BSc Second Year (Sem 3 & 4) Mathematics – Daily Revision MCQ (English Medium)
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What is the supremum of the set S = {1 − 1/n : n ∈ ℕ}?
Chapter 1: Real Numbers: Bounded Sets and Completeness
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Answer: C. 1
The terms 0, ½, ⅔, ¾, … increase towards 1 and never exceed it, so sup S = 1 (it is not attained).The p-series Σ 1/nᵖ (n = 1 to ∞) is convergent when:
Chapter 3: Infinite Series
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Answer: A. p > 1
By the p-series test Σ 1/nᵖ converges for p > 1 and diverges for p ≤ 1 (p = 1 is the harmonic series).What is the order of the symmetric group S₄?
Chapter 5: Permutation Groups
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Answer: D. 24
Sₙ has n! elements, so |S₄| = 4! = 24.Which of the following is a field?
Chapter 8: Rings and Fields
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Answer: C. ℤ₇
ℤₙ is a field exactly when n is prime; 7 is prime. ℤ has no inverse for 2, and ℤ₆, ℤ₈ have zero divisors.The general solution of y'' − 5y' + 6y = 0 is:
Chapter 10: Linear Differential Equations with Constant Coefficients
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Answer: B. y = c₁e^(2x) + c₂e^(3x)
Auxiliary equation m² − 5m + 6 = 0 gives m = 2, 3 (real, distinct), so y = c₁e^(2x) + c₂e^(3x).The Laplace transform of t² is:
Chapter 15: Laplace Transform
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Answer: C. 2/s³
L{tⁿ} = n!/sⁿ⁺¹, so L{t²} = 2!/s³ = 2/s³ (s > 0).The inverse Laplace transform of 1/(s² + 9) is:
Chapter 16: Inverse Laplace Transform and Applications
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Answer: D. (1/3) sin 3t
L{sin at} = a/(s² + a²); with a = 3, 1/(s² + 9) = (1/3)·3/(s² + 9) ↔ (1/3) sin 3t.The Fourier series of an odd function f(x) on (−π, π) contains:
Chapter 17: Fourier Series
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Answer: B. Only sine terms
For an odd function a₀ = aₙ = 0 (odd × even integrates to zero), so only the bₙ sin nx terms remain.Using the Newton–Raphson method for f(x) = x² − 2 with x₀ = 1, the next approximation x₁ is:
Chapter 20: Numerical Methods
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Answer: B. 1.5
x₁ = x₀ − f(x₀)/f'(x₀) = 1 − (1 − 2)/(2×1) = 1 + 0.5 = 1.5.The Legendre polynomial P₂(x) is:
Chapter 14: Legendre and Bessel Functions
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Answer: C. (3x² − 1)/2
P₀ = 1, P₁ = x, P₂ = (3x² − 1)/2, P₃ = (5x³ − 3x)/2.
BSc Second Year (Sem 3 & 4): 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.