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Day 268: MHT-CET Maths

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

  1. Question 1

    Binomial Distribution. Asked once: 20 Apr 2026 S2 (same type asked 10 times) See all 10 of this type

    98
    Four cards are drawn successively with replacement from well shuffled deck of 52 cards, then the probability that only two cards are club cards is ...........

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  2. Question 2

    Differential Equations. Asked once: 19 Apr 2026 S1 (same type asked 10 times) See all 10 of this type

    86
    The solution of the differential equation dydx=x−yx+y\dfrac{dy}{dx} = \dfrac{x - y}{x + y}, when x=0x = 0 and y=0y = 0 represents ....

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  3. Question 3

    Limits. Asked once: 14 May 2026 S1 (same type asked 10 times) See all 10 of this type

    61
    If the function f(x)f(x) is defined as below f(x)={(3x+3−x−2)log⁡(1+4x)(1−cos⁡4x)tan⁡(2x),x≠0(log⁡p)rq,x=0f(x) = \begin{cases} \dfrac{(3^x + 3^{-x} - 2)\log(1 + 4x)}{(1 - \cos 4x)\tan(2x)}, & x \neq 0 \\ \dfrac{(\log p)^r}{q}, & x = 0 \end{cases} is continuous at x=0x = 0 then p+q−r=…p + q - r = \ldots

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  4. Question 4

    Limits. Asked once: 16 Apr 2026 S2 (same type asked 10 times) See all 10 of this type

    70
    If the function f is continuous at x=πx = \pi, where f(x)=1−cos⁡[7(x−π)]5(x−π)2f(x) = \dfrac{1 - \cos[7(x - \pi)]}{5(x - \pi)^2}, for x≠πx \neq \pi, then f(π)=f(\pi) =

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  5. Question 5

    Differentiation. Asked once: 17 Apr 2026 S2 (same type asked 10 times) See all 10 of this type

    71
    The derivative of tan⁡−1(1+x2−1x)\tan^{-1}\left(\dfrac{\sqrt{1 + x^2} - 1}{x}\right) with respect to tan⁡−1(x1−x2)\tan^{-1}\left(\dfrac{x}{\sqrt{1 - x^2}}\right) at x=12x = \dfrac{1}{2} is

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