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Day 1: MHT-CET Maths

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

  1. Question 1

    Mathematical Logic. This type asked 19 times: 3 in 2023, 4 in 2024, 2 in 2025, 10 in 2026. This one: 19 May 2026 S2 See all 19 of this type

    59
    The statement pattern [p∧(q∨r)]∨[∼r∧∼q∧p][p \wedge (q \vee r)] \vee [\sim r \wedge \sim q \wedge p] is equivalent to _____

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  2. Question 2

    Differential Equations. This type asked 15 times: May 2021 S1, 3 May 2023 S2, 4 May 2023 S2, 10 May 2023 S2, 15 May 2023 S2, 10 May 2024 S1, 11 May 2024 S1, 12 May 2024 S2, 14 May 2024 S1, 21 Apr 2025 S1, 21 Apr 2025 S2, 26 Apr 2025 S1, 15 Apr 2026 S1, 15 Apr 2026 S2, 19 May 2026 S1. This one: 19 May 2026 S1 See all 15 of this type

    89
    The solution of the differential equation dydx=xy+yxy+x\dfrac{dy}{dx} = \dfrac{xy + y}{xy + x} is

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  3. Question 3

    Vectors. This type asked 15 times: May 2022 S1, 2 May 2023 S2, 3 May 2023 S1, 9 May 2023 S2, 15 May 2023 S1, 10 May 2024 S1, 10 May 2024 S2, 12 May 2024 S2, 20 Apr 2025 S1, 22 Apr 2025 S1, 23 Apr 2025 S1, 15 Apr 2026 S2, 18 Apr 2026 S1, 12 May 2026 S1, 15 May 2026 S2. This one: 15 May 2026 S2 See all 15 of this type

    90
    Let aˉ=2i^−j^+k^\bar{a} = 2\hat{i} - \hat{j} + \hat{k} and bˉ=i^+2j^−2k^\bar{b} = \hat{i} + 2\hat{j} - 2\hat{k}. If a third vector cˉ=xi^+yj^+zk^\bar{c} = x\hat{i} + y\hat{j} + z\hat{k} is coplanar with aˉ\bar{a} and bˉ\bar{b}, is perpendicular to aˉ\bar{a}, and satisfies ∣cˉ∣=45|\bar{c}| = \sqrt{45}, then the sum of all possible values of yy is:

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  4. Question 4

    Binomial Distribution. This type asked 14 times: May 2022 S1, 3 May 2023 S1, 4 May 2023 S2, 16 May 2023 S2, 12 May 2024 S1, 14 May 2024 S1, 14 May 2024 S2, 21 Apr 2025 S2, 22 Apr 2025 S1, 13 Apr 2026 S1, 16 Apr 2026 S2, 17 Apr 2026 S2, 15 May 2026 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 14 of this type

    98
    If XX follows a Binomial distribution with parameters n=8n = 8 and p=12p = \dfrac{1}{2} then P(∣X−4∣≤2)P(|X - 4| \le 2)

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  5. Question 5

    Trigonometric Functions. This type asked 14 times: 4 May 2023 S2, 9 May 2023 S2, 15 May 2023 S1, 11 May 2024 S1, 11 May 2024 S2, 14 May 2024 S2, 21 Apr 2025 S1, 11 Apr 2026 S1, 16 Apr 2026 S1, 17 Apr 2026 S1, 19 Apr 2026 S2, 12 May 2026 S2, 14 May 2026 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 14 of this type

    63
    If tan⁡−1(13)+tan⁡−1(15)+tan⁡−1(17)=π4−tan⁡−1(1k)\tan^{-1}\left(\dfrac{1}{3}\right) + \tan^{-1}\left(\dfrac{1}{5}\right) + \tan^{-1}\left(\dfrac{1}{7}\right) = \dfrac{\pi}{4} - \tan^{-1}\left(\dfrac{1}{k}\right) then the value of kk is

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