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Day 256: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1

    Sets & Relations. Asked once: NDA 2 2021

    37
    Consider the following statements in respect of sets: 1. The union over intersection of sets is distributive. 2. The complement of union of two sets is equal to intersection of their complements. 3. If the difference of two sets is equal to empty set, then the two sets must be equal. Which of the above statements are correct?

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  2. Question 2

    Statistics. Asked once: NDA 1 2024

    105
    If two random variables XX and YY are connected by relation 2X−3Y5X+4Y=4\dfrac{2X-3Y}{5X+4Y}=4 and XX follows Binomial distribution with parameters n=10n=10 and p=12p=\dfrac{1}{2}, then what is the variance of YY?

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  3. Question 3 (case study, 2 parts)

    Trigonometric Equations. Asked once: NDA 1 2025

    Let 2sin⁡α+cos⁡α=22\sin\alpha + \cos\alpha = 2, where 0<α<90°0 < \alpha < 90°.
    44
    What is tan⁡α\tan\alpha equal to?

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    45
    What is 2sin⁡2α+cos⁡2α2\sin 2\alpha + \cos 2\alpha equal to?

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  4. Question 4

    Trigonometric Identities. Asked once: NDA 1 2026

    78
    If A and B are acute angles such that 2A+2B=π2A+2B=\pi, then what is the maximum value of sin⁡A⋅sin⁡B\sin A\cdot\sin B?

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  5. Question 5 (case study, 2 parts)

    Vectors. Asked once: NDA 1 2026

    For the next two (02) items that follow: P(-2,-3,5), Q(4,-1,5), R(6,-4,8) and S(2,-6,10) are four points.
    53
    Consider the following statements: I. PQ is parallel to RS. II. PR is perpendicular to QS. Which of the statements given above is/are correct?

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    54
    What is (PQ2+2QS2−2PR2)(PQ^2+2QS^2-2PR^2) equal to?

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