Class 12 Mathematics and Statistics (Commerce) Part 1 – Daily Revision MCQ (English Medium)

📅 26 October 2026 · 10 questions · from the Balbharati textbook

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1. The conditional statement p → q is FALSE in which case?

   Chapter 1: Mathematical Logic

   • Ap is true and q is true
   • Bp is false and q is true
   • Cp is true and q is false
   • Dp is false and q is false
   Show answer

   Answer: C. p is true and q is false
   An implication fails only when the 'if' part is true and the 'then' part is false; in every other row of the truth table it is true.

2. By De Morgan's law, the negation ∼(p ∧ q) is logically equivalent to:

   Chapter 1: Mathematical Logic

   • A∼p ∧ ∼q (not p AND not q)
   • B∼p ∨ ∼q (not p OR not q)
   • Cp ∨ q (p OR q)
   • D∼p ∨ q (not p OR q)
   Show answer

   Answer: B. ∼p ∨ ∼q (not p OR not q)
   Negating a conjunction turns ∧ into ∨ and negates each part: ∼(p ∧ q) ≡ ∼p ∨ ∼q.

3. Matrix A has first row (k, 4) and second row (2, 2). For which value of k is A a singular matrix?

   Chapter 2: Matrices

   • Ak = 2
   • Bk = 8
   • Ck = 6
   • Dk = 4
   Show answer

   Answer: D. k = 4
   A is singular when |A| = 0: |A| = 2k − 8 = 0, so k = 4.

4. If y = e³ˣ, then the second order derivative d²y/dx² is:

   Chapter 3: Differentiation

   • A9e³ˣ
   • B3e³ˣ
   • C6e³ˣ
   • De³ˣ
   Show answer

   Answer: A. 9e³ˣ
   dy/dx = 3e³ˣ, and differentiating again gives d²y/dx² = 3 × 3e³ˣ = 9e³ˣ.

5. If the elasticity of demand η is greater than 1, the demand is said to be:

   Chapter 4: Applications of Derivatives

   • Arelatively elastic
   • Brelatively inelastic
   • Cperfectly inelastic
   • Dunitary elastic
   Show answer

   Answer: A. relatively elastic
   The book's cases: η = 0 perfectly inelastic, 0 < η < 1 relatively inelastic, η = 1 unitary elastic, η > 1 relatively elastic.

6. For a person, the marginal propensity to consume (MPC) is 0.65. What is the marginal propensity to save (MPS)?

   Chapter 4: Applications of Derivatives

   • A0.65
   • B0.35
   • C1.65
   • D0.5
   Show answer

   Answer: B. 0.35
   Income is either consumed or saved, so MPC + MPS = 1; MPS = 1 − 0.65 = 0.35.

7. The indefinite integral ∫ (1/x) dx (x ≠ 0) equals:

   Chapter 5: Integration

   • Aeˣ + c
   • Blog |x| + c
   • C−1/x² + c
   • D1/(2x²) + c
   Show answer

   Answer: B. log |x| + c
   Since d/dx (log |x|) = 1/x, the integral of 1/x is log |x| + c.

8. The value of the definite integral ∫₀² (2x + 1) dx is:

   Chapter 6: Definite Integration

   • A4
   • B5
   • C6
   • D8
   Show answer

   Answer: C. 6
   An antiderivative is x² + x; so the value is (4 + 2) − (0 + 0) = 6.

9. The area bounded by the curve y = x², the X-axis and the lines x = 0 and x = 3 is:

   Chapter 7: Application of Definite Integration

   • A27 sq. units
   • B3 sq. units
   • C18 sq. units
   • D9 sq. units
   Show answer

   Answer: D. 9 sq. units
   Area = ∫₀³ x² dx = [x³/3]₀³ = 27/3 = 9 square units.

10. What are the order and degree of the differential equation (d²y/dx²)³ + (dy/dx)⁴ + y = 0?

    Chapter 8: Differential Equation and Applications

    • AOrder 2, degree 3
    • BOrder 3, degree 2
    • COrder 2, degree 4
    • DOrder 4, degree 2
    Show answer

    Answer: A. Order 2, degree 3
    The highest order derivative is d²y/dx² (order 2) and its power is 3 (degree 3); the power 4 belongs to a lower derivative.

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All questions are written by PadhaiNotes in our own words from the chapters of the official Maharashtra State Board Balbharati textbook (ebalbharati.in). Each question shows its chapter.