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Day 70: MHT-CET Maths

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

  1. Question 1

    Circle. Asked 3 times: 2 May 2023 S2*, 9 May 2024 S1, 26 Apr 2025 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    130
    Two tangents to the circle x2+y2=4x^{2}+y^{2}= 4 at the points A and B meet at P(−4,0)P( - 4,0). Then the area of quadrilateral PAOB, where ' O ' is the origin is

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  2. Question 2

    Vectors. Asked 3 times: 4 May 2023 S1*, 9 May 2023 S2*, 26 Apr 2025 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    110
    Let aˉ=αi^+3j^−k^,bˉ=3i^−j^+βk^\bar{a}=\alpha\widehat{i}+ 3\widehat{j}-\widehat{k},\bar{b}= 3\widehat{i}-\widehat{j}+\beta\widehat{k} and c‾=i^+2j^−2k^\overline{c}=\widehat{i}+ 2\widehat{j}- 2\widehat{k} where α,β∈R\alpha,\beta\in\mathbb{R}, be three vectors. If the projection of aˉ\bar{a} on cˉ\bar{c} is 103\frac{10}{3} and b‾×c‾=−6i^+10j^+7k^\overline{b}\times\overline{c}= - 6\widehat{i}+ 10\widehat{j}+ 7\widehat{k}, then the value of (α+β)(\alpha+\beta) is equal to

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  3. Question 3

    Probability Distribution. Asked 3 times: 4 May 2023 S1*, 15 May 2023 S1*, 25 Apr 2025 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    114
    Consider the probability distribution
    X=xX = x12345
    P(X=x)P(X = x)KK2K2KK2K^{2}2K2K5K25K^{2}
    Then the value of P(X>2)P(X > 2) is

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  4. Question 4

    Applications of Derivative. Asked 3 times: 11 May 2023 S1*, 16 May 2023 S2*, 25 Apr 2025 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    130
    The rate of change of the volume of a sphere with respect to its surface area, when the radius is 5 m is

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  5. Question 5

    Differential Equations. Asked 3 times: 9 May 2023 S1*, 22 Apr 2025 S1*, 25 Apr 2025 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    104
    The rate at which the population of a city increases varies as the population. In a period of 20 years, the population increased from 4 lakhs to 6 lakhs. In another 20 years the population will be

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