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Day 11: MHT-CET Maths

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

  1. Question 1

    Binomial Distribution. This type asked 9 times: May 2022 S1, 3 May 2023 S2, 11 May 2023 S1, 16 May 2023 S1, 9 May 2024 S1, 9 May 2024 S2, 11 May 2024 S2, 21 Apr 2025 S2, 15 Apr 2026 S1. This one: 15 Apr 2026 S1 See all 9 of this type

    99
    The Variance of the following probability distribution of X is
    X00112233
    P(X)q3q^33q2p3q^2p3qp23qp^2p3p^3
    where 0<p<1,q=1−p0 < p < 1, q = 1 - p

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  2. Question 2

    Vectors. Asked 8 times: 9 May 2023 S2*, 10 May 2023 S1*, 11 May 2024 S1, 22 Apr 2025 S2*, 26 Apr 2025 S1*, 19 Apr 2026 S1*, 19 Apr 2026 S2*, 12 May 2026 S2 (* = numbers or wording changed that year) See all 8 times it was asked

    89
    If a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} are three vectors such that a⃗⋅(b⃗+c⃗)+b⃗⋅(c⃗+a⃗)+c⃗⋅(a⃗+b⃗)=0\vec{a}\cdot(\vec{b} + \vec{c}) + \vec{b}\cdot(\vec{c} + \vec{a}) + \vec{c}\cdot(\vec{a} + \vec{b}) = 0 and ∣a⃗∣=8,∣b⃗∣=1,∣c⃗∣=4|\vec{a}| = 8, |\vec{b}| = 1, |\vec{c}| = 4, then ∣a⃗+b⃗+c⃗∣=…|\vec{a} + \vec{b} + \vec{c}| = \ldots

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  3. Question 3

    Differential Equations. This type asked 8 times: May 2022 S1, 9 May 2024 S1, 10 May 2024 S1, 20 Apr 2025 S2, 25 Apr 2025 S1, 11 Apr 2026 S2, 19 Apr 2026 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 8 of this type

    85
    The differential equation dydx=1−y2y\dfrac{dy}{dx} = \dfrac{\sqrt{1 - y^2}}{y} determines a family of circles with

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  4. Question 4

    Line and Plane. This type asked 8 times: 9 May 2023 S1, 9 May 2024 S1, 12 May 2024 S1, 14 May 2024 S2, 19 Apr 2025 S1, 17 Apr 2026 S2, 12 May 2026 S2, 19 May 2026 S1. This one: 19 May 2026 S1 See all 8 of this type

    96
    The distance of the point (1,1,1)(1, 1, 1) from the line passing through the point (2,3,4)(2, 3, 4) whose direction ratios are 2,−3,62, -3, 6 is:

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  5. Question 5

    Definite Integration. This type asked 8 times: 2 May 2023 S2, 15 May 2023 S2, 20 Apr 2025 S2, 21 Apr 2025 S1, 23 Apr 2025 S1, 25 Apr 2025 S1, 26 Apr 2025 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 8 of this type

    82
    ∫π/53π/1011+tan⁡x dx=⋯\displaystyle\int_{\pi/5}^{3\pi/10}\dfrac{1}{1 + \sqrt{\tan x}}\, dx = \cdots

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