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Differentiation

MHT-CET Maths. Try each one first, then open its answer.

Top 10 MHT-CET PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 10 times: May 2021 S1, 10 May 2023 S2, 15 May 2023 S2, 11 May 2024 S1, 22 Apr 2025 S2, 11 Apr 2026 S2, 16 Apr 2026 S2, 17 Apr 2026 S2, 18 Apr 2026 S1, 14 May 2026 S2. This one: 14 May 2026 S2 See all 10 of this type

    67
    If u=tan⁡−1(1+x2−1x)u = \tan^{-1}\left(\dfrac{\sqrt{1 + x^2} - 1}{x}\right) and v=tan⁡−1(2x1−x21−2x2)v = \tan^{-1}\left(\dfrac{2x\sqrt{1 - x^2}}{1 - 2x^2}\right) then dudv=…\dfrac{du}{dv} = \ldots

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  2. Question 2

    This type asked 10 times: May 2022 S1, 2 May 2023 S2, 3 May 2023 S1, 10 May 2023 S2, 16 May 2023 S1, 21 Apr 2025 S2, 13 Apr 2026 S2, 19 Apr 2026 S1, 20 Apr 2026 S2, 13 May 2026 S2. This one: 13 May 2026 S2 See all 10 of this type

    73
    If y=sin⁡(2sin⁡−1x)y = \sin(2\sin^{-1}x), then dydx=\dfrac{dy}{dx} = ______

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  3. Question 3

    This type asked 9 times: 11 May 2023 S2, 20 Apr 2025 S1, 20 Apr 2025 S2, 22 Apr 2025 S2, 20 Apr 2026 S1, 13 May 2026 S2, 14 May 2026 S1, 14 May 2026 S2, 15 May 2026 S1. This one: 15 May 2026 S1 See all 9 of this type

    75
    If y=(log⁡x)log⁡xy = (\log x)^{\log x} and dydx=yx×f(x)\dfrac{dy}{dx} = \dfrac{y}{x} \times f(x) then f(x)=…f(x) = \ldots

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  4. Question 4

    This type asked 9 times: 10 May 2023 S1, 10 May 2023 S2, 15 May 2023 S1, 9 May 2024 S2, 10 May 2024 S2, 12 May 2024 S1, 13 May 2024 S2, 18 Apr 2026 S1, 19 Apr 2026 S2. This one: 19 Apr 2026 S2 See all 9 of this type

    74
    If 3y2−2xy−x=03y^2 - 2xy - x = 0, then the value of dydx\dfrac{dy}{dx} at y=2y = 2 is...

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  5. Question 5

    This type asked 9 times: 15 May 2023 S2, 16 May 2023 S1, 16 May 2023 S2, 9 May 2024 S1, 10 May 2024 S2, 20 Apr 2025 S1, 22 Apr 2025 S2, 13 Apr 2026 S1, 18 Apr 2026 S1. This one: 18 Apr 2026 S1 See all 9 of this type

    75
    If g(x)=(x2+2x+1)⋅f(x)g(x) = (x^2 + 2x + 1)\cdot f(x) such that f(0)=5f(0) = 5 and lim⁡x→0f(x)−5x=4\lim_{x \to 0}\dfrac{f(x) - 5}{x} = 4 then g′(0)=g'(0) =

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  6. Question 6

    This type asked 9 times: 3 May 2023 S2, 4 May 2023 S1, 11 May 2023 S1, 15 May 2023 S1, 11 May 2024 S2, 12 May 2024 S1, 13 May 2024 S2, 14 May 2024 S1, 17 Apr 2026 S1. This one: 17 Apr 2026 S1 See all 9 of this type

    72
    If y=[(x+1)(2x+1)(3x+1)……(nx+1)]4y = [(x + 1)(2x + 1)(3x + 1)\ldots\ldots(nx + 1)]^4, where n∈Nn \in N and dydx\dfrac{dy}{dx} at x=0x = 0 is 2k2k, then the value of kk is

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  7. Question 7

    This type asked 8 times: 15 May 2023 S1, 15 May 2023 S2, 14 May 2024 S2, 21 Apr 2025 S1, 19 Apr 2026 S1, 20 Apr 2026 S2, 12 May 2026 S1, 12 May 2026 S2. This one: 12 May 2026 S2 See all 8 of this type

    71
    The second derivative of asin⁡3ta\sin^3 t with respect to acos⁡3ta\cos^3 t at t=π4t = \dfrac{\pi}{4} is...

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  8. Question 8

    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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  9. Question 9

    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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  10. Question 10

    This type asked 7 times: 2 May 2023 S2, 13 May 2024 S2, 22 Apr 2025 S1, 23 Apr 2025 S1, 13 May 2026 S1, 14 May 2026 S1, 14 May 2026 S2. This one: 14 May 2026 S2 See all 7 of this type

    73
    If x=1+log⁡tt2x = \dfrac{1 + \log t}{t^2} and y=3+2log⁡tty = \dfrac{3 + 2\log t}{t}, then the value of dydx\dfrac{dy}{dx} is

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