PYQ Vault

Day 246: NDA Maths

5 questions (8 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 3 parts)

    Binomial Distribution. Asked once: NDA 1 2022

    Consider the following data for the next three (03) items that follow: The incidence of suffering from a disease among workers in an industry has a chance of 3313%33\frac{1}{3}\%.
    115
    What is the probability that exactly 3 out of 6 workers suffer from a disease?

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    116
    What is the probability that no one out of 6 workers suffers from a disease?

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    117
    What is the probability that at least one out of 6 workers suffers from a disease?

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  2. Question 2

    Binomial Theorem. Asked once: NDA 1 2025

    20
    What is the number of rational terms in the expansion of (312+514)12\left(3^{\frac{1}{2}} + 5^{\frac{1}{4}}\right)^{12}?

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  3. Question 3

    Circles. Asked once: NDA 1 2025

    56
    What is the equation of the circle whose diameter is 10 cm and the equations of two of its diameters are x+y=0x + y = 0 and x−y=0x - y = 0?

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  4. Question 4

    Complex Numbers. Asked once: NDA 2 2026

    26
    If x=4+ix = 4 + i, where i=−1i = \sqrt{-1}, then what is x3+2x2−63x+171x^3 + 2x^2 - 63x + 171 equal to?

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  5. Question 5 (case study, 2 parts)

    Conics. Asked once: NDA 1 2026

    For the next two (02) items that follow: The foci of the ellipse px2+16y2=16ppx^2+16y^2=16p and the foci of the hyperbola 25(81x2−144y2)=1166425(81x^2-144y^2)=11664 coincide (assume p<16p<16).
    61
    What is the value of p?

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    62
    What is the difference between the eccentricities of the hyperbola and the ellipse?

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