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Day 321: NDA Maths

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

  1. Question 1 (case study, 2 parts)

    Properties of Triangle. Asked once: NDA 1 2020

    Directions for the following two (02) items: Read the following information and answer the two items that follow: ABCD is a trapezium such that AB and CD are parallel and BC is perpendicular to them. Let ∠ADB = θ, ∠ABD = α, BC = p and CD = q.
    21
    Consider the following: 1. ADsin⁡θ=ABsin⁡αAD\sin\theta = AB\sin\alpha 2. BDsin⁡θ=ABsin⁡(θ+α)BD\sin\theta = AB\sin(\theta+\alpha). Which of the above is/are correct?

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    22
    What is AB equal to?

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  2. Question 2 (case study, 2 parts)

    Quadratic Equations. Asked once: NDA 1 2023

    Consider the following for the next two (02) items that follow: A quadratic equation is given by (3+22)x2−(4+23)x+(8+43)=0(3+2\sqrt{2})x^{2}-(4+2\sqrt{3})x+(8+4\sqrt{3})=0.
    49
    What is the HM of the roots of the equation?

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    50
    What is the GM of the roots of the equation?

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  3. Question 3

    Sequence & Series. Asked once: NDA 2 2021

    33
    Let pp, qq and 33 be respectively the first, third and fifth terms of an AP. Let dd be the common difference. If the product (pq)(pq) is minimum, then what is the value of dd?

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  4. Question 4

    Statistics. Asked once: NDA 2 2021

    110
    What is the mean of natural numbers contained in the interval [15,64][15,64]?

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  5. Question 5

    Trigonometric Equations. Asked once: NDA 2 2018

    42
    What is/are the solution(s) of the trigonometric equation csc⁡x+cot⁡x=3\csc x + \cot x = \sqrt{3}, where 0<x<2π0 < x < 2\pi?

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