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Day 5: MHT-CET Maths

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

  1. Question 1

    Binomial Distribution. This type asked 10 times: May 2021 S1, 11 May 2023 S1, 22 Apr 2025 S2, 25 Apr 2025 S1, 25 Apr 2025 S2, 26 Apr 2025 S1, 15 Apr 2026 S1, 20 Apr 2026 S2, 13 May 2026 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 10 of this type

    98
    It is known that 10%10\% of certain articles manufactured are defective. What is the probability that in a random sample of 1212 such articles, 99 are defective?

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  2. Question 2

    Differential Equations. This type asked 10 times: May 2022 S1, 2 May 2023 S1, 11 May 2023 S1, 23 Apr 2025 S1, 25 Apr 2025 S2, 13 Apr 2026 S1, 17 Apr 2026 S1, 19 Apr 2026 S1, 13 May 2026 S1, 15 May 2026 S2. This one: 15 May 2026 S2 See all 10 of this type

    86
    If the general solution of the differential equation ysec⁡2(xy)dx−(xsec⁡2(xy)−y)dy=0y\sec^2\left(\dfrac{x}{y}\right)dx - \left(x\sec^2\left(\dfrac{x}{y}\right) - y\right)dy = 0 is tan⁡(xy)+g(y)=c\tan\left(\dfrac{x}{y}\right) + g(y) = c, then g(y)=…g(y) = \ldots

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  3. Question 3

    Limits. This type asked 10 times: 21 Apr 2025 S1, 21 Apr 2025 S2, 23 Apr 2025 S1, 25 Apr 2025 S2, 16 Apr 2026 S2, 18 Apr 2026 S2, 12 May 2026 S1, 14 May 2026 S1, 15 May 2026 S1, 15 May 2026 S2. This one: 15 May 2026 S2 See all 10 of this type

    65
    If k>5k > 5 and lim⁡x→0k2x+25x−2⋅(5k)xtan⁡3x⋅ln⁡(1+3x)=lim⁡n→∞(n+1)!+n!(n+1)!−n!\lim_{x \to 0}\dfrac{k^{2x} + 25^x - 2\cdot(5k)^x}{\tan 3x \cdot \ln(1 + 3x)} = \lim_{n \to \infty}\dfrac{(n + 1)! + n!}{(n + 1)! - n!}, then value of kk is...

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  4. Question 4

    Limits. This type asked 10 times: 4 May 2023 S1, 9 May 2024 S2, 10 May 2024 S2, 12 May 2024 S1, 25 Apr 2025 S1, 16 Apr 2026 S2, 19 Apr 2026 S1, 13 May 2026 S2, 14 May 2026 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 10 of this type

    64
    Let f(x)f(x) be a function continuous at x=0x = 0, defined for x≠0x \ne 0 as f(x)=1−cos⁡(1−cos⁡(6x))x2sin⁡2(3x)f(x) = \dfrac{1 - \cos(1 - \cos(6x))}{x^2\sin^2(3x)}. Then the value of f(0)f(0) is...

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  5. Question 5

    Differentiation. 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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