D) 1

    Correct Answer: (B) 1 / det(A)

33. Integral of 1/x dx is:

    (A) log |x| + C

    (B) 1 + C

    (C) x squared / 2 + C

    (D) -1/x squared + C

    Correct Answer: (A) log |x| + C

34. The area of a circle with radius 'r' is:

    (A) pi * r

    (B) 2 * pi * r

    (C) pi * r squared

    (D) 4 * pi * r squared

    Correct Answer: (C) pi * r squared

35. A differential equation of the form dy/dx + P(x)y = Q(x) is called a:

    (A) Variable separable form

    (B) Homogeneous differential equation

    (C) Linear differential equation

    (D) Exact differential equation

    Correct Answer: (C) Linear differential equation

36. The value of tan inverse(1) is:

    (A) 0

    (B) pi/4

    (C) pi/2

    (D) pi

    Correct Answer: (B) pi/4

37. If y = e to the power (2x), then dy/dx is:

    (A) e to the power (2x)

    (B) 2 * e to the power (2x)

    (C) 2x * e to the power (2x-1)

    (D) e to the power x

    Correct Answer: (B) 2 * e to the power (2x)

38. A function f(x) is strictly increasing if f'(x) is:

    (A) Less than 0

    (B) Greater than 0

    (C) Equal to 0

    (D) Not defined

    Correct Answer: (B) Greater than 0

39. If x = t squared and y = t cubed, then dy/dx is:

    (A) 3t/2

    (B) 2t/3

    (C) 3/2

    (D) t

    Correct Answer: (A) 3t/2

40. Definite integral of x dx from -1 to 1 is:

    (A) 0

    (B) 1

    (C) 2

    (D) -1

    Correct Answer: (A) 0

41. The area bounded by the line y = x and the x-axis from x = 0 to x = 2 is:

    (A) 1 unit squared

    (B) 2 unit squared

    (C) 4 unit squared

    (D) 0 unit squared

    Correct Answer: (B) 2 unit squared

42. The general solution of dy/dx = y is:

    (A) y = Ce to the power x

    (B) y = x + C

    (C) y = log x + C

    (D) y = e to the power x + C

    **Correct Answer: (A) y = Ce to the power x**

43. If A is a square matrix, then (A - Transpose of A) is a:

    (A) Symmetric matrix

    (B) Skew-symmetric matrix

    (C) Diagonal matrix

    (D) Identity matrix

    Correct Answer: (B) Skew-symmetric matrix

44. For continuity at a point, Left Hand Limit = Right Hand Limit = :

    (A) 0

    (B) f(a)

    (C) 1

    (D) Infinity

    Correct Answer: (B) f(a)

45. The minimum value of f(x) = x squared is:

    (A) 1

    (B) 0

    (C) -1

    (D) 2

    Correct Answer: (B) 0

46. Integral of 1 / sqrt(1 - x squared) dx is:

    (A) sin inverse(x) + C

    (B) cos inverse(x) + C

    (C) tan inverse(x) + C

    (D) log x + C

    Correct Answer: (A) sin inverse(x) + C

47. The degree of the differential equation (dy/dx) squared + y = 0 is:

    (A) 0

    (B) 1

    (C) 2

    (D) Not defined

    Correct Answer: (C) 2

48. If matrix A = [1 2; 3 4], then 2A is:

    (A) [2 4; 6 8]

    (B) [1 4; 9 16]

    (C) [2 2; 3 4]

    (D) [1 2; 6 8]

    Correct Answer: (A) [2 4; 6 8]

49. If y = x cubed, then the second derivative (d squared y / dx squared) is:

    (A) 3x squared

    (B) 6x

    (C) 6

    (D) x cubed

    Correct Answer: (B) 6x

50. If a matrix A has order 3x2 and matrix B has order 2x4, the order of AB is:

    (A) 3x4

    (B) 2x2

    (C) 3x2

    (D) Not possible

    Correct Answer: (A) 3x4

Mastering these 50 MCQs is a significant step towards excelling in your CBSE Class 12 Maths Half Yearly Exam 2025. Consistent practice and a clear understanding of the concepts behind these questions will not only prepare you for the exam but also build a strong foundation for future mathematical challenges. Keep reviewing, stay confident, and you'll be well on your way to achieving outstanding results!

Also Check: 

• Class 12 Maths Case-Based Questions with Solutions
• CBSE Class 12 Maths Half Yearly Sample Paper 2025