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Day 219: NDA Maths

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

  1. Question 1

    Probability. Asked once: NDA 1 2017 (same type asked 4 times)

    103
    A committee of two persons is constituted from two men and two women. What is the probability that the committee will have only women?

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  2. Question 2

    Quadratic Equations. Asked once: NDA 1 2017 (same type asked 4 times)

    4
    If the difference between the roots of the equation x2+kx+1=0x^2 + kx + 1 = 0 is strictly less than 5\sqrt{5}, where ∣k∣≥2|k| \geq 2, then kk can be any element of the interval

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  3. Question 3

    Statistics. Asked once: NDA 1 2019 (same type asked 4 times)

    109
    The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, then what will be the new mean and the new standard deviation respectively?

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  4. Question 4

    Complex Numbers. Asked once: NDA 1 2018 (same type asked 4 times)

    18
    What is i1000+i1001+i1002+i1003i^{1000} + i^{1001} + i^{1002} + i^{1003} equal to (where i=−1i = \sqrt{-1})?

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  5. Question 5

    Definite Integration. Asked once: NDA 1 2017 (same type asked 4 times)

    100
    What is ∫e−1e2∣ln⁡xx∣ dx\int_{e^{-1}}^{e^2}\left|\dfrac{\ln x}{x}\right|\,dx equal to?

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