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Day 14: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. This type asked 8 times: 19 Apr 2025 S1, 20 Apr 2025 S2, 13 Apr 2026 S1, 17 Apr 2026 S1, 18 Apr 2026 S1, 19 Apr 2026 S1, 19 Apr 2026 S2, 12 May 2026 S2. This one: 12 May 2026 S2 See all 8 of this type

    55
    In △ABC\triangle ABC, if l(AB)=8,l(BC)=5,l(AC)=7l(AB) = 8, l(BC) = 5, l(AC) = 7, then cot⁡A2+cot⁡B2+cot⁡C2\cot\dfrac{A}{2} + \cot\dfrac{B}{2} + \cot\dfrac{C}{2} is equal to......

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  2. Question 2

    Line and Plane. This type asked 8 times: 10 May 2023 S2, 9 May 2024 S2, 12 May 2024 S2, 21 Apr 2025 S1, 13 Apr 2026 S1, 19 Apr 2026 S1, 19 Apr 2026 S2, 20 Apr 2026 S1. This one: 20 Apr 2026 S1 See all 8 of this type

    94
    The shortest distance between the lines x−33=y−8−1=z−31\dfrac{x - 3}{3} = \dfrac{y - 8}{-1} = \dfrac{z - 3}{1} and x+3−3=y+72=z−64\dfrac{x + 3}{-3} = \dfrac{y + 7}{2} = \dfrac{z - 6}{4} is

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  3. Question 3

    Differentiation. This type asked 8 times: 2 May 2023 S2, 4 May 2023 S2, 11 May 2023 S1, 10 May 2024 S1, 12 May 2024 S2, 22 Apr 2025 S1, 16 Apr 2026 S2, 19 Apr 2026 S2. This one: 19 Apr 2026 S2 See all 8 of this type

    72
    If y=sin⁡−1(25−x225+x2)y = \sin^{-1}\left(\dfrac{25 - x^2}{25 + x^2}\right), then y′(1)y'(1) is...

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  4. Question 4

    Vectors. This type asked 8 times: 2 May 2023 S1, 4 May 2023 S1, 9 May 2024 S1, 10 May 2024 S2, 14 May 2024 S2, 11 Apr 2026 S2, 19 Apr 2026 S1, 19 Apr 2026 S2. This one: 19 Apr 2026 S2 See all 8 of this type

    89
    The maximum volume of a parallelopiped (in cubic units) with vectors (2ai^+k^),(aj^−ak^)(2a\hat{i} + \hat{k}), (a\hat{j} - a\hat{k}), and (3i^+aj^)(3\hat{i} + a\hat{j}), where a∈[0,1]a \in [0, 1], as its coterminous edges is...

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  5. Question 5

    Differentiation. This type asked 8 times: 3 May 2023 S2, 16 May 2023 S2, 10 May 2024 S2, 23 Apr 2025 S1, 25 Apr 2025 S1, 13 Apr 2026 S2, 18 Apr 2026 S1, 18 Apr 2026 S2. This one: 18 Apr 2026 S2 See all 8 of this type

    65
    For x>0x > 0 and (xlog⁡x)<1(x\log x) < 1, if y=cot⁡−1(x−log⁡xx2log⁡ex2+log⁡xx)y = \cot^{-1}\left(\dfrac{x - \log x^{x^2}}{\log e^{x^2} + \log x^x}\right), then dydx=…\dfrac{dy}{dx} = \ldots

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