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Day 276: NDA Maths

5 questions (8 parts). Try each one first, then open its answer.

  1. Question 1

    Height & Distance. Asked once: NDA 2 2017

    31
    The angle of elevation of a stationary cloud from a point 25 m above a lake is 15° and the angle of depression of its image in the lake is 45°. The height of the cloud above the lake level is

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  2. Question 2

    Indefinite Integration. Asked once: NDA 2 2022

    76
    What is ∫(cos⁡x)1.5−(sin⁡x)1.5sin⁡x⋅cos⁡x dx\int \frac{(\cos x)^{1.5}-(\sin x)^{1.5}}{\sqrt{\sin x\cdot\cos x}}\,dx equal to?

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  3. Question 3

    Inverse Trigonometry. Asked once: NDA 2 2023

    28
    What is 1+sin⁡ ⁣(2cos⁡−1 ⁣317)\sqrt{1+\sin\!\left(2\cos^{-1}\!\frac{3}{\sqrt{17}}\right)} equal to?

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  4. Question 4 (case study, 3 parts)

    Limits & Continuity. Asked once: NDA 2 2025

    For the following three (03) items: Consider the function f(x)=x∣x∣f(x)=x|x|.
    73
    What is lim⁡x→−1f(x)\displaystyle\lim_{x\to-1}f(x) equal to?

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    74
    What is the area bounded by the curve f(x)f(x), the xx-axis and the lines x=−2x=-2 and x=1x=1?

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    75
    Consider the following statements: I. The function is increasing in the interval (−∞,∞)(-\infty,\infty). II. The function is differentiable at x=0x=0. Which of the statements given above is/are correct?

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  5. Question 5 (case study, 2 parts)

    Lines. Asked once: NDA 1 2026

    For the next two (02) items that follow: Let X(a,p), Y(b,q) and Z(c,r) be the points such that a, b and c are in AP.
    57
    If p, q and r are in AP, then the points X, Y and Z are

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    58
    If p, q and r are not in AP and b=cb=c, then the line joining the points X, Y and Z is parallel to

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