Class 12 Mathematics and Statistics Part 1 – Daily Revision MCQ (English Medium)
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For two statements p and q, when is the conditional p → q FALSE?
Chapter 1: Mathematical Logic
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Answer: C. When p is true and q is false
A conditional is false only in the single case where the hypothesis p is true and the conclusion q is false.The statement pattern p ∨ ~p is a:
Chapter 1: Mathematical Logic
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Answer: A. Tautology
Whether p is T or F, one of p and ~p is true, so p ∨ ~p is true in every row of its truth table: a tautology.If A is the 2×2 matrix with rows (2, 1) and (5, 3), then A⁻¹ is the matrix with rows:
Chapter 2: Matrices
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Answer: D. (3, −1) and (−5, 2)
|A| = 6 − 5 = 1 and adj A has rows (3, −1), (−5, 2); A⁻¹ = (1/|A|)·adj A = adj A.What is the principal value of tan⁻¹(−1)?
Chapter 3: Trigonometric Functions
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Answer: B. −π/4
The principal value of tan⁻¹ lies in (−π/2, π/2), and tan(−π/4) = −1; 3π/4 and 7π/4 also give −1 but lie outside this range (tan 5π/4 = 1).What is the general solution of sin θ = sin α (n ∈ Z)?
Chapter 3: Trigonometric Functions
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Answer: C. θ = nπ + (−1)ⁿα
Theorem: sin θ = sin α gives θ = α, π − α, 2π + α, 3π − α, …, i.e. θ = nπ + (−1)ⁿα.The pair of lines ax² + 2hxy + by² = 0 is perpendicular if and only if:
Chapter 4: Pair of Straight Lines
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Answer: A. a + b = 0
Slopes satisfy m₁m₂ = a/b; perpendicular means m₁m₂ = −1, so a = −b, i.e. a + b = 0 (h² = ab is the condition for parallel/coincident lines).If a = î + 2ĵ + 3k̂ and b = 2î − ĵ + k̂, what is a · b?
Chapter 5: Vectors
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Answer: B. 3
a · b = (1)(2) + (2)(−1) + (3)(1) = 2 − 2 + 3 = 3.Four points A, B, C, D are coplanar if and only if:
Chapter 5: Vectors
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Answer: D. AB · (AC × AD) = 0
Points are coplanar exactly when the scalar triple product of AB, AC, AD is zero (the parallelepiped on them has zero volume).What is the perpendicular distance of the origin from the plane x + 2y + 2z = 12?
Chapter 6: Line and Plane
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Answer: A. 4
Distance = |−12| / √(1² + 2² + 2²) = 12/3 = 4.A feasible region has corner points (0, 0), (5, 0), (3, 4) and (0, 6). What is the maximum value of Z = 3x + 2y?
Chapter 7: Linear Programming
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Answer: C. 17 at (3, 4)
Z at the corners: 0, 15, 9 + 8 = 17, 12. The largest is 17, at (3, 4); an optimum of an LPP occurs at a corner point.
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.