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Day 34: MHT-CET Maths

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

  1. Question 1

    Probability Distribution. This type asked 5 times: 3 May 2023 S1, 19 Apr 2025 S1, 20 Apr 2025 S1, 25 Apr 2025 S1, 15 May 2026 S2. This one: 15 May 2026 S2 See all 5 of this type

    99
    The probability distribution of a discrete random variable (r.v.) XX is given below:
    X=xX = x0011223344
    P(X=x)P(X = x)kk2k2k4k4k2k2kkk
    Then the value of P[X≤E(X)]P[X \le E(X)] is:

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  2. Question 2

    Trigonometric Functions. This type asked 5 times: 11 May 2023 S2, 16 May 2023 S1, 13 Apr 2026 S2, 19 Apr 2026 S1, 15 May 2026 S2. This one: 15 May 2026 S2 See all 5 of this type

    53
    If x∈(0,2π)x \in (0, 2\pi) satisfies the equation cos⁡x+sin⁡x=12\cos x + \sin x = \frac{1}{2}, then the sum of all distinct values of tan⁡x\tan x is...

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  3. Question 3

    Indefinite Integration. This type asked 5 times: 19 Apr 2025 S2, 11 Apr 2026 S1, 11 Apr 2026 S2, 17 Apr 2026 S2, 15 May 2026 S1. This one: 15 May 2026 S1 See all 5 of this type

    78
    ∫2x4−3x−x2 dx=…\int \dfrac{2x}{4 - 3x - x^2}\, dx = \ldots

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  4. Question 4

    Line and Plane. This type asked 5 times: 12 May 2024 S1, 25 Apr 2025 S1, 15 Apr 2026 S1, 16 Apr 2026 S2, 15 May 2026 S1. This one: 15 May 2026 S1 See all 5 of this type

    93
    If the lines 1−x3=3y−12λ+1=4−z\dfrac{1 - x}{3} = \dfrac{3y - 1}{2\lambda + 1} = 4 - z and x+22μ=1−2y6=5−z7\dfrac{x + 2}{2\mu} = \dfrac{1 - 2y}{6} = \dfrac{5 - z}{7} are perpendicular, then 3μ+λ=…3\mu + \lambda = \ldots

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  5. Question 5

    Trigonometric Functions. This type asked 5 times: 9 May 2024 S1, 22 Apr 2025 S1, 26 Apr 2025 S1, 16 Apr 2026 S1, 15 May 2026 S1. This one: 15 May 2026 S1 See all 5 of this type

    53
    In △ABC\triangle ABC, if b=3+1b = \sqrt{3} + 1, c=3−1c = \sqrt{3} - 1 and A=π3A = \dfrac{\pi}{3}, then B−C=…B - C = \ldots

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