BSc First Year (Sem 1 & 2) Mathematics – Daily Revision MCQ (English Medium)
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A relation on a set that is reflexive, symmetric and transitive is called:
Chapter 1: Sets, Relations and Equivalence Classes
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Answer: A. an equivalence relation
By definition, a relation having all three properties (reflexive, symmetric, transitive) is an equivalence relation; it splits the set into equivalence classes.What is the remainder when 2¹⁰ is divided by 7?
Chapter 2: Theory of Numbers: Divisibility and Congruences
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Answer: C. 2
2³ = 8 ≡ 1 (mod 7), so 2¹⁰ = (2³)³·2 ≡ 1·2 = 2 (mod 7). Check: 1024 = 7×146 + 2.What is the rank of the matrix [[1, 2], [2, 4]]?
Chapter 3: Matrices
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Answer: B. 1
Its determinant is 1×4 − 2×2 = 0, so rank < 2; it has a non-zero element, so rank = 1 (second row = 2 × first row).If α, β, γ are the roots of x³ − 6x² + 11x − 6 = 0, what is α + β + γ?
Chapter 4: Theory of Equations
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Answer: D. 6
For ax³ + bx² + cx + d = 0, sum of roots = −b/a = −(−6)/1 = 6 (the roots are 1, 2, 3).Using De Moivre's theorem, what is the value of (cos π/6 + i sin π/6)⁶?
Chapter 5: De Moivre's Theorem and Complex Numbers
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Answer: D. −1
(cos θ + i sin θ)ⁿ = cos nθ + i sin nθ, so the value is cos π + i sin π = −1 + 0i = −1.What is the value of lim (x→0) (1 − cos x)/x²?
Chapter 10: Indeterminate Forms and L'Hospital's Rule
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Answer: D. ½
It is 0/0; by L'Hospital's rule: sin x/(2x) → then cos x/2 → 1/2 at x = 0.If u = x³ + y³ + 3x²y, then by Euler's theorem on homogeneous functions, x ∂u/∂x + y ∂u/∂y equals:
Chapter 11: Partial Differentiation
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Answer: C. 3u
Every term has degree 3, so u is homogeneous of degree n = 3 and Euler's theorem gives x uₓ + y u_y = nu = 3u.What is the value of Γ(5)?
Chapter 14: Beta and Gamma Functions
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Answer: A. 24
For a positive integer n, Γ(n) = (n − 1)!, so Γ(5) = 4! = 24.What is the integrating factor of the linear differential equation dy/dx + Py = Q (P, Q functions of x)?
Chapter 16: Differential Equations of First Order
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Answer: B. e^(∫P dx)
Multiplying by I.F. = e^(∫P dx) turns the left side into d/dx (y·e^(∫P dx)), which can then be integrated.If r = xi + yj + zk is the position vector, what is div r (∇·r)?
Chapter 19: Vector Differentiation
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Answer: A. 3
∇·r = ∂x/∂x + ∂y/∂y + ∂z/∂z = 1 + 1 + 1 = 3.
BSc First Year (Sem 1 & 2): MCQ in other subjects
All questions are written by PadhaiNotes in our own words from the common syllabus of Maharashtra universities (NEP). Your own university's syllabus may differ a little.