PYQ Vault

Day 541: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. Asked once: 16 May 2023 S2

    102
    If tan⁡−114+tan⁡−129=12cos⁡−1x\tan^{-1}\frac{1}{4} + \tan^{-1}\frac{2}{9} = \frac{1}{2}\cos^{-1} x, then xx is

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  2. Question 2

    Vectors. Asked once: 15 May 2023 S1

    150
    Let u⃗=i^+j^,v⃗=i^−j^\vec{u}=\hat{i}+\hat{j}, \vec{v}=\hat{i}-\hat{j} and w⃗=i^+2j^+3k^\vec{w}=\hat{i}+2\hat{j}+3\hat{k}. If n^\hat{n} is a unit vector such that u⃗⋅n^=0\vec{u}\cdot\hat{n}=0 and v⃗⋅n^=0\vec{v}\cdot\hat{n}=0, then ∣w⃗⋅n^∣|\vec{w}\cdot\hat{n}| is equal to

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  3. Question 3

    Indefinite Integration. Asked once: 11 May 2024 S1

    138
    ∫ex(1+x)cos⁡2(ex⋅x) dx=\int \frac{e^x(1+x)}{\cos^2(e^x \cdot x)}\,dx =

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  4. Question 4

    Line and Plane. Asked once: May 2021 S1

    134
    What will be the equation of the plane passing through a point (1,4,−2)(1,4,-2) and parallel to the given plane −2x+y−3z=9-2x + y - 3z = 9?

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  5. Question 5

    Trigonometric Functions. Asked once: 15 May 2023 S1

    121
    The equation esin⁡x−e−sin⁡x=4e^{\sin x}-e^{-\sin x}=4 has

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