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Day 424: MHT-CET Maths

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

  1. Question 1

    Permutations and Combinations. Asked once: 14 May 2026 S2

    55
    A man has seven relatives, 4 of them are ladies and 3 gentlemen, his wife also has 7 relatives out of which 3 are ladies and 4 gentlemen. The number of ways in which they can invite a dinner party of 3 ladies and 3 gentlemen, so that there are 3 of the man's relatives and 3 of the wife's relatives, are

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  2. Question 2

    Probability Distribution. Asked once: 13 May 2026 S1

    99
    A continuous random variable X has the following probability distribution function (p.d.f.) f(x)={kx2for 0≤x≤30otherwisef(x) = \begin{cases} kx^2 & \text{for } 0 \le x \le 3 \\ 0 & \text{otherwise} \end{cases} If P(X>a)=0.5P(X > a) = 0.5, then the value of aa is...

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  3. Question 3

    Quadratic Equations. Asked once: 13 Apr 2026 S2

    51
    The quadratic polynomial p(x)p(x) has roots 11 and α\alpha, while quadratic polynomial q(x)q(x) has roots 11 and β\beta. Let α\alpha and β\beta be the roots of r(x)=p(x)+q(x)r(x) = p(x) + q(x). Then lim⁡x→∞[p(x)−q(x)]=\lim_{x \to \infty}\left[\sqrt{p(x)} - \sqrt{q(x)}\right] =

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  4. Question 4

    Sequences and Series. Asked once: 26 Apr 2025 S2

    117
    If p3=q4=r6=t7=s2p^{3}=q^{4}=r^{6}=t^{7}=s^{2}, then log⁡t(pqrs)=\log_{t}(pqrs) =......

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  5. Question 5

    Sets, Relations and Functions. Asked once: 15 May 2026 S2

    51
    If f(x)+2f(1−x)=x2+5f(x) + 2f(1 - x) = x^2 + 5 for all real xx, then f(x)f(x) is equal to...

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