Assertion-Reason MCQs Class 12 Maths
Assertion–Reason MCQs Class 12 Mathematics
Class: CBSE Class 12
Subject: Mathematics
Section: Exam‑Focused Practice
Topic: Assertion–Reason MCQs
Board: CBSE Board Examinations (NCERT Based)
Subject: Mathematics
Section: Exam‑Focused Practice
Topic: Assertion–Reason MCQs
Board: CBSE Board Examinations (NCERT Based)
Q1. Assertion (A): The function f(x)=x³ is strictly increasing on R.
Reason (R): f′(x)=3x² ≥ 0 for all x ∈ R.
Reason (R): f′(x)=3x² ≥ 0 for all x ∈ R.
Answer: A
Since derivative is non‑negative and zero only at x=0, function is strictly increasing. Hence R explains A.
Since derivative is non‑negative and zero only at x=0, function is strictly increasing. Hence R explains A.
Q2. Assertion (A): If lim f(x) exists at a point, function is continuous there.
Reason (R): Continuity requires limit equals function value.
Reason (R): Continuity requires limit equals function value.
Answer: D
Limit may exist but if not equal to f(a), continuity fails.
Limit may exist but if not equal to f(a), continuity fails.
Q3. Assertion (A): Determinant of identity matrix is 1.
Reason (R): Product of diagonal elements equals determinant.
Reason (R): Product of diagonal elements equals determinant.
Answer: A
Identity matrix determinant equals product of diagonal 1s.
Identity matrix determinant equals product of diagonal 1s.
Q4. A: If vectors are collinear, cross product is zero.
R: Parallel vectors have zero sine angle.
R: Parallel vectors have zero sine angle.
Answer: A
Cross product magnitude ∝ sinθ; θ=0 ⇒ 0.
Cross product magnitude ∝ sinθ; θ=0 ⇒ 0.
Q5. A: Integration is inverse of differentiation.
R: d/dx ∫f(x)dx = f(x).
R: d/dx ∫f(x)dx = f(x).
Answer: A
Fundamental theorem confirms.
Fundamental theorem confirms.
Q6. A: If derivative zero ⇒ function constant.
R: Slope zero everywhere.
R: Slope zero everywhere.
Answer: A
Constant slope zero ⇒ constant function.
Constant slope zero ⇒ constant function.
Q7. A: |A|=0 ⇒ matrix singular.
R: Inverse exists only if determinant non‑zero.
R: Inverse exists only if determinant non‑zero.
Answer: A
Zero determinant ⇒ no inverse.
Zero determinant ⇒ no inverse.
Q8. A: Probability lies between 0 and 1.
R: It is ratio of favorable to total outcomes.
R: It is ratio of favorable to total outcomes.
Answer: A
Q9. A: dy/dx of constant is 0.
R: Constant has no change.
R: Constant has no change.
Answer: A
Q10. A: Tangent slope = derivative.
R: Derivative defined as limit of slope.
R: Derivative defined as limit of slope.
Answer: A
Q11. A: e^x derivative is e^x.
R: Exponential base e unique.
R: Exponential base e unique.
Answer: A
Q12. A: ln1=0.
R: e^0=1.
R: e^0=1.
Answer: A
Q13. A: sin²x+cos²x=1.
R: Pythagorean identity.
R: Pythagorean identity.
Answer: A
Q14. A: Area under curve via integration.
R: Integration sums infinitesimals.
R: Integration sums infinitesimals.
Answer: A
Q15. A: Vector magnitude always positive.
R: Length cannot be negative.
R: Length cannot be negative.
Answer: A
Q16. A: Dot product scalar.
R: Depends on cosine angle.
R: Depends on cosine angle.
Answer: A
Q17. A: Independent events ⇒ P(A∩B)=P(A)P(B).
R: Occurrence unaffected.
R: Occurrence unaffected.
Answer: A
Q18. A: Differentiable ⇒ continuous.
R: Derivative limit exists.
R: Derivative limit exists.
Answer: A
Q19. A: Continuous not always differentiable.
R: Sharp corners exist.
R: Sharp corners exist.
Answer: A
Q20. A: Rank ≤ order.
R: Max independent rows limited.
R: Max independent rows limited.
Answer: A
Q21. A: Determinant changes sign on row swap.
R: Orientation reverses.
R: Orientation reverses.
Answer: A
Q22. A: ∫0 dx = C.
R: Integral of zero constant.
R: Integral of zero constant.
Answer: A
Q23. A: Normal slope = −1/m.
R: Perpendicular slopes product −1.
R: Perpendicular slopes product −1.
Answer: A
Q24. A: Max/min where derivative zero.
R: Stationary points.
R: Stationary points.
Answer: A
Q25. A: Second derivative test confirms extrema.
R: Concavity check.
R: Concavity check.
Answer: A
Q26. A: Mean value theorem needs continuity.
R: Applies on closed interval.
R: Applies on closed interval.
Answer: A
Q27. A: Rolle’s theorem special MVT.
R: End values equal.
R: End values equal.
Answer: A
Q28. A: |λI−A| gives characteristic equation.
R: Eigenvalues roots.
R: Eigenvalues roots.
Answer: A
Q29. A: Unit vector magnitude 1.
R: Direction only.
R: Direction only.
Answer: A
Q30. A: Direction cosines squares sum 1.
R: Unit vector property.
R: Unit vector property.
Answer: A
Q31. A: Conditional probability uses given event.
R: Sample space reduced.
R: Sample space reduced.
Answer: A
Q32. A: Bayes theorem updates probability.
R: Uses prior knowledge.
R: Uses prior knowledge.
Answer: A
Q33. A: ∫1/x dx = ln|x|.
R: Standard integral.
R: Standard integral.
Answer: A
Q34. A: Improper integral infinite limit.
R: Bound tends infinity.
R: Bound tends infinity.
Answer: A
Q35. A: Differential equation relates derivatives.
R: Contains unknown function.
R: Contains unknown function.
Answer: A
Q36. A: Order highest derivative.
R: Degree power of highest derivative.
R: Degree power of highest derivative.
Answer: A
Q37. A: Homogeneous DE separable.
R: Ratio y/x form.
R: Ratio y/x form.
Answer: A
Q38. A: Linear programming optimizes function.
R: Constraints linear.
R: Constraints linear.
Answer: A
Q39. A: Feasible region convex.
R: Intersection half‑planes.
R: Intersection half‑planes.
Answer: A
Q40. A: Optimum at corner points.
R: Linear objective.
R: Linear objective.
Answer: A
Q41. A: Matrix multiplication non‑commutative.
R: AB ≠ BA generally.
R: AB ≠ BA generally.
Answer: A
Q42. A: Zero vector dot any vector =0.
R: Magnitude zero.
R: Magnitude zero.
Answer: A
Q43. A: Angle acute if dot product positive.
R: cosθ positive.
R: cosθ positive.
Answer: A
Q44. A: Cross product vector.
R: Perpendicular direction.
R: Perpendicular direction.
Answer: A
Q45. A: Skew lines non‑coplanar.
R: Never intersect.
R: Never intersect.
Answer: A
Q46. A: Distance point‑plane uses normal form.
R: Projection length.
R: Projection length.
Answer: A
Q47. A: Direction ratios proportional cosines.
R: Same direction.
R: Same direction.
Answer: A
Q48. A: Scalar triple product volume.
R: Parallelepiped volume.
R: Parallelepiped volume.
Answer: A
Q49. A: If vectors coplanar ⇒ triple product 0.
R: Volume zero.
R: Volume zero.
Answer: A
Q50. A: Derivative gives rate of change.
R: Defined via limits.
R: Defined via limits.
Answer: A
Fundamental definition of derivative.
Fundamental definition of derivative.