PYQ Vault

Day 297: NDA Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Indefinite Integration. Asked once: NDA 1 2021

    85
    What is ∫dxsec⁡x+tan⁡x\int\frac{dx}{\sec x+\tan x} equal to?

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  2. Question 2

    Inverse Trigonometry. Asked once: NDA 1 2019

    40
    If sin⁡−12p1+p2−cos⁡−11−q21+q2=tan⁡−12x1−x2\sin^{-1}\dfrac{2p}{1+p^2} - \cos^{-1}\dfrac{1-q^2}{1+q^2} = \tan^{-1}\dfrac{2x}{1-x^2}, then what is x equal to?

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  3. Question 3 (case study, 2 parts)

    Limits & Continuity. Asked once: NDA 1 2025

    Let the function f(x)=x2−1f(x) = x^2 - 1.
    89
    What is lim⁡x→1{f∘f(x)}\lim_{x\to1}\{f \circ f(x)\} equal to?

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    90
    What is the area bounded by the function f(x)f(x) and the xx-axis?

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  4. Question 4

    Lines. Asked once: NDA 1 2025

    55
    ABC is an equilateral triangle and AD is the altitude on BC. If the coordinates of A are (1,2)(1, 2) and that of D are (−2,6)(-2, 6), then what is the equation of BC?

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  5. Question 5

    Logarithms. Asked once: NDA 2 2021

    3
    If log⁡102\log_{10} 2, log⁡10(2x−1)\log_{10}(2^{x}-1), log⁡10(2x+3)\log_{10}(2^{x}+3) are in AP, then what is xx equal to?

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