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Day 16: MHT-CET Maths

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

  1. Question 1

    Line and Plane. Asked 7 times: 10 May 2023 S1*, 10 May 2023 S2*, 15 May 2023 S2*, 11 May 2024 S2*, 14 May 2024 S2*, 23 Apr 2025 S1*, 11 Apr 2026 S1 (* = numbers or wording changed that year) See all 7 times it was asked

    94
    If the lines x−12=y+13=z−14\dfrac{x - 1}{2} = \dfrac{y + 1}{3} = \dfrac{z - 1}{4} and x−21=y+m2=z−21\dfrac{x - 2}{1} = \dfrac{y + m}{2} = \dfrac{z - 2}{1} intersect each other, then the value of mm is....

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  2. Question 2

    Binomial Distribution. This type asked 7 times: 3 May 2023 S2, 9 May 2023 S1, 9 May 2023 S2, 11 May 2024 S2, 11 Apr 2026 S1, 17 Apr 2026 S1, 19 May 2026 S1. This one: 19 May 2026 S1 See all 7 of this type

    99
    The sum and product of mean and variance of a binomial distribution are 3 and 2 respectively. Then, P(X>0)=…P(X > 0) = \ldots

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  3. Question 3

    Mathematical Logic. This type asked 7 times: 2 May 2023 S2, 13 May 2024 S2, 16 Apr 2026 S2, 20 Apr 2026 S1, 13 May 2026 S2, 14 May 2026 S2, 19 May 2026 S1. This one: 19 May 2026 S1 See all 7 of this type

    66
    The negation of the inverse of ∼p→q\sim p \rightarrow q is equivalent to:

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  4. Question 4

    Indefinite Integration. This type asked 7 times: 2 May 2023 S2, 3 May 2023 S1, 10 May 2023 S1, 11 May 2023 S1, 14 May 2024 S1, 14 May 2024 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 7 of this type

    81
    If ∫x(a−x)9 dx=[f(x)]1111−a[f(x)]1010+c\int x(a - x)^9\, dx = \dfrac{[f(x)]^{11}}{11} - a\dfrac{[f(x)]^{10}}{10} + c, where cc is a constant of integration, then f′(x)=⋯f'(x) = \cdots

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  5. Question 5

    Limits. This type asked 7 times: 3 May 2023 S2, 10 May 2023 S2, 22 Apr 2025 S1, 22 Apr 2025 S2, 11 Apr 2026 S1, 19 Apr 2026 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 7 of this type

    63
    If lim⁡x→0(f(x)x2)\lim_{x \to 0}\left(\dfrac{f(x)}{x^2}\right) exists finitely and lim⁡x→0(1+x+f(x)x)1/x=e3\lim_{x \to 0}\left(1 + x + \dfrac{f(x)}{x}\right)^{1/x} = e^3, then ∫f(x)⋅log⁡x dx\int f(x) \cdot \log x\, dx is equal to:

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