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Day 82: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. This type asked 3 times: 20 Apr 2025 S2, 25 Apr 2025 S2, 14 May 2026 S2. This one: 14 May 2026 S2 See all 3 of this type

    82
    ∫x3sin⁡(tan⁡−1(x4))1+x8 dx=\displaystyle\int\dfrac{x^3\sin(\tan^{-1}(x^4))}{1 + x^8}\,dx =

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  2. Question 2

    Indefinite Integration. This type asked 3 times: May 2022 S1, 11 May 2023 S1, 14 May 2026 S2. This one: 14 May 2026 S2 See all 3 of this type

    79
    The value of the integral ∫dxx4+x3\displaystyle\int\dfrac{dx}{x^4 + x^3} is

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  3. Question 3

    Limits. This type asked 3 times: 9 May 2023 S1, 18 Apr 2026 S1, 14 May 2026 S2. This one: 14 May 2026 S2 See all 3 of this type

    63
    If lim⁡x→∞[x3+1x2+1−(ax+b)]=2\displaystyle\lim_{x \to \infty}\left[\dfrac{x^3 + 1}{x^2 + 1} - (ax + b)\right] = 2 then

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  4. Question 4

    Straight Line. This type asked 3 times: 12 May 2026 S1, 13 May 2026 S2, 14 May 2026 S2. This one: 14 May 2026 S2 See all 3 of this type

    58
    If the polar coordinates of the point P are (1,7π4)\left(1, \dfrac{7\pi}{4}\right), then the sum of the squares of abscissa and ordinate of Cartesian coordinates of point P is

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  5. Question 5

    Trigonometry - II. This type asked 3 times: 11 Apr 2026 S2, 18 Apr 2026 S1, 14 May 2026 S2. This one: 14 May 2026 S2 See all 3 of this type

    52
    In ΔABC\Delta ABC, ∠C=2π3\angle C = \dfrac{2\pi}{3}, then the value of cos⁡2A+cos⁡2B−cos⁡Acos⁡B\cos^2 A + \cos^2 B - \cos A \cos B is

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