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Day 535: MHT-CET Maths

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

  1. Question 1

    Applications of Derivative. Asked once: 3 May 2023 S1

    106
    A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length xx. The maximum area (in sq. units) enclosed by the park is

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  2. Question 2

    Differentiation. Asked once: May 2022 S1

    118
    If y=log⁡1+sin⁡x1−sin⁡xy = \log\sqrt{\frac{1+\sin x}{1-\sin x}}, then dydx\frac{dy}{dx} at x=π3x = \frac{\pi}{3} is

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  3. Question 3

    Indefinite Integration. Asked once: 12 May 2024 S1

    149
    If ∫cos⁡3/5x⋅sin⁡3x dx=−1mcos⁡mx+1ncos⁡nx+c\displaystyle\int\cos^{3/5}x\cdot\sin^{3}x\,dx=-\frac{1}{m}\cos^{m}x+\frac{1}{n}\cos^{n}x+c (where cc is the constant of integration), then (m,n)=(m,n)=

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  4. Question 4

    Line and Plane. Asked once: 16 May 2023 S1

    133
    If the distance between the plane Ax−2y+z=dAx-2y+z=d and the plane containing the lines x−12=y−23=z−34\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4} and x−23=y−34=z−45\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5} is 6\sqrt{6} units, then ∣d∣|d| is

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  5. Question 5

    Trigonometric Functions. Asked once: 11 May 2024 S2

    124
    If cos⁡−1p+cos⁡−11−p+cos⁡−11−q=3π4\cos^{-1}\sqrt{p}+\cos^{-1}\sqrt{1-p}+\cos^{-1}\sqrt{1-q}=\frac{3\pi}{4}, then q is:

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