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Day 119: NDA Maths

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

  1. Question 1

    Sets & Relations. Asked once: NDA 2 2023 (same type asked 3 times)

    22
    Let A={1,2,…,20}A=\{1,2,\ldots,20\}. Define R={(x,y):4x−3y=1}, x,y∈AR=\{(x,y):4x-3y=1\},\ x,y\in A. Which statements are correct? (1) Domain of RR is {1,4,7,10,13,16}\{1,4,7,10,13,16\}. (2) Range of RR is {1,5,9,13,17}\{1,5,9,13,17\}. (3) Range of RR equals codomain.

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  2. Question 2

    Statistics. Asked once: NDA 1 2023 (same type asked 3 times)

    115
    If HH is the harmonic mean of numbers 1,2,22,23,…,2n−11,2,2^{2},2^{3},\ldots,2^{n-1}, then what is nH\dfrac{n}{H} equal to?

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  3. Question 3

    Vectors. Asked once: NDA 2 2018 (same type asked 3 times)

    69
    A spacecraft located at i^+2j^+3k^\hat{i}+2\hat{j}+3\hat{k} is subjected to a force λk^\lambda\hat{k} by firing a rocket. The spacecraft is subjected to a moment of magnitude

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  4. Question 4

    Vectors. Asked once: NDA 2 2018 (same type asked 3 times)

    65
    A unit vector perpendicular to each of the vectors 2i^−j^+k^2\hat{i}-\hat{j}+\hat{k} and 3i^−4j^−k^3\hat{i}-4\hat{j}-\hat{k} is

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  5. Question 5

    3D Geometry. Asked once: NDA 2 2021 (same type asked 3 times)

    65
    ABCDEFGH is a cuboid with base ABCD. Let A(0, 0, 0), B(12, 0, 0), C(12, 6, 0) and G(12, 6, 4) be the vertices. If α\alpha is the angle between AB and AG; β\beta is the angle between AC and AG, then what is the value of cos⁡2α+cos⁡2β\cos 2\alpha+\cos 2\beta?

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