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Day 169: MHT-CET Maths

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

  1. Question 1

    Probability Distribution. This type asked 2 times: May 2022 S1, 4 May 2023 S1. This one: 4 May 2023 S1 See all 2 of this type

    116
    Let A and B be two events such that the probability that exactly one of them occurs is 25\frac{2}{5} and the probability that A or B occurs is 12\frac{1}{2}, then the probability of both of them occur together is

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  2. Question 2

    Differentiation. This type asked 2 times: 2 May 2023 S1, 3 May 2023 S1. This one: 3 May 2023 S1 See all 2 of this type

    110
    If y=log⁡e ⁣(x5⋅(3x−4)4/3(x+5)4/3)y=\log_e\!\left(\dfrac{x^{5}\cdot(3x-4)^{4/3}}{(x+5)^{4/3}}\right), then dydx\dfrac{dy}{dx} is equal to

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  3. Question 3

    Indefinite Integration. This type asked 2 times: May 2021 S1, 2 May 2023 S2. This one: 2 May 2023 S2 See all 2 of this type

    141
    ∫log⁡x3x dx\displaystyle\int \dfrac{\log\sqrt{x}}{3x}\,dx is equal to

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  4. Question 4

    Measures of Dispersion. This type asked 2 times: May 2021 S1, 2 May 2023 S1. This one: 2 May 2023 S1 See all 2 of this type

    145
    The mean of 100 observations is 50 and their standard deviation is 5, then the sum of all squares of all the observations is

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  5. Question 5

    Determinants and Matrices. This type asked 2 times: May 2021 S1, May 2022 S1. This one: May 2022 S1 See all 2 of this type

    139
    Given A=(x321y422z)A = \begin{pmatrix} x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z \end{pmatrix}, if xyz=60xyz = 60 and 8x+4y+3z=208x + 4y + 3z = 20, then A(adj A)A(\text{adj}\,A)

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