Important Board Exam Objective Questions Maths
Important Board Exam Objective Questions – Class 12 Mathematics
Class: CBSE Class 12
Subject: Mathematics
Section: Exam‑Focused MCQs
Topic: Important Board Exam Objective Questions
Board: CBSE Board Examinations (NCERT Based)
Subject: Mathematics
Section: Exam‑Focused MCQs
Topic: Important Board Exam Objective Questions
Board: CBSE Board Examinations (NCERT Based)
Q1. If f(x)=x³, then f′(x)=?
Answer: A
Using power rule d/dx(xⁿ)=nxⁿ⁻¹.
Using power rule d/dx(xⁿ)=nxⁿ⁻¹.
Q2. Derivative of sin x:
Answer: A
Q3. Maximum occurs where first derivative:
Answer: B
Critical point when slope zero.
Critical point when slope zero.
Q4. ∫x dx equals:
Answer: A
Q5. Increasing function when f′(x):
Answer: A
Q6. ∫e^x dx:
Answer: e^x + C.
Q7. Derivative of ln x:
Answer: 1/x.
Q8. Area under curve uses:
Answer: Integration.
Q9. Second derivative tests:
Answer: Concavity.
Q10. Tangent slope equals:
Answer: Derivative.
Q11. Determinant of identity matrix:
Answer: 1.
Q12. Inverse exists if determinant:
Answer: Non‑zero.
Q13. Singular matrix determinant:
Answer: 0.
Q14. Rank of matrix ≤:
Answer: Order.
Q15. AB ≠ BA shows:
Answer: Non‑commutative.
Q16. Adjoint used for:
Answer: Inverse.
Q17. Cofactor relates to:
Answer: Minor.
Q18. Determinant geometric meaning:
Answer: Area/volume scale.
Q19. Row interchange effect:
Answer: Sign change.
Q20. Triangular determinant:
Answer: Diagonal product.
Q21. Dot product result:
Answer: Scalar.
Q22. Cross product result:
Answer: Vector.
Q23. Parallel vectors cross product:
Answer: Zero.
Q24. Unit vector magnitude:
Answer: 1.
Q25. Direction cosines satisfy:
Answer: l²+m²+n²=1.
Q26. Triple product gives:
Answer: Volume.
Q27. Coplanar vectors triple product:
Answer: 0.
Q28. Distance formula in 3D uses:
Answer: √[(x₂−x₁)²+…].
Q29. Skew lines are:
Answer: Non‑coplanar.
Q30. Perpendicular vectors dot product:
Answer: 0.
Q31. Probability range:
Answer: 0 to 1.
Q32. Sure event probability:
Answer: 1.
Q33. Impossible event probability:
Answer: 0.
Q34. Independent events formula:
Answer: P(A)P(B).
Q35. Conditional probability uses:
Answer: Reduced sample space.
Q36. Feasible region is:
Answer: Convex.
Q37. Optimum solution at:
Answer: Corner points.
Q38. Constraints are:
Answer: Linear.
Q39. Objective function represents:
Answer: Quantity to optimize.
Q40. Unbounded solution means:
Answer: Infinite optimum.
Q41. Order of DE:
Answer: Highest derivative.
Q42. Degree defined when:
Answer: Polynomial in derivatives.
Q43. dy/dx = ky solution:
Answer: Ce^{kx}.
Q44. General solution contains:
Answer: Arbitrary constant.
Q45. Particular solution uses:
Answer: Initial conditions.
Q46. Linear DE form:
Answer: dy/dx + Py = Q.
Q47. Homogeneous DE substitution:
Answer: y=vx.
Q48. Exponential growth constant:
Answer: Positive k.
Q49. Exponential decay constant:
Answer: Negative k.
Q50. Differential equation relates:
Answer: Function & derivatives.