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Day 144: NDA Maths

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

  1. Question 1

    Properties of Triangle. Asked once: NDA 2 2017 (same type asked 2 times)

    29
    In △PQR\triangle PQR, ∠R=π2\angle R = \dfrac{\pi}{2}. If tan⁡ ⁣(P2)\tan\!\left(\dfrac{P}{2}\right) and tan⁡ ⁣(Q2)\tan\!\left(\dfrac{Q}{2}\right) are the roots of the equation ax2+bx+c=0ax^2 + bx + c = 0, then which one of the following is correct?

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  2. Question 2 (case study, 3 parts)

    Sequence & Series. Asked once: NDA 2 2022 (same type asked 2 times)

    Consider the following for the next three (03) items that follow: Let P be the sum of first n positive terms of an increasing arithmetic progression A. Let Q be the sum of first n positive terms of another increasing arithmetic progression B. Let P : Q = (5n+4) : (9n+6)
    19
    What is the ratio of the first term of A to that of B?

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    20
    What is the ratio of their 10th terms?

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    21
    If d is the common difference of A, and D is the common difference of B, then which one of the following is always correct?

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  3. Question 3

    Sets & Relations. Asked once: NDA 1 2022 (same type asked 2 times)

    45
    Consider the following statements in respect of any relation RR on a set AA: 1. If RR is reflexive, then R−1R^{-1} is also reflexive 2. If RR is symmetric, then R−1R^{-1} is also symmetric 3. If RR is transitive, then R−1R^{-1} is also transitive Which of the above statements are correct?

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  4. Question 4

    Statistics. Asked once: NDA 2 2019 (same type asked 2 times)

    118
    If VV is the variance and MM is the mean of first 15 natural numbers, then what is V+M2V + M^{2} equal to ?

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  5. Question 5

    Vectors. Asked once: NDA 1 2022 (same type asked 2 times)

    96
    If 4i^+j^−3k^4\hat{i}+\hat{j}-3\hat{k} and pi^+qj^−2k^p\hat{i}+q\hat{j}-2\hat{k} are collinear vectors, then what are the possible values of pp and qq respectively?

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