Competency-Based Questions Class 12 Maths
Competency‑Based Questions – Class 12 Mathematics
Class: CBSE Class 12
Subject: Mathematics
Section: Exam‑Focused MCQs
Topic: Competency‑Based Questions
Board: CBSE Board Examinations (NCERT Based)
Subject: Mathematics
Section: Exam‑Focused MCQs
Topic: Competency‑Based Questions
Board: CBSE Board Examinations (NCERT Based)
Q1. If f(x)=x²−4x+3 represents cost, minimum cost occurs at:
Answer: B
Vertex of parabola at x=−b/2a=2 gives minimum cost.
Vertex of parabola at x=−b/2a=2 gives minimum cost.
Q2. Rate of change of volume of sphere w.r.t radius depends on:
Answer: A
dV/dr=4πr² ⇒ proportional to r².
dV/dr=4πr² ⇒ proportional to r².
Q3. If determinant =0, system of equations is:
Answer: B
Zero determinant ⇒ no unique solution.
Zero determinant ⇒ no unique solution.
Q4. Probability of sure event:
Answer: B
Q5. Angle between perpendicular vectors:
Answer: C
Q6. Increasing function when derivative:
Answer: A
Q7. Tangent slope equals:
Answer: Derivative at that point.
Q8. Maximum occurs where first derivative:
Answer: Zero & second derivative negative.
Q9. Area under curve found by:
Answer: Integration.
Q10. Marginal cost means:
Answer: Derivative of cost function.
Q11. If f′(x)=0 ∀x ⇒ function:
Answer: Constant.
Q12. Concave up when second derivative:
Answer: Positive.
Q13. Inflection point when concavity:
Answer: Changes sign.
Q14. ∫f′(x)dx equals:
Answer: f(x)+C.
Q15. Optimization problems use:
Answer: Derivatives.
Q16. Identity matrix determinant:
Answer: 1.
Q17. Inverse exists if determinant:
Answer: Non‑zero.
Q18. Rank equals number of:
Answer: Independent rows/columns.
Q19. AB ≠ BA shows:
Answer: Non‑commutativity.
Q20. Singular matrix determinant:
Answer: Zero.
Q21. Cofactor used in:
Answer: Inverse calculation.
Q22. Adjoint transpose of:
Answer: Cofactor matrix.
Q23. Determinant measures:
Answer: Area/volume scaling.
Q24. Row swap effect:
Answer: Sign change.
Q25. Upper triangular determinant:
Answer: Product of diagonal.
Q26. Dot product gives:
Answer: Scalar.
Q27. Cross product gives:
Answer: Vector.
Q28. Parallel vectors cross product:
Answer: Zero.
Q29. Unit vector magnitude:
Answer: 1.
Q30. Direction cosines relation:
Answer: l²+m²+n²=1.
Q31. Distance point‑plane uses:
Answer: Projection formula.
Q32. Coplanar vectors triple product:
Answer: Zero.
Q33. Volume via triple product:
Answer: Parallelepiped volume.
Q34. Acute angle if dot product:
Answer: Positive.
Q35. Skew lines are:
Answer: Non‑coplanar.
Q36. Conditional probability depends on:
Answer: Given event.
Q37. Independent events product rule:
Answer: P(A)P(B).
Q38. Bayes theorem updates:
Answer: Prior probability.
Q39. Feasible region is:
Answer: Convex.
Q40. Optimum solution lies at:
Answer: Corner points.
Q41. Constraints in LPP are:
Answer: Linear inequalities.
Q42. Objective function represents:
Answer: Quantity to optimize.
Q43. Infeasible region means:
Answer: No solution.
Q44. Redundant constraint:
Answer: Does not affect region.
Q45. Unbounded solution:
Answer: Infinite optimum.
Q46. Order of DE defined by:
Answer: Highest derivative.
Q47. Degree defined when equation:
Answer: Polynomial in derivatives.
Q48. dy/dx = ky models:
Answer: Exponential growth/decay.
Q49. General solution contains:
Answer: Arbitrary constant.
Q50. Particular solution found using:
Answer: Initial conditions.