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Day 45: MHT-CET Maths

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

  1. Question 1

    Applications of Derivative. Asked 4 times: 10 May 2023 S2*, 14 May 2024 S2*, 17 Apr 2026 S2*, 20 Apr 2026 S2 (* = numbers or wording changed that year) See all 4 times it was asked

    76
    The line x+y=0x + y = 0 touches the curve y2=ax3+by^2 = ax^3 + b at (1,−1)(1, -1) then values of aa and bb respectively are ...........

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  2. Question 2

    Differentiation. Asked 4 times: 10 May 2023 S2*, 21 Apr 2025 S2*, 13 Apr 2026 S2*, 20 Apr 2026 S2 (* = numbers or wording changed that year) See all 4 times it was asked

    71
    If y=cos⁡2[cot⁡−1(1−x1+x)]y = \cos^2\left[\cot^{-1}\left(\sqrt{\dfrac{1 - x}{1 + x}}\right)\right] then dydx=\dfrac{dy}{dx} = ........

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  3. Question 3

    Vectors. Asked 4 times: 12 May 2024 S1, 12 May 2024 S2, 17 Apr 2026 S1, 19 Apr 2026 S2 See all 4 times it was asked

    88
    Two adjacent sides of a parallelogram ABCD are given by AB‾=2i^+10j^+11k^\overline{AB} = 2\hat{i} + 10\hat{j} + 11\hat{k} and AD‾=−i^+2j^+2k^\overline{AD} = -\hat{i} + 2\hat{j} + 2\hat{k}. The side ADAD is rotated by an acute angle α\alpha in the plane of the parallelogram so that ADAD becomes AD′AD'. If AD′AD' makes a right angle with the side ABAB, then the cosine of the angle α\alpha is...

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  4. Question 4

    Vectors. Asked 4 times: 2 May 2023 S1, 4 May 2023 S1, 10 May 2024 S2, 19 Apr 2026 S1 See all 4 times it was asked

    90
    The value of xx so that the volume of the parallelopiped formed by the vectors i^+xj^+k^\hat{i} + x\hat{j} + \hat{k}, j^+xk^\hat{j} + x\hat{k} and xi^+k^x\hat{i} + \hat{k} is minimum, is

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  5. Question 5

    Vectors. Asked 4 times: May 2022 S1, 10 May 2023 S1, 21 Apr 2025 S1, 18 Apr 2026 S1 See all 4 times it was asked

    88
    If aˉ=i^−k^,bˉ=xi^+j^+(1−x)k^\bar{a} = \hat{i} - \hat{k}, \bar{b} = x\hat{i} + \hat{j} + (1 - x)\hat{k} and cˉ=yi^+xj^+(1+x−y)k^\bar{c} = y\hat{i} + x\hat{j} + (1 + x - y)\hat{k} then [aˉ bˉ cˉ][\bar{a}\ \bar{b}\ \bar{c}] depends on

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