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Day 517: MHT-CET Maths

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

  1. Question 1

    Differentiation. Asked once: 20 Apr 2025 S2

    135
    If a(4+x2)=xa\left( 4 +x^{2} \right)=x and y−x3=a2y-x^{3}=a^{2} then dy dx\frac{dy}{\text{ }dx} at x=1x= 1 is

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  2. Question 2

    Indefinite Integration. Asked once: 11 Apr 2026 S2

    78
    ∫4x(4x+4) dx=⋯\displaystyle\int\sqrt{4^x(4^x + 4)}\,dx = \cdots

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  3. Question 3

    Line and Plane. Asked once: 22 Apr 2025 S1

    111
    The perimeter of a square whose two sides have equations x−12=y+23=z−34\frac{x- 1}{2}=\frac{y+ 2}{3}=\frac{z- 3}{4} and x2=y−13=z+14\frac{x}{2}=\frac{y- 1}{3}=\frac{z+ 1}{4} is

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  4. Question 4

    Trigonometric Functions. Asked once: 21 Apr 2025 S2

    104
    If sin⁡−1x+sin⁡−1y=π3\sin^{- 1}x+\sin^{- 1}y=\frac{\pi}{3} and cot⁡−1(1x)−cot⁡−1(1y)=0\cot^{- 1}\left( \frac{1}{x} \right)-\cot^{- 1}\left( \frac{1}{y} \right)= 0 then 2x2+y2−xy=2x^{2}+y^{2}-xy= ____\_\_\_\_

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  5. Question 5

    Trigonometry - II. Asked once: May 2021 S1

    102
    If θ\theta lies in the first quadrant and 5tan⁡θ=45\tan\theta = 4, then 5sin⁡θ−3cos⁡θsin⁡θ+2cos⁡θ\frac{5\sin\theta - 3\cos\theta}{\sin\theta + 2\cos\theta} is equal to

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