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Day 25: NDA Maths

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

  1. Question 1

    Sets & Relations. This type asked 3 times: NDA 1 2019, NDA 1 2022, NDA 2 2026. This one: NDA 2 2026

    46
    Consider the following statements in respect of sets AA and BB : I. If x∈Ax \in A and A∈BA \in B, then x∈Bx \in B. II. If A⊂BA \subset B and x∉Bx \notin B, then x∉Ax \notin A. Which of the statements given above is/are correct?

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  2. Question 2

    Statistics. This type asked 3 times: NDA 2 2017, NDA 1 2020, NDA 2 2026. This one: NDA 2 2026

    108
    The standard deviation of XX is 4 and the standard deviation of YY is 5. If the correlation coefficient rr is 0.8, then what is the regression coefficient of YY on XX?

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  3. Question 3

    Trigonometric Identities. This type asked 3 times: NDA 1 2020, NDA 2 2022, NDA 2 2026. This one: NDA 2 2026

    11
    What is 6sin⁡(π/18)−8sin⁡3(π/18)6 \sin(\pi/18) - 8 \sin^3(\pi/18) equal to?

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  4. Question 4

    Trigonometric Identities. This type asked 3 times: NDA 1 2021, NDA 2 2022, NDA 2 2026. This one: NDA 2 2026

    15
    What is tan⁡(1125∘)cot⁡(405∘)+tan⁡(765∘)cot⁡(675∘)\tan(1125^\circ) \cot(405^\circ) + \tan(765^\circ) \cot(675^\circ) equal to?

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  5. Question 5

    Vectors. This type asked 3 times: NDA 2 2018, NDA 2 2025, NDA 2 2026. This one: NDA 2 2026

    69
    Let a⃗\vec{a} and b⃗\vec{b} be unit vectors inclined at 30∘30^\circ. What is the area of the parallelogram whose sides are represented by the vectors a⃗+3b⃗\vec{a} + 3\vec{b} and 3a⃗+b⃗3\vec{a} + \vec{b}?

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