Class 12 Mathematics and Statistics (Commerce) Part 1 – Daily Revision MCQ (English Medium)
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For the conditional statement p → q, which statement is its converse?
Chapter 1: Mathematical Logic
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Answer: C. q → p
The converse is obtained by interchanging the antecedent and the consequent, so the converse of p → q is q → p.Matrix A is of order 2 × 3 and matrix B is of order 3 × 4. What is the order of the product AB?
Chapter 2: Matrices
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Answer: A. 2 × 4
AB is defined because the columns of A (3) equal the rows of B (3); AB has the rows of A and the columns of B, i.e. 2 × 4.Matrix A has first row (2, 1) and second row (5, 3). What is A⁻¹?
Chapter 2: Matrices
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Answer: D. first row (3, −1), second row (−5, 2)
|A| = 2×3 − 1×5 = 1, so A⁻¹ = (1/|A|) adj A = adj A, which has rows (3, −1) and (−5, 2).If y = (2x + 3)⁵, then dy/dx is:
Chapter 3: Differentiation
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Answer: B. 10(2x + 3)⁴
By the chain rule, dy/dx = 5(2x + 3)⁴ × d/dx(2x + 3) = 5(2x + 3)⁴ × 2 = 10(2x + 3)⁴.If x = at² and y = 2at (parametric form), then dy/dx is:
Chapter 3: Differentiation
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Answer: B. 1/t
dy/dt = 2a and dx/dt = 2at, so dy/dx = (dy/dt) ÷ (dx/dt) = 2a/(2at) = 1/t.What is the minimum value of f(x) = x² − 4x + 5?
Chapter 4: Applications of Derivatives
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Answer: A. 1
f′(x) = 2x − 4 = 0 gives x = 2, and f″(x) = 2 > 0, so the minimum is f(2) = 4 − 8 + 5 = 1.The total revenue from selling x units is R = 50x − x². What is the marginal revenue when x = 10?
Chapter 4: Applications of Derivatives
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Answer: C. 30
Marginal revenue = dR/dx = 50 − 2x; at x = 10 it is 50 − 20 = 30.∫ 2x/(x² + 1) dx equals:
Chapter 5: Integration
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Answer: D. log(x² + 1) + c
The numerator 2x is the derivative of the denominator x² + 1, and ∫ f′(x)/f(x) dx = log|f(x)| + c, so the answer is log(x² + 1) + c.Using the property of definite integrals, what is the value of ∫ from −2 to 2 of x³ dx?
Chapter 6: Definite Integration
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Answer: A. 0
x³ is an odd function (f(−x) = −f(x)), so its definite integral from −a to a is 0.What is the general solution of the differential equation dy/dx = y/x?
Chapter 8: Differential Equation and Applications
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Answer: C. y = cx
Separating variables, dy/y = dx/x; integrating, log y = log x + log c, so y = cx.
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.