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Day 317: MHT-CET Maths

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

  1. Question 1

    Differentiation. Asked once: 14 May 2024 S2 (same type asked 3 times) See all 3 of this type

    109
    If f′(x)=sin⁡(log⁡x)f'(x) = \sin(\log x) and y=f ⁣(2x+33−2x)y = f\!\left(\frac{2x+3}{3-2x}\right), then dydx\frac{dy}{dx} at x=1x=1 is

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  2. Question 2

    Line and Plane. Asked once: May 2022 S1 (same type asked 3 times) See all 3 of this type

    148
    The equation of the plane passing through the points (2,3,1)(2,3,1), (4,−5,3)(4,-5,3) and parallel to X-axis is

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  3. Question 3

    Probability Distribution. Asked once: 22 Apr 2025 S2 (same type asked 3 times) See all 3 of this type

    124
    If a random variable XX has p.d.f. f(x)={ax22+bx, if 1≤x≤30, otherwisef(x)=\begin{cases}\dfrac{ax^{2}}{2}+bx & ,\text{ if }1\le x\le 3\\ 0 & ,\text{ otherwise}\end{cases} and f(2)=2f(2)=2, then the values of aa and bb are, respectively

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  4. Question 4

    Trigonometric Functions. Asked once: 11 May 2024 S1 (same type asked 3 times) See all 3 of this type

    118
    The value of sec⁡2(tan⁡−12)+csc⁡2(cot⁡−13)\sec^2(\tan^{-1} 2) + \csc^2(\cot^{-1} 3) is

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  5. Question 5

    Differential Equations. Asked once: 16 May 2023 S2 (same type asked 3 times) See all 3 of this type

    124
    The function y(x)y(x) represented by x=sin⁡tx = \sin t, y=aet2+be−t2y = ae^{t\sqrt{2}} + be^{-t\sqrt{2}}, t∈(−π2,π2)t \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) satisfies the equation (1−x2)y′′−xy′=ky(1-x^2)y'' - xy' = ky, then the value of kk is

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