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Day 111: NDA Maths

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

  1. Question 1

    Differentiation. Asked once: NDA 2 2026 (same type asked 3 times)

    92
    If y=∣sin⁡(π4−x)∣y = \left| \sin\left(\frac{\pi}{4} - x\right) \right|, then what is dydx\frac{dy}{dx} at x=π4x = \frac{\pi}{4} equal to?

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  2. Question 2

    Functions. Asked once: NDA 1 2019 (same type asked 3 times)

    86
    If f(x)=x−2x+2f(x)=\dfrac{x-2}{x+2}, x≠−2x\neq-2, then what is f−1(x)f^{-1}(x) equal to?

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  3. Question 3

    Height & Distance. Asked once: NDA 2 2018 (same type asked 3 times)

    41
    The top of a hill observed from the top and bottom of a building of height h is at angles of elevation π6\frac{\pi}{6} and π3\frac{\pi}{3} respectively. What is the height of the hill?

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  4. Question 4

    Indefinite Integration. Asked once: NDA 1 2020 (same type asked 3 times)

    78
    If p(x)=(4e)2xp(x)=(4e)^{2x}, then what is ∫p(x) dx\int p(x)\,dx equal to?

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  5. Question 5

    Inverse Trigonometry. Asked once: NDA 2 2025 (same type asked 3 times)

    50
    What is the value of tan⁡ ⁣[12sec⁡−1 ⁣(23)]\tan\!\left[\dfrac{1}{2}\sec^{-1}\!\left(\dfrac{2}{\sqrt{3}}\right)\right]?

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