Class 12 Mathematics and Statistics (Commerce) Part 1 – Daily Revision MCQ (English Medium)
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Which statement is the contrapositive of the conditional p → q?
Chapter 1: Mathematical Logic
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Answer: C. ∼q → ∼p
The contrapositive negates both parts and swaps them: ∼q → ∼p, and it is logically equivalent to p → q.How many rows does a truth table need for a compound statement made of 3 simple statements p, q, r?
Chapter 1: Mathematical Logic
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Answer: B. 8
Each statement can be T or F, so the number of rows is 2³ = 8.Matrix A has first row (4, 7) and second row (1, 2). What is adj A?
Chapter 2: Matrices
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Answer: D. first row (2, −7), second row (−1, 4)
For a 2 × 2 matrix, adj A swaps the diagonal elements and changes the signs of the other two: (2, −7; −1, 4).If x² + y² = 25, then dy/dx equals:
Chapter 3: Differentiation
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Answer: A. −x/y
Differentiating implicitly: 2x + 2y(dy/dx) = 0, so dy/dx = −x/y.Using logarithmic differentiation, the derivative of y = xˣ (x > 0) is:
Chapter 3: Differentiation
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Answer: C. xˣ(1 + log x)
log y = x log x, so (1/y)dy/dx = log x + 1, giving dy/dx = xˣ(1 + log x).The total cost of producing x units is C = 100 + 4x + x². What is the marginal cost when x = 5?
Chapter 4: Applications of Derivatives
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Answer: B. 14
Marginal cost = dC/dx = 4 + 2x; at x = 5 it is 4 + 10 = 14.Using integration by parts, ∫ x eˣ dx equals:
Chapter 5: Integration
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Answer: D. eˣ(x − 1) + c
∫ x eˣ dx = x eˣ − ∫ eˣ dx = eˣ(x − 1) + c; differentiating it gives x eˣ back.The value of the definite integral ∫ from 1 to e of (1/x) dx is:
Chapter 6: Definite Integration
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Answer: A. 1
∫(1/x)dx = log x, so the value is log e − log 1 = 1 − 0 = 1.The area bounded by the line y = 2x, the X-axis and the lines x = 0 and x = 4 is:
Chapter 7: Application of Definite Integration
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Answer: B. 16 sq. units
Area = ∫₀⁴ 2x dx = [x²]₀⁴ = 16 sq. units.What is the integrating factor (I.F.) of the linear differential equation dy/dx + (2/x)y = x?
Chapter 8: Differential Equation and Applications
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Answer: C. x²
I.F. = e^∫P dx with P = 2/x, so I.F. = e^(2 log x) = x².
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.