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Day 292: MHT-CET Maths

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

  1. Question 1

    Differentiation. Asked once: 9 May 2023 S2 (same type asked 5 times) See all 5 of this type

    118
    If log⁡(x+y)=sin⁡(x+y)\log(x+y) = \sin(x+y), then dydx\frac{dy}{dx} is

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  2. Question 2

    Applications of Definite Integral. Asked once: 16 Apr 2026 S2 (same type asked 5 times) See all 5 of this type

    83
    The area of the region common to the parabolas 4y2=9x4y^2 = 9x and 3x2=16y3x^2 = 16y is...

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  3. Question 3

    Determinants and Matrices. Asked once: 15 Apr 2026 S2 (same type asked 5 times) See all 5 of this type

    67
    If A=[31−12],C=[7306]A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}, C = \begin{bmatrix} 7 & 3 \\ 0 & 6 \end{bmatrix} and AB=CAB = C, then the inverse of matrix B is

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  4. Question 4

    Probability Distribution. Asked once: 20 Apr 2026 S1 (same type asked 5 times) See all 5 of this type

    99
    Let X be a continuous random variable with the probability density function(p.d.f.) given by f(x)={kx,0≤x<1k,1≤x<2−kx+3k,2≤x<30,otherwisef(x) = \begin{cases} kx, & 0 \le x < 1 \\ k, & 1 \le x < 2 \\ -kx + 3k, & 2 \le x < 3 \\ 0, & \text{otherwise} \end{cases} P(2<X≤3)=⋯P(2 < X \le 3) = \cdots

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  5. Question 5

    Differential Equations. Asked once: 25 Apr 2025 S1 (same type asked 5 times) See all 5 of this type

    123
    The solution of the equation x2y−x3⋅ dy dx=y4cos⁡xx^{2}y-x^{3}\cdot\frac{\text{ }dy}{\text{ }dx}=y^{4}\cos x, where y(0)=1y(0) = 1, is

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