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Day 114: MHT-CET Maths

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

  1. Question 1

    Differentiation. Asked 2 times: May 2021 S1, 11 Apr 2026 S2 See all 2 times it was asked

    70
    The derivative of tan⁡−1(1+x2−1x)\tan^{-1}\left(\dfrac{\sqrt{1 + x^2} - 1}{x}\right) with respect to sin⁡−1(2x1+x2)\sin^{-1}\left(\dfrac{2x}{1 + x^2}\right) is...

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  2. Question 2

    Differentiation. Asked 2 times: 25 Apr 2025 S2*, 11 Apr 2026 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    73
    If x=sin⁡(t),y=cos⁡(pt)x = \sin(t), y = \cos(pt), then (1−x2)d2ydx2−xdydx=(1 - x^2)\dfrac{d^2y}{dx^2} - x\dfrac{dy}{dx} =

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  3. Question 3

    Mathematical Logic. Asked 2 times: 11 Apr 2026 S1*, 11 Apr 2026 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    62
    If A={1,2,3,4,5,6}A = \{1, 2, 3, 4, 5, 6\} then which of the following is not true?

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  4. Question 4

    Vectors. Asked 2 times: 15 May 2023 S2, 11 Apr 2026 S2 See all 2 times it was asked

    87
    If aˉ=i^+j^+k^,bˉ=i^−j^+2k^\bar{a} = \hat{i} + \hat{j} + \hat{k}, \bar{b} = \hat{i} - \hat{j} + 2\hat{k} and cˉ=xi^+(x−2)j^−k^\bar{c} = x\hat{i} + (x - 2)\hat{j} - \hat{k} are three vectors in which cˉ\bar{c} lies in the plane of aˉ\bar{a} and bˉ\bar{b}, then x=⋯x = \cdots

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  5. Question 5

    Line and Plane. Asked 2 times: 4 May 2023 S2*, 11 Apr 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    93
    If the points (1,1,μ)(1, 1, \mu) and (−3,0,1)(-3, 0, 1) are equidistant from the plane r⃗⋅(3i^+4j^−12k^)+13=0\vec{r}\cdot(3\hat{i} + 4\hat{j} - 12\hat{k}) + 13 = 0, then the value of μ\mu are

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