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Day 377: MHT-CET Maths

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

  1. Question 1

    Applications of Derivative. Asked once: 16 May 2023 S1 (same type asked 5 times) See all 5 of this type

    146
    The abscissa of the point on the curve y=a ⁣(ex/a+e−x/a)y = a\!\left(e^{x/a} + e^{-x/a}\right) where the tangent is parallel to the X-axis is

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  2. Question 2

    Probability Distribution. Asked once: 3 May 2023 S1 (same type asked 5 times) See all 5 of this type

    109
    A random variable X has the following probability distribution. Then value of k is___ and P(3<x≤6)P(3<x\leq6) has the value. \begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline X=x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\\ \hline P(x) & k & 2k & 3k & 4k & 4k & 3k & 2k & k & k\\ \hline\end{array}

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  3. Question 3

    Determinants and Matrices. Asked once: May 2022 S1 (same type asked 5 times) See all 5 of this type

    110
    If A=[121313]A = \begin{bmatrix} 1 & 2 & 1 \\ 3 & 1 & 3 \end{bmatrix} and B=[231212]B = \begin{bmatrix} 2 & 3 \\ 1 & 2 \\ 1 & 2 \end{bmatrix}, then (AB)−1=(AB)^{-1} =

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  4. Question 4

    Probability Distribution. Asked once: 14 May 2024 S1 (same type asked 5 times) See all 5 of this type

    109
    If f(x)={3(1−2x2)4;0<x<10;otherwisef(x)=\begin{cases}\dfrac{3(1-2x^2)}{4}; & 0<x<1\\0; & \text{otherwise}\end{cases} is a probability density function of XX, then P ⁣(14<x<13)P\!\left(\dfrac{1}{4}<x<\dfrac{1}{3}\right) is:

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  5. Question 5

    Differential Equations. Asked once: 16 May 2023 S2 (same type asked 5 times) See all 5 of this type

    142
    The general solution of the differential equation dydx=ytan⁡x−y2sec⁡x\frac{dy}{dx} = y\tan x - y^2\sec x is

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