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Class 12 Mathematics and Statistics Part 1 – Daily Revision MCQ (English Medium)

📅 28 October 2026 · 10 questions · from the Balbharati textbook

Timed quiz: 15 seconds per question, the next one loads by itself when time runs out. Or solve without the timer: tap an option, right turns green, wrong turns red. 10 new questions every morning at 8.

  1. 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.

  2. 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).

  3. 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.

  4. 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.

  5. 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.

  6. 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).

  7. 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.

  8. 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.

  9. 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).

  10. 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).

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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.