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Day 110: MHT-CET Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Definite Integration. Asked 2 times: 9 May 2023 S1*, 15 Apr 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    82
    The value of the integral ∫−π/2π/2(x2cos⁡x1+ex)dx\displaystyle\int_{-\pi/2}^{\pi/2}\left(\dfrac{x^2\cos x}{1 + e^x}\right)dx is equal to (π2A)−B\left(\dfrac{\pi^2}{A}\right) - B. Then (AB)=\left(\dfrac{A}{B}\right) =

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  2. Question 2

    Differentiation. Asked 2 times: 4 May 2023 S1*, 15 Apr 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    73
    Let f(x)=3x3+4ex2f(x) = 3x^3 + 4e^{\frac{x}{2}} and g(x)=f−1(x)g(x) = f^{-1}(x). Then the value of g′(4)g'(4) is equal to...

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  3. Question 3

    Indefinite Integration. Asked 2 times: 13 Apr 2026 S2*, 15 Apr 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    77
    If ∫21+sin⁡x dx=−4cos⁡(ax+b)+c\displaystyle\int\sqrt{2}\sqrt{1 + \sin x}\,dx = -4\cos(ax + b) + c, then the value of a,ba, b respectively are...

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  4. Question 4

    Limits. Asked 2 times: 2 May 2023 S1, 15 Apr 2026 S1 See all 2 times it was asked

    69
    If the function f is continuous at x=1x = 1, where f(x)=1+cos⁡(πx)π(1−x)2f(x) = \dfrac{1 + \cos(\pi x)}{\pi(1 - x)^2}, for x≠1x \neq 1, then the value of f(1)f(1) is....

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  5. Question 5

    Line and Plane. Asked 2 times: 22 Apr 2025 S1, 15 Apr 2026 S1 See all 2 times it was asked

    95
    The equation of the plane containing the lines x−12=y+1λ=z2\dfrac{x - 1}{2} = \dfrac{y + 1}{\lambda} = \dfrac{z}{2} and x+15=y+12=zλ\dfrac{x + 1}{5} = \dfrac{y + 1}{2} = \dfrac{z}{\lambda} is

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