BSc First Year (Sem 1 & 2) Mathematics – Daily Revision MCQ (English Medium)
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. New sets are added regularly.
Or scroll down and solve without the timer.
For every real x, cosh²x − sinh²x equals:
Chapter 6: Hyperbolic Functions and Logarithm of Complex Numbers
Show answer
Answer: B. 1
With cosh x = (eˣ + e⁻ˣ)/2 and sinh x = (eˣ − e⁻ˣ)/2, the difference of squares is (4eˣe⁻ˣ)/4 = 1.The nth derivative of y = e^(3x) is:
Chapter 7: Successive Differentiation
Show answer
Answer: D. 3ⁿe^(3x)
Each differentiation of e^(3x) brings down a factor 3, so after n steps yₙ = 3ⁿe^(3x).For f(x) = x² − 4x + 3 on [1, 3], the value of c given by Rolle's theorem is:
Chapter 8: Mean Value Theorems
Show answer
Answer: C. 2
f(1) = f(3) = 0 and f′(c) = 2c − 4 = 0 gives c = 2, which lies in (1, 3).The coefficient of x³ in the Maclaurin series of sin x is:
Chapter 9: Taylor's and Maclaurin's Series
Show answer
Answer: B. −1/6
sin x = x − x³/3! + x⁵/5! − …, so the x³ coefficient is −1/3! = −1/6.At a stationary point of f(x, y), with r = fxx, s = fxy, t = fyy, if rt − s² > 0 and r < 0, the point is a:
Chapter 12: Maxima and Minima of Two Variables and Lagrange's Multipliers
Show answer
Answer: A. maximum
rt − s² > 0 means an extremum; r < 0 makes it a maximum (r > 0 would give a minimum).Using the reduction formula, the value of ∫₀^(π/2) sin⁴x dx is:
Chapter 13: Reduction Formulae
Show answer
Answer: C. 3π/16
∫₀^(π/2) sin⁴x dx = (3/4)(1/2)(π/2) = 3π/16.The value of the double integral ∫₀¹ ∫₀² (x + y) dy dx is:
Chapter 15: Double and Triple Integrals
Show answer
Answer: D. 3
Inner integral: [xy + y²/2] from 0 to 2 = 2x + 2; then ∫₀¹ (2x + 2) dx = 1 + 2 = 3.The general solution of Clairaut's equation y = px + p², where p = dy/dx, is:
Chapter 17: First Order Higher Degree Equations and Clairaut's Form
Show answer
Answer: A. y = cx + c²
For Clairaut's form y = px + f(p), the general solution is obtained by replacing p with a constant c: y = cx + c².If a = 2i, b = 3j and c = i + j + 4k, the scalar triple product [a b c] equals:
Chapter 18: Scalar and Vector Triple Products
Show answer
Answer: B. 24
b × c = 12i − 3k, so a · (b × c) = 2 × 12 = 24 (the determinant of the components also gives 24).Which theorem equates the surface integral of F · n over a closed surface S to the volume integral of div F over the region enclosed by S?
Chapter 20: Vector Integration
Show answer
Answer: C. Gauss divergence theorem
Gauss's divergence theorem: ∬ F · n dS over a closed surface = ∭ div F dV over the enclosed volume.
BSc First Year (Sem 1 & 2): MCQ in other subjects
Previous days
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.