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Day 117: NDA Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Application of Derivatives. Asked once: NDA 1 2021 (same type asked 3 times)

    87
    If x+y=20x+y=20 and P=xyP=xy, then what is the maximum value of PP?

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  2. Question 2 (case study, 2 parts)

    Binomial Distribution. Asked once: NDA 1 2025 (same type asked 3 times)

    Let X be a random variable following binomial distribution with parameters n=6n = 6 and p=kp = k. Further, 9P(X=4)=P(X=2)9P(X=4) = P(X=2).
    107
    What is the value of kk?

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    108
    What is the value of P(X=3)P(X=3)?

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  3. Question 3

    Binomial Theorem. Asked once: NDA 1 2025 (same type asked 3 times)

    21
    If the sum of binomial coefficients in the expansion of (x+y)n(x+y)^n is 256, then the greatest binomial coefficient occurs in which one of the following terms?

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  4. Question 4

    Circles. Asked once: NDA 2 2023 (same type asked 3 times)

    87
    Consider 4x2+4y2−4ax−4ay+a2=04x^2+4y^2-4ax-4ay+a^2=0. (1) Circle touches both axes. (2) Diameter is 2a2a. (3) Centre lies on x+y=ax+y=a. How many statements are correct?

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  5. Question 5

    Complex Numbers. Asked once: NDA 1 2021 (same type asked 3 times)

    1
    The smallest positive integer nn for which (1−i1+i)n2=1\left(\frac{1-i}{1+i}\right)^{n^2} = 1, where i=−1i = \sqrt{-1}, is

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