Chapter-Wise MCQs for Class 12 Mathematics Board Exam

Chapter‑Wise MCQs for Class 12 Mathematics Board Exam

Class: CBSE Class 12 Mathematics
Section: Exam‑Focused MCQs
Topic: Chapter‑Wise MCQs for Board Examination
Exam Focus: CBSE Board Examinations

These Multiple Choice Questions (MCQs) are designed strictly as per the NCERT syllabus, making them ideal for CBSE Class 12 Board Examination practice with concept‑clearing explanations.

Q1. If f(x)=x³, then f’(x) equals:

A) x² B) 3x² C) 3x D) x³

Answer: B
Derivative of xⁿ is nxⁿ⁻¹ ⇒ 3x².

Q2. ∫ dx/x equals:

A) x B) 1/x C) ln|x| D) eˣ

Answer: C
Standard integral formula.

Q3. Determinant of identity matrix is:

A) 0 B) 1 C) −1 D) 2

Answer: B
Product of diagonal ones.

Q4. If A⁻¹ exists, det(A) ≠

A) 1 B) 0 C) −1 D) 2

Answer: B
Inverse exists only if determinant non‑zero.

Q5. Order of matrix with 3 rows, 2 columns:

A) 2×3 B) 3×2 C) 3×3 D) 2×2

Answer: B
Rows × Columns.

Q6. Solution of sinx=0 in [0,π]:

A) 0 B) π C) Both D) None

Answer: C
sin0=0, sinπ=0.

Q7. If vectors are parallel, cross product is:

A) 1 B) 0 C) −1 D) ∞

Answer: B
Magnitude = |a||b|sinθ, θ=0.

Q8. Direction cosines satisfy:

A) l+m+n=1 B) l²+m²+n²=1 C) 0 D) ∞

Answer: B
Property of direction cosines.

Q9. Probability lies between:

A) −1 to 1 B) 0 to 1 C) 0 to ∞ D) −∞ to ∞

Answer: B
Fundamental probability axiom.

Q10. Mean of binomial distribution:

A) np B) pq C) n+p D) npq

Answer: A
Expected successes.

Q11. Variance of binomial distribution:

A) np B) npq C) pq D) n²

Answer: B
Spread measure.

Q12. dy/dx of eˣ:

A) eˣ B) xeˣ C) 1 D) ln x

Answer: A
Self‑derivative.

Q13. ∫ eˣ dx:

A) eˣ B) eˣ+C C) ln x D) 0

Answer: B

Q14. If slope=0, tangent is:

A) Vertical B) Horizontal C) Inclined D) None

Answer: B

Q15. Distance between parallel lines is constant because:

A) Same slope B) Same intercept C) Same constant difference D) None

Answer: C

Q16. If vectors perpendicular, dot product:

A) 1 B) 0 C) −1 D) ∞

Answer: B

Q17. Equation of plane involves:

A) 1 variable B) 2 C) 3 D) 4

Answer: C

Q18. If A and B independent:

A) P(A∩B)=0 B) P(A)P(B) C) P(A+B) D) 1

Answer: B

Q19. Conditional probability formula:

A) P(A/B) B) P(A∩B)/P(B) C) P(A)+P(B) D) None

Answer: B

Q20. Random variable takes:

A) Values B) Probabilities C) Constants D) None

Answer: A

Q21. Maximum value of sinx:

A) 0 B) 1 C) −1 D) 2

Answer: B

Q22. Determinant changes sign if rows:

A) Multiplied B) Interchanged C) Added D) None

Answer: B

Q23. Rank of identity matrix:

A) 0 B) 1 C) n D) −1

Answer: C

Q24. If f’(x)>0, function is:

A) Decreasing B) Increasing C) Constant D) None

Answer: B

Q25. Local maxima occurs when:

A) f’=0,f’’<0 B) f’=0,f’’>0 C) f’≠0 D) None

Answer: A

Q26. ∫ cosx dx:

A) sinx B) −sinx C) tanx D) secx

Answer: A

Q27. Vector magnitude formula:

A) √(x²+y²+z²) B) x+y+z C) xyz D) None

Answer: A

Q28. Unit vector magnitude:

A) 0 B) 1 C) 2 D) ∞

Answer: B

Q29. P(Sample space)=

A) 0 B) 1 C) n D) −1

Answer: B

Q30. Complement probability:

A) P(A) B) 1−P(A) C) 0 D) 2

Answer: B

Q31. Binomial trials are:

A) Dependent B) Independent C) Constant D) None

Answer: B

Q32. Mean of probability distribution called:

A) Expectation B) Mode C) Median D) Range

Answer: A

Q33. SD = √(variance):

A) True B) False

Answer: A

Q34. Equation of line needs:

A) Point & slope B) Only slope C) Only point D) None

Answer: A

Q35. Angle between perpendicular lines:

A) 0° B) 45° C) 90° D) 180°

Answer: C

Q36. ∫0 dx =

A) 0 B) 1 C) x D) C

Answer: D

Q37. Scalar product gives:

A) Vector B) Scalar C) Matrix D) None

Answer: B

Q38. Cross product gives:

A) Scalar B) Vector C) Number D) None

Answer: B

Q39. Matrix multiplication possible when:

A) Rows equal B) Columns equal C) Inner equal D) Outer equal

Answer: C

Q40. Inverse method solves:

A) Integration B) Linear equations C) Probability D) Vectors

Answer: B

Q41. Adjoint of A used for:

A) Determinant B) Inverse C) Rank D) Trace

Answer: B

Q42. If det=0 system is:

A) Unique B) Infinite/Inconsistent C) Constant D) None

Answer: B

Q43. Random experiment result:

A) Fixed B) Uncertain C) Constant D) Zero

Answer: B

Q44. Sample space is:

A) Event set B) All outcomes C) Probability D) None

Answer: B

Q45. Sure event probability:

A) 0 B) 1 C) ½ D) 2

Answer: B

Q46. Impossible event probability:

A) 0 B) 1 C) −1 D) ∞

Answer: A

Q47. Continuous function has:

A) Break B) No break C) Jump D) None

Answer: B

Q48. Differentiability implies:

A) Continuity B) Discontinuity C) Zero D) None

Answer: A

Q49. Area under curve found by:

A) Differentiation B) Integration C) Matrix D) Vector

Answer: B

Q50. Differential equation contains:

A) Matrix B) Derivatives C) Probability D) Vector

Answer: B

Chapter-Wise MCQs for Class 12 Mathematics Board Exam

Chapter‑Wise MCQs for Class 12 Mathematics Board Exam

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