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Day 69: MHT-CET Maths

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

  1. Question 1

    Applications of Derivative. Asked 3 times: 9 May 2024 S2*, 22 Apr 2025 S2*, 13 Apr 2026 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    76
    Let f(x)f(x) be the differentiable function for all xx such that f′(x)≤5f'(x) \le 5 and f(1)=4f(1) = 4. The maximum value of f(5)f(5) is...

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  2. Question 2

    Vectors. Asked 3 times: 11 May 2024 S1*, 20 Apr 2025 S2*, 13 Apr 2026 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    88
    If aˉ=i^+j^\bar{a} = \hat{i} + \hat{j} and bˉ=i^−k^\bar{b} = \hat{i} - \hat{k}, then the point of intersection of the lines rˉ×aˉ=bˉ×aˉ\bar{r} \times \bar{a} = \bar{b} \times \bar{a} and rˉ×bˉ=aˉ×bˉ\bar{r} \times \bar{b} = \bar{a} \times \bar{b} is

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  3. Question 3

    Vectors. Asked 3 times: 11 May 2023 S1, 10 May 2024 S2, 13 Apr 2026 S1 See all 3 times it was asked

    87
    The volume of a tetrahedron with vertices 5i^−j^+k^,7i^−4j^+pk^,i^−6j^+10k^5\hat{i} - \hat{j} + \hat{k}, 7\hat{i} - 4\hat{j} + p\hat{k}, \hat{i} - 6\hat{j} + 10\hat{k} and −i^−3j^+7k^-\hat{i} - 3\hat{j} + 7\hat{k} is 11 cubic units, then one of the values of p is

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  4. Question 4

    Probability Distribution. Asked 3 times: 10 May 2024 S1*, 25 Apr 2025 S2*, 11 Apr 2026 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    98
    A player tosses two fair coins, he wins Rs. 55 if two heads appear, Rs. 33 if one head appears and Rs. 22 if no head appears, then the variance of the winning amount is

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  5. Question 5

    Binomial Distribution. Asked 3 times: 9 May 2023 S1*, 9 May 2023 S2*, 11 Apr 2026 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    98
    Let X∼B(n,p)X \sim B(n, p). If E(X)=2E(X) = 2 and Var(X)=1\mathrm{Var}(X) = 1, then the probability of getting at most one success is .....

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