Class 12 Mathematics and Statistics Part 2 – Daily Revision MCQ (English Medium)
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If x = t³ and y = t², then dy/dx = ?
Chapter 1: Differentiation
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Answer: C. 2/(3t)
dy/dt = 2t and dx/dt = 3t², so dy/dx = (dy/dt)/(dx/dt) = 2t/3t² = 2/(3t).For |x| < 1, the derivative of tan⁻¹(2x/(1 − x²)) with respect to x is:
Chapter 1: Differentiation
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Answer: A. 2/(1 + x²)
Put x = tan θ: the expression becomes tan⁻¹(tan 2θ) = 2θ = 2 tan⁻¹x, whose derivative is 2/(1 + x²).For f(x) = x² + 2x on [0, 4], the value of c given by Lagrange's Mean Value Theorem is:
Chapter 2: Applications of Derivatives
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Answer: B. 2
(f(4) − f(0))/(4 − 0) = (24 − 0)/4 = 6, and f′(c) = 2c + 2 = 6 gives c = 2, which lies in (0, 4).The radius of a circle increases at 2 cm/s. How fast is its area increasing when the radius is 5 cm?
Chapter 2: Applications of Derivatives
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Answer: D. 20π cm²/s
A = πr², so dA/dt = 2πr · dr/dt = 2π × 5 × 2 = 20π cm²/s.∫ dx/(x² + 9) = ?
Chapter 3: Indefinite Integration
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Answer: C. (1/3) tan⁻¹(x/3) + c
Use ∫ dx/(x² + a²) = (1/a) tan⁻¹(x/a) + c with a = 3.∫ from 0 to π/2 of cos²x dx = ?
Chapter 4: Definite Integration
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Answer: B. π/4
cos²x = (1 + cos 2x)/2, so the integral is [x/2 + (sin 2x)/4] from 0 to π/2 = π/4.What is the area enclosed by the ellipse x²/25 + y²/4 = 1?
Chapter 5: Application of Definite Integration
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Answer: A. 10π sq. units
The area of the ellipse x²/a² + y²/b² = 1 is πab; here a = 5 and b = 2, so 10π.What is the integrating factor of the differential equation dy/dx + y/x = x² (x > 0)?
Chapter 6: Differential Equations
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Answer: D. x
For dy/dx + Py = Q, IF = e^(∫P dx); here P = 1/x, so IF = e^(log x) = x.f(x) = kx for 0 ≤ x ≤ 2 (and 0 otherwise) is the p.d.f. of a continuous random variable. What is k?
Chapter 7: Probability Distributions
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Answer: C. 1/2
Total probability is 1: ∫ from 0 to 2 of kx dx = k[x²/2] = 2k = 1, so k = 1/2.A fair coin is tossed 4 times. What is the probability of getting exactly 2 heads?
Chapter 8: Binomial Distribution
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Answer: B. 3/8
X ~ B(4, ½): P(X = 2) = ⁴C₂ × (½)⁴ = 6/16 = 3/8.
Class 12: MCQ in other subjects
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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.