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Day 347: MHT-CET Maths

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

  1. Question 1

    Probability Distribution. Asked once: 22 Apr 2025 S1 (same type asked 5 times) See all 5 of this type

    122
    The p.d.f. of a continuous random variable X is f(x)={x218 if −3<x<30 otherwise f(x) =\left\{ \begin{matrix} \frac{x^{2}}{18} & \text{~if~}- 3 <x< 3 \\ 0 & \text{~otherwise~} \end{matrix} \right. Then P[∣X∣<2]=P\lbrack|X| < 2\rbrack =

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  2. Question 2

    Differential Equations. Asked once: 11 May 2024 S2 (same type asked 5 times) See all 5 of this type

    107
    The solution of dxdy+xy=x2\frac{dx}{dy} + xy = x^2 is:

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  3. Question 3

    Differentiation. Asked once: 11 Apr 2026 S2 (same type asked 5 times) See all 5 of this type

    72
    If x3+y3=6x^3 + y^3 = 6 and d2ydx2⋅d2xdy2=m(xy)n\dfrac{d^2y}{dx^2} \cdot \dfrac{d^2x}{dy^2} = \dfrac{m}{(xy)^n}, where m,n∈Rm, n \in R then mn=\dfrac{m}{n} =

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  4. Question 4

    Indefinite Integration. Asked once: 15 May 2023 S1 (same type asked 5 times) See all 5 of this type

    105
    If ∫dx1+3sin⁡2x=12tan⁡−1(f(x))+c\int \frac{dx}{1+3\sin^{2}x} = \frac{1}{2}\tan^{-1}(f(x))+c, where c is a constant of integration, then f(x)f(x) is equal to

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  5. Question 5

    Limits. Asked once: 15 May 2023 S1 (same type asked 5 times) See all 5 of this type

    107
    Let f:[−1,3]→Rf:[-1,3]\to\mathbb{R} be defined as f(x)={∣x∣+[x],−1≤x<1x+∣x∣,1≤x<2x+[x],2≤x≤3f(x) = \begin{cases}|x|+[x],&-1\leq x<1\\x+|x|,&1\leq x<2\\x+[x],&2\leq x\leq3\end{cases} where [t][t] denotes the greatest integer function. Then ff is discontinuous at

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