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Day 13: MHT-CET Maths

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

  1. Question 1

    Applications of Derivative. 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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  2. Question 2

    Definite Integration. This type asked 8 times: May 2022 S1, 11 May 2023 S1, 19 Apr 2025 S1, 21 Apr 2025 S1, 17 Apr 2026 S2, 18 Apr 2026 S1, 19 Apr 2026 S1, 12 May 2026 S2. This one: 12 May 2026 S2 See all 8 of this type

    83
    If f(x)={[x]⋅∣x∣x,x≠00,x=0f(x) = \begin{cases} \dfrac{[x] \cdot |x|}{x}, & x \neq 0 \\ 0, & x = 0 \end{cases}, where [x][x] and ∣x∣|x| denote the greatest integer function and the modulus function respectively, then ∫−21f(x) dx=…\int_{-2}^{1} f(x)\,dx = \ldots

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  3. Question 3

    Differentiation. 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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  4. Question 4

    Mathematical Logic. This type asked 8 times: 4 May 2023 S2, 10 May 2023 S1, 15 May 2023 S2, 23 Apr 2025 S1, 15 Apr 2026 S1, 18 Apr 2026 S1, 20 Apr 2026 S2, 12 May 2026 S2. This one: 12 May 2026 S2 See all 8 of this type

    65
    The inverse of a statement (p∨q)→r(p \vee q) \to r is

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  5. Question 5

    Probability Distribution. This type asked 8 times: 20 Apr 2025 S2, 23 Apr 2025 S1, 25 Apr 2025 S2, 13 Apr 2026 S2, 16 Apr 2026 S2, 18 Apr 2026 S2, 20 Apr 2026 S1, 12 May 2026 S2. This one: 12 May 2026 S2 See all 8 of this type

    100
    A man is known to speak the truth in 75%75\% of cases. If he throws an unbiased die and tells his friend that it is a six. Assuming that when he tells a lie, he specifically reports the result as a six, the probability that it is actually a six is...

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