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Day 74: MHT-CET Maths

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

  1. Question 1

    Differential Equations. Asked 3 times: 10 May 2023 S1, 15 May 2023 S1, 13 May 2024 S2 See all 3 times it was asked

    140
    A radioactive substance, with initial mass m0m_0, has a half-life of hh days. Then its initial decay rate is given by

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  2. Question 2

    Line and Plane. Asked 3 times: 11 May 2024 S1*, 12 May 2024 S1*, 13 May 2024 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    138
    A plane is parallel to two lines whose direction ratios are 2,0,−22,0,-2 and −2,2,0-2,2,0 and it contains the point (2,2,2)(2,2,2). If it cuts co-ordinate axes at A, B, C, then the volume of the tetrahedron OABC (in cubic units) is

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  3. Question 3

    Probability Distribution. Asked 3 times: 11 May 2023 S1*, 9 May 2024 S1*, 12 May 2024 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    140
    Three fair coins with faces numbered 1 and 0 are tossed simultaneously. Then variance (X) of the probability distribution of random variable XX, where XX is the sum of numbers on the upper most faces, is

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  4. Question 4

    Applications of Derivative. Asked 3 times: 15 May 2023 S1*, 10 May 2024 S1*, 11 May 2024 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    125
    A rod AB, 13 feet long moves with its ends A and B on two perpendicular lines OX and OY respectively. When A is 5 feet from O, it is moving away at the rate of 3 feet/sec. At this instant, B is moving at the rate

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  5. Question 5

    Trigonometric Functions. Asked 3 times: 9 May 2023 S2*, 15 May 2023 S1*, 11 May 2024 S2 (* = numbers or wording changed that year) See all 3 times it was asked

    134
    π+sin⁡−1 ⁣45+sin⁡−1 ⁣513+sin⁡−1 ⁣1665\pi+\sin^{-1}\!\frac{4}{5}+\sin^{-1}\!\frac{5}{13}+\sin^{-1}\!\frac{16}{65} is equal to

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