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Day 104: NDA Maths

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

  1. Question 1

    Probability. Asked once: NDA 1 2020 (same type asked 4 times)

    115
    A committee of 3 is to be formed from a group of 2 boys and 2 girls. What is the probability that the committee consists of 2 boys and 1 girl?

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  2. Question 2

    Quadratic Equations. Asked once: NDA 1 2022 (same type asked 4 times)

    20
    Let α\alpha and β\beta (α>β\alpha>\beta) be the roots of the equation x2−8x+q=0x^2-8x+q=0. If α2−β2=16\alpha^2-\beta^2=16, then what is the value of qq?

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  3. Question 3

    Statistics. Asked once: NDA 2 2021 (same type asked 4 times)

    112
    The mean of 10 observations is 5·5. If each observation is multiplied by 4 and subtracted from 44, then what is the new mean?

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  4. Question 4

    Complex Numbers. Asked once: NDA 2 2021 (same type asked 4 times)

    13
    What is ∑n=18n+7in\sum_{n=1}^{8n+7}i^{n} equal to, where i=−1i=\sqrt{-1}?

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  5. Question 5 (case study, 2 parts)

    Conics. Asked once: NDA 1 2023 (same type asked 4 times)

    Consider the following for the next two (02) items that follow: P(x,y)P(x,y) is any point on the ellipse x2+4y2=1x^{2}+4y^{2}=1. Let EE, FF be the foci of the ellipse.
    57
    What is PE+PFPE+PF equal to?

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    58
    Consider the following points: 1. (32,0)\left(\frac{\sqrt{3}}{2},0\right) 2. (32,14)\left(\frac{\sqrt{3}}{2},\frac{1}{4}\right) 3. (32,−14)\left(\frac{\sqrt{3}}{2},-\frac{1}{4}\right) Which of the above points lie on latus rectum of ellipse?

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