Class 12 Mathematics and Statistics Part 1 – Daily Revision MCQ (English Medium)
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What is the negation of the statement “∀ x ∈ N, x + 3 > 2”?
Chapter 1: Mathematical Logic
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Answer: B. ∃ x ∈ N such that x + 3 ≤ 2
Negation changes ∀ into ∃ and negates the condition: the negation of x + 3 > 2 is x + 3 ≤ 2.What is the dual of the statement pattern p ∧ (q ∨ c)? (t = tautology, c = contradiction)
Chapter 1: Mathematical Logic
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Answer: D. p ∨ (q ∧ t)
To write the dual, interchange ∧ with ∨ and c with t; the statements p and q stay as they are.If A is the 2×2 matrix with rows (1, 2) and (3, 4), then adj A is the matrix with rows:
Chapter 2: Matrices
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Answer: A. (4, −2) and (−3, 1)
Cofactors are A11 = 4, A12 = −3, A21 = −2, A22 = 1; adj A is the transpose of the cofactor matrix: rows (4, −2) and (−3, 1).What are the principal solutions of cos θ = 1/2? (0 ≤ θ < 2π)
Chapter 3: Trigonometric Functions
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Answer: C. π/3 and 5π/3
cos θ is positive in the first and fourth quadrants: θ = π/3 and θ = 2π − π/3 = 5π/3.In ΔABC, a = 3, b = 5 and c = 7. What is the measure of angle C?
Chapter 3: Trigonometric Functions
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Answer: D. 120°
Cosine rule: cos C = (a² + b² − c²)/2ab = (9 + 25 − 49)/30 = −1/2, so C = 120°.What is the sum of the slopes of the lines represented by x² − 5xy + 6y² = 0?
Chapter 4: Pair of Straight Lines
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Answer: A. 5/6
Sum of slopes = −2h/b with 2h = −5 and b = 6, so 5/6 (the lines are y = x/2 and y = x/3).What is the area of the parallelogram whose adjacent sides are a = î + ĵ and b = ĵ + k̂?
Chapter 5: Vectors
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Answer: C. √3 sq. units
Area = |a × b|; here a × b = î − ĵ + k̂, whose magnitude is √(1 + 1 + 1) = √3.Which point lies on the line (x − 1)/2 = (y + 2)/3 = (z − 3)/4?
Chapter 6: Line and Plane
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Answer: B. (3, 1, 7)
Put each ratio equal to 1: x = 1 + 2 = 3, y = −2 + 3 = 1, z = 3 + 4 = 7, giving (3, 1, 7).What is the Cartesian equation of the plane through (1, 1, 1) with normal vector 2î + 3ĵ − k̂?
Chapter 6: Line and Plane
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Answer: D. 2x + 3y − z = 4
The plane is 2x + 3y − z = d; putting (1, 1, 1) gives d = 2 + 3 − 1 = 4.In a linear programming problem, a feasible solution that maximizes or minimizes the objective function as required is called:
Chapter 7: Linear Programming
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Answer: B. An optimal feasible solution
The book defines an optimal (optimum) feasible solution as the feasible solution that optimizes the objective function.
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.