Class 12 Mathematics and Statistics Part 2 – Daily Revision MCQ (English Medium)

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

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1. If y = sin(x²), then dy/dx = ?

   Chapter 1: Differentiation

   • Acos(x²)
   • B2x sin(x²)
   • C2x cos(x²)
   • D2 cos x
   Show answer

   Answer: C. 2x cos(x²)
   By the chain rule (derivative of a composite function): d/dx sin(x²) = cos(x²) · 2x.

2. What is the derivative of y = cot⁻¹x with respect to x?

   Chapter 1: Differentiation

   • A−1/(1 + x²)
   • B−cosec² x
   • Cx/(1 + x²)
   • D1/(x√(x² − 1))
   Show answer

   Answer: A. −1/(1 + x²)
   Put x = cot y: dx/dy = −cosec²y = −(1 + x²), so dy/dx = −1/(1 + x²). (−cosec²x is the derivative of cot x, not cot⁻¹x.)

3. What is the slope of the tangent to the curve y = x² at the point (2, 4)?

   Chapter 2: Applications of Derivatives

   • A2
   • B8
   • C1/4
   • D4
   Show answer

   Answer: D. 4
   Slope of tangent = dy/dx at the point = 2x = 2 × 2 = 4.

4. The function f(x) = x³ − 3x has a local minimum at:

   Chapter 2: Applications of Derivatives

   • Ax = 0
   • Bx = 1
   • Cx = 3
   • Dx = 2
   Show answer

   Answer: B. x = 1
   f′(x) = 3x² − 3 = 0 gives x = ±1; f″(x) = 6x, f″(1) = 6 > 0, so x = 1 is a minimum (x = −1 is a maximum).

5. ∫ eˣ (sin x + cos x) dx = ?

   Chapter 3: Indefinite Integration

   • Aeˣ cos x + c
   • Beˣ tan x + c
   • Ceˣ sin x + c
   • Deˣ (sin x − cos x) + c
   Show answer

   Answer: C. eˣ sin x + c
   It is of the form ∫ eˣ[f(x) + f′(x)] dx = eˣ f(x) + c with f(x) = sin x, f′(x) = cos x.

6. ∫ from −1 to 1 of x³ dx = ?

   Chapter 4: Definite Integration

   • A0
   • B1/2
   • C2
   • D1/4
   Show answer

   Answer: A. 0
   x³ is an odd function (f(−x) = −f(x)), and the definite integral of an odd function from −a to a is 0.

7. What is the area bounded by the curve y = x², the X-axis and the lines x = 0 and x = 3?

   Chapter 5: Application of Definite Integration

   • A27 sq. units
   • B9 sq. units
   • C3 sq. units
   • D6 sq. units
   Show answer

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

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

   Chapter 6: Differential Equations

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

   Answer: D. Order 2, degree 3
   Highest derivative is d²y/dx² (order 2), and its power is 3 (degree 3).

9. A random variable X takes values 1, 2, 3, 4 with probabilities k, 2k, 3k, 4k. What is k?

   Chapter 7: Probability Distributions

   • A1/10
   • B1/4
   • C1/5
   • D1/8
   Show answer

   Answer: A. 1/10
   The probabilities of a p.m.f. add up to 1: k + 2k + 3k + 4k = 10k = 1, so k = 1/10.

10. If X ~ B(n = 20, p = 0.25), what is Var(X)?

    Chapter 8: Binomial Distribution

    • A5
    • B15
    • C3.75
    • D1.875
    Show answer

    Answer: C. 3.75
    Var(X) = npq = 20 × 0.25 × 0.75 = 3.75 (mean np = 5 is a different quantity).

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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.