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Day 495: MHT-CET Maths

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

  1. Question 1

    Applications of Derivative. Asked once: 25 Apr 2025 S1

    127
    f(x)=x2+2x,x≠0f(x) =\frac{x}{2}+\frac{2}{x},x\neq 0 is strictly decreasing in

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  2. Question 2

    Definite Integration. Asked once: 22 Apr 2025 S1

    116
    For a real number x,[x]x,\lbrack x\rbrack denotes the greatest integer less than or equal to xx. Then the value of [12]+[12+1100]+[12+2100]+[12+3100]+\left\lbrack \frac{1}{2} \right\rbrack+\left\lbrack \frac{1}{2}+\frac{1}{100} \right\rbrack+\left\lbrack \frac{1}{2}+\frac{2}{100} \right\rbrack+\left\lbrack \frac{1}{2}+\frac{3}{100} \right\rbrack+.........+[12+99100]=+\left\lbrack \frac{1}{2}+\frac{99}{100} \right\rbrack=

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  3. Question 3

    Differentiation. Asked once: 15 Apr 2026 S2

    72
    The derivative of sin⁡(log⁡(x+3x))\sin\left(\log\left(\dfrac{x + 3}{x}\right)\right) is

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  4. Question 4

    Indefinite Integration. Asked once: 17 Apr 2026 S2

    72
    If y=cos⁡x2+cos⁡x2+cos⁡x2+…∞y = \sqrt{\cos x^2 + \sqrt{\cos x^2 + \sqrt{\cos x^2 + \ldots\infty}}} and dydx=f(x)2y−1\dfrac{dy}{dx} = \dfrac{f(x)}{2y - 1} then, ∫f(x) dx=…\displaystyle\int f(x)\,dx = \ldots

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  5. Question 5

    Limits. Asked once: May 2021 S1

    131
    Evaluate lim⁡x→2x4−4x2+32 x−8\lim_{x \to \sqrt{2}} \dfrac{x^{4} - 4}{x^{2} + 3\sqrt{2}\,x - 8}.

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