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Applications of Derivative

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 9 times: 2 May 2023 S1, 13 May 2024 S2, 25 Apr 2025 S1, 25 Apr 2025 S2, 11 Apr 2026 S2, 15 Apr 2026 S1, 18 Apr 2026 S2, 12 May 2026 S2, 14 May 2026 S2. This one: 14 May 2026 S2 See all 9 of this type

    78
    If Rolle's theorem holds for the function f(x)=x2−px+10f(x) = x^2 - px + 10, x∈[0,4]x \in [0, 4] with c=2c = 2, then p=p =

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  2. Question 2

    This type asked 9 times: 2 May 2023 S2, 9 May 2023 S1, 10 May 2023 S2, 9 May 2024 S1, 10 May 2024 S2, 13 May 2024 S2, 19 Apr 2025 S1, 21 Apr 2025 S2, 14 May 2026 S1. This one: 14 May 2026 S1 See all 9 of this type

    77
    In the Lagrange's Mean Value Theorem, f(b)−f(a)=(b−a)f′(c);(a<c<b)f(b) - f(a) = (b - a)f'(c); (a < c < b). If a=2,b=4a = 2, b = 4 and f(x)=x2−4f(x) = \sqrt{x^2 - 4}, then the value of cc is

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  3. Question 3

    This type asked 8 times: 3 May 2023 S2, 15 May 2023 S2, 11 May 2024 S1, 21 Apr 2025 S1, 13 Apr 2026 S2, 19 Apr 2026 S1, 20 Apr 2026 S2, 14 May 2026 S1. This one: 14 May 2026 S1 See all 8 of this type

    75
    The value of cc for which the function f(x)=log⁡(x2+65x)f(x) = \log\left(\dfrac{x^2 + 6}{5x}\right) satisfies Rolle's theorem in the interval [2,3][2, 3] is ____

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  4. Question 4

    This type asked 8 times: 10 May 2023 S2, 10 May 2024 S2, 13 Apr 2026 S1, 15 Apr 2026 S2, 16 Apr 2026 S2, 19 Apr 2026 S2, 13 May 2026 S1, 13 May 2026 S2. This one: 13 May 2026 S2 See all 8 of this type

    78
    The radius of a spherical balloon increases at the rate of 44 cm/sec. The rate at which its surface area increases, when the radius is 55 metres is

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  5. Question 5

    This type asked 6 times: 2 May 2023 S2, 3 May 2023 S1, 9 May 2023 S2, 11 May 2023 S1, 16 Apr 2026 S2, 18 Apr 2026 S1. This one: 18 Apr 2026 S1 See all 6 of this type

    76
    If the line x+By+C=0x + By + C = 0 is the normal to the curve given by x=asin⁡3t,y=bcos⁡3tx = a\sin^3 t, y = b\cos^3 t, (where a,b≠0a, b \neq 0) at a point t=π2t = \dfrac{\pi}{2}, then B−C=B - C =

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  6. Question 6

    This type asked 6 times: 2 May 2023 S2, 9 May 2023 S2, 11 May 2023 S1, 22 Apr 2025 S1, 11 Apr 2026 S1, 15 Apr 2026 S2. This one: 15 Apr 2026 S2 See all 6 of this type

    55
    The approximate value of (0.007)13(0.007)^{\frac{1}{3}} is

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  7. Question 7

    This type asked 6 times: 3 May 2023 S2, 11 May 2023 S2, 16 May 2023 S1, 16 May 2023 S2, 12 May 2024 S1, 26 Apr 2025 S1. This one: 26 Apr 2025 S1 See all 6 of this type

    136
    If y=αlog⁡x+βx3−xy=\alpha \log x+\beta x^{3}-x has extreme values at x=−1x= - 1 and x=1x= 1, then α\alpha and β\beta are respectively

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  8. Question 8

    This type asked 6 times: 4 May 2023 S2, 15 May 2023 S1, 10 May 2024 S1, 11 May 2024 S2, 12 May 2024 S1, 12 May 2024 S2. This one: 12 May 2024 S2 See all 6 of this type

    137
    A ladder, 5 meters long, rests against a vertical wall. If its top slides downwards at the rate of 10 cm/s, then the angle between the ladder and the floor is decreasing at the rate of ___ radians/second when its lower end is 4 m away from the wall.

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  9. Question 9

    Asked 5 times: 3 May 2023 S2*, 11 May 2023 S2*, 16 May 2023 S1*, 16 May 2023 S2*, 12 May 2024 S1 (* = numbers or wording changed that year) See all 5 times it was asked

    121
    If x=−1x=-1 and x=2x=2 are extreme points of f(x)=αlog⁡∣x∣+βx2+xf(x)=\alpha\log|x|+\beta x^{2}+x, α\alpha and β\beta are constants, then the value of α2+2β\alpha^{2}+2\beta is

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  10. Question 10

    This type asked 5 times: 10 May 2023 S2, 14 May 2024 S2, 17 Apr 2026 S2, 20 Apr 2026 S2, 19 May 2026 S2. This one: 19 May 2026 S2 See all 5 of this type

    75
    If the slope of the tangent to the curve 2y2=ax2+b2y^2 = ax^2 + b at (1,−1)(1, -1) is −1-1, then ...

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