PYQ Vault

Day 164: MHT-CET Maths

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

  1. Question 1

    Definite Integration. This type asked 2 times: 10 May 2024 S2, 22 Apr 2025 S1. This one: 22 Apr 2025 S1 See all 2 of this type

    128
    ∫π32π3x1+sin⁡x dx=\int_{\frac{\pi}{3}}^{\frac{2\pi}{3}} \frac{x}{1 + \sin x}\text{ }dx=

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  2. Question 2

    Sequences and Series. This type asked 2 times: 9 May 2024 S2, 21 Apr 2025 S2. This one: 21 Apr 2025 S2 See all 2 of this type

    110
    If log⁡3x16+9log⁡273x3=5\sqrt{\log_{3}x^{16}}+ 9\log_{27}\sqrt[3]{\frac{3}{x}}= 5, then x=…x= \ldots.

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  3. Question 3

    Applications of Derivative. This type asked 2 times: 2 May 2023 S1, 21 Apr 2025 S1. This one: 21 Apr 2025 S1 See all 2 of this type

    108
    The maximum value and minimum value of the volume of the parallelepiped having coterminous edges i^+xj^+k^,j^+xk^\widehat{i}+x\widehat{j}+\widehat{k},\widehat{j}+x\widehat{k} and xi^+k^x\widehat{i}+\widehat{k} are respectively

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  4. Question 4

    Complex Numbers. This type asked 2 times: 13 May 2024 S2, 21 Apr 2025 S1. This one: 21 Apr 2025 S1 See all 2 of this type

    136
    The complex numbers sin⁡x+icos2x\sin x+icos2x and cos⁡x−isin2x,(i=−1)\cos x- isin2x,(i =\sqrt{- 1}) are conjugate to each other for,

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  5. Question 5

    Probability Distribution. This type asked 2 times: 9 May 2023 S1, 21 Apr 2025 S1. This one: 21 Apr 2025 S1 See all 2 of this type

    109
    The following is the probability distribution of X
    XX0123
    P(X=x)P(X = x)1+p5\frac{1 + p}{5}2−2p5\frac{2 - 2p}{5}2−p5\frac{2 - p}{5}2p5\frac{2p}{5}
    For a minimum value of pp, the value of 5E(X)5E(X) is

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