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Day 107: MHT-CET Maths

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

  1. Question 1

    Differentiation. Asked 2 times: 16 Apr 2026 S2*, 17 Apr 2026 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    73
    If f(x)=cot⁡−1(3x−x31−3x2)f(x) = \cot^{-1}\left(\dfrac{3x - x^3}{1 - 3x^2}\right) and g(x)=cos⁡−1(1−x21+x2)g(x) = \cos^{-1}\left(\dfrac{1 - x^2}{1 + x^2}\right), then lim⁡x→af(x)−f(a)g(x)−g(a), (0<a<12)\lim_{x \to a}\dfrac{f(x) - f(a)}{g(x) - g(a)},\ \left(0 < a < \dfrac{1}{2}\right) is

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  2. Question 2

    Indefinite Integration. Asked 2 times: 9 May 2023 S1*, 17 Apr 2026 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    78
    If ∫f(x) dx=g(x)\displaystyle\int f(x)\,dx = g(x) then ∫x3f(x2) dx\displaystyle\int x^3 f(x^2)\,dx is equal to

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  3. Question 3

    Indefinite Integration. Asked 2 times: 11 Apr 2026 S2, 17 Apr 2026 S2 See all 2 times it was asked

    77
    If ∫sin⁡xsin⁡4x dx=αlog⁡∣1+sin⁡x1−sin⁡x∣+βlog⁡∣1+2sin⁡x1−2sin⁡x∣+c\displaystyle\int\dfrac{\sin x}{\sin 4x}\,dx = \alpha\log\left|\dfrac{1 + \sin x}{1 - \sin x}\right| + \beta\log\left|\dfrac{1 + \sqrt{2}\sin x}{1 - \sqrt{2}\sin x}\right| + c, then the value of 32(α+β2)=32(\alpha + \beta^2) =

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  4. Question 4

    Vectors. Asked 2 times: 9 May 2024 S1, 17 Apr 2026 S2 See all 2 times it was asked

    89
    The value of bb such that the scalar product of the vector i^+j^+k^\hat{i} + \hat{j} + \hat{k} with the unit vector parallel to the sum of the vectors 2i^+4j^−5k^2\hat{i} + 4\hat{j} - 5\hat{k} and bi^+2j^+3k^b\hat{i} + 2\hat{j} + 3\hat{k} is one, is...

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  5. Question 5

    Applications of Definite Integral. Asked 2 times: 15 May 2023 S1*, 16 Apr 2026 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    82
    The area of the region enclosed by the lines y=2x,2y=xy = 2x, 2y = x and x=2x = 2 (in sq.units) is...

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