PYQ Vault

Day 291: MHT-CET Maths

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

  1. Question 1

    Probability Distribution. Asked once: 20 Apr 2025 S1 (same type asked 5 times) See all 5 of this type

    120
    A random variable XX has the following probability distribution
    XX01234
    P(X)P(X)kk2k2k4k4k2k2kkk
    then the value of P(1⩽X<4∣X⩽2)=P(1 \leqslant X< 4 \mid X\leqslant 2) =

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  2. Question 2

    Trigonometric Functions. Asked once: 16 May 2023 S1 (same type asked 5 times) See all 5 of this type

    109
    The general solution of the equation 3cos⁡θ+sin⁡θ=2\sqrt{3}\cos\theta + \sin\theta = \sqrt{2} is

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  3. Question 3

    Indefinite Integration. Asked once: 11 Apr 2026 S1 (same type asked 5 times) See all 5 of this type

    78
    ∫x+2x2−7x+12 dx\displaystyle\int\dfrac{x + 2}{x^2 - 7x + 12}\,dx is equal to

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  4. Question 4

    Line and Plane. Asked once: 15 Apr 2026 S1 (same type asked 5 times) See all 5 of this type

    92
    If the lines x−55m+2=2−y5=1−z−1\dfrac{x - 5}{5m + 2} = \dfrac{2 - y}{5} = \dfrac{1 - z}{-1} and x=2y+14m=1−z−3x = \dfrac{2y + 1}{4m} = \dfrac{1 - z}{-3} are perpendicular to each other, then the value of m is ...

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  5. Question 5

    Trigonometric Functions. Asked once: 26 Apr 2025 S1 (same type asked 5 times) See all 5 of this type

    120
    In a triangle ABC , with usual notations, cot⁡(A+B2)⋅tan⁡(A−B2)=\cot\left( \frac{A + B}{2} \right)\cdot \tan\left( \frac{A - B}{2} \right)=

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