Case Study Based Maths MCQs CBSE
Case Study Based Maths MCQs – CBSE Class 12
Class: CBSE Class 12
Subject: Mathematics
Section: Exam‑Focused MCQs
Topic: Case Study Based Maths MCQs
Board: CBSE Board Examinations (NCERT Based)
Subject: Mathematics
Section: Exam‑Focused MCQs
Topic: Case Study Based Maths MCQs
Board: CBSE Board Examinations (NCERT Based)
Case Study 1: A company’s profit P(x) (in lakhs) is given by P(x)=x³−6x²+9x+15 where x is units produced.
Q1. Profit is maximum at:
Answer: C
Maximum profit occurs where P′(x)=0 and second derivative negative. x=3 satisfies maxima.
Maximum profit occurs where P′(x)=0 and second derivative negative. x=3 satisfies maxima.
Q2. Nature at x=1 is:
Answer: B
Second derivative positive ⇒ minimum.
Second derivative positive ⇒ minimum.
Q3. Marginal profit at x=2 equals:
Answer: B
P′(2)=3(4)−12(2)+9=3.
P′(2)=3(4)−12(2)+9=3.
Q4. Profit increasing where P′(x)>0:
Answer: C
Q5. Maximum profit value:
Answer: C
P(3)=21.
P(3)=21.
Case Study 2: A matrix A = [[2,1],[3,4]] represents production data.
Q6. |A| equals:
Answer: C
|A|=8−3=5? Correction: 2×4−3×1=5 → Correct value 5 (Option A).
|A|=8−3=5? Correction: 2×4−3×1=5 → Correct value 5 (Option A).
Q7. Matrix is invertible because:
Answer: A
Q8. A⁻¹ exists when determinant:
Answer: C
Q9. Order of A:
Answer: B
Q10. Rank of A:
Answer: C
Case Study 3: A bag has 3 red, 2 blue, 5 green balls.
Q11. Total outcomes:
Answer: C
Q12. P(Red):
Answer: A
Q13. P(Blue or Green):
Answer: A
Q14. Independent draws with replacement because:
Answer: B
Q15. P(Green then Red with replacement):
Answer: B
Case Study 4: Area bounded by y=x² and x‑axis from 0 to 2.
Q16. Integral form:
Answer: A
Q17. Area value:
Answer: A
Q18. Integration gives:
Answer: A
Q19. Units of area:
Answer: A
Q20. Curve lies:
Answer: A
Case Study 5: Vector a=(2,3,1), b=(1,0,4)
Q21. a·b:
Answer: 6
Q22. Dot product type:
Answer: Scalar
Q23. Angle nature:
Answer: Acute
Q24. |a|:
Answer: √14
Q25. Projection uses:
Answer: Dot product
Case Study 6: Linear Programming – Maximize Z=3x+2y
Q26–Q30 Corner point principle applies.
Answers: Optimum at vertices due to linear objective & convex feasible region.
Case Study 7: Differential Equation dy/dx = y
Q31–Q35 Solution form:
Answer: y=Ce^x (exponential growth model).
Case Study 8: 3D Geometry Distance Problems
Q36–Q40 Use distance formula.
Concept: √[(x₂−x₁)²+(y₂−y₁)²+(z₂−z₁)²].
Case Study 9: Continuity & Differentiability Graph
Q41–Q45 Corner ⇒ not differentiable.
Concept: Sharp turns break derivative.
Case Study 10: Application of Integrals – Area Between Curves
Q46–Q50 Area = ∫(upper−lower)dx
Concept: Difference of functions gives bounded region area.