Class 12 Mathematics and Statistics Part 1 – Daily Revision MCQ (English Medium)
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When is the biconditional statement p ↔ q TRUE?
Chapter 1: Mathematical Logic
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Answer: B. When p and q have the same truth value
p ↔ q is true when p and q are both true or both false, i.e. when they have the same truth value.Which of these is the contrapositive of the implication p → q?
Chapter 1: Mathematical Logic
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Answer: C. ~q → ~p
The contrapositive negates both parts and swaps them: ~q → ~p (q → p is the converse, ~p → ~q the inverse).For which value of k is the 2×2 matrix with rows (k, 2) and (3, 6) singular (so it has no inverse)?
Chapter 2: Matrices
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Answer: D. k = 1
A matrix is singular when its determinant is 0: 6k − 6 = 0 gives k = 1.What is the principal value of cos⁻¹(−1/2)?
Chapter 3: Trigonometric Functions
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Answer: C. 2π/3
The principal value of cos⁻¹ lies in [0, π], and cos(2π/3) = −1/2, so the answer is 2π/3.In ΔABC, a = 4, A = 30° and B = 90°. Using the sine rule, what is b?
Chapter 3: Trigonometric Functions
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Answer: A. 8
Sine rule: a/sin A = b/sin B, so b = 4 × sin 90° / sin 30° = 4 × 1 / (1/2) = 8.The lines represented by ax² + 2hxy + by² = 0 are coincident when:
Chapter 4: Pair of Straight Lines
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Answer: B. h² = ab
If h² − ab = 0, both slopes are equal and the two lines coincide (h² > ab gives distinct lines, a + b = 0 perpendicular lines).For what value of m are the vectors 2î + mĵ + k̂ and î − 2ĵ + 3k̂ perpendicular?
Chapter 5: Vectors
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Answer: A. 5/2
Perpendicular vectors have dot product 0: 2(1) + m(−2) + 1(3) = 5 − 2m = 0, so m = 5/2.A and B have position vectors a and b. What is the position vector of the point dividing AB internally in the ratio 2 : 1?
Chapter 5: Vectors
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Answer: D. (2b + a)/3
Section formula (internal, m : n): r = (mb + na)/(m + n) = (2b + a)/3.The line r = a + λb is parallel to the plane r · n = d if and only if:
Chapter 6: Line and Plane
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Answer: B. b · n = 0
The line is parallel to the plane exactly when its direction b is perpendicular to the normal n, i.e. b · n = 0 (b × n = 0 would make it perpendicular to the plane).The corner points of a feasible region are (0, 4), (2, 2) and (6, 0). What is the minimum value of Z = 2x + 5y?
Chapter 7: Linear Programming
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Answer: C. 12 at (6, 0)
Evaluate Z at each corner: (0, 4) → 20, (2, 2) → 14, (6, 0) → 12, so the minimum is 12 at (6, 0).
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.