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Day 241: NDA Maths

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

  1. Question 1

    Differential Equations. Asked once: NDA 2 2025

    93
    Consider the following statements: I. y=xe2xy=xe^{2x} is the solution of dydx=y ⁣(2+1x)\dfrac{dy}{dx}=y\!\left(2+\dfrac{1}{x}\right). II. y=xln⁡∣x∣+cxy=x\ln|x|+cx is the solution of dydx=x+yx\dfrac{dy}{dx}=\dfrac{x+y}{x}. Which of the statements given above is/are correct?

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  2. Question 2

    Differentiation. Asked once: NDA 2 2026

    94
    If f(x)=xn−1+xn−2+xn−3+…+1f(x) = x^{n-1} + x^{n-2} + x^{n-3} + \ldots + 1 then what is f′(2)f'(2) equal to?

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  3. Question 3

    Functions. Asked once: NDA 2 2026

    93
    Let ff be a differentiable function such that f(x+y)=f(x)+f(y)f(x + y) = f(x) + f(y) for all x,y∈Rx, y \in R. Which of the following statements is/are correct? I. If f(x)=x g(x)f(x) = x\, g(x), then the derivative of f(x)f(x) with respect to xx is equal to g(0)g(0). II. If f(x)=x2g(x)f(x) = x^2 g(x), then the derivative of f(x)f(x) with respect to xx is equal to 0. (Here gg is a continuous function) Select the answer using the code given below.

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  4. Question 4 (case study, 2 parts)

    Height & Distance. Asked once: NDA 1 2025

    The top (M) of a tower is observed from three points P, Q and R lying in a horizontal straight line which passes directly along the foot (N) of the tower. The angles of elevations of M from P, Q and R are 30°, 45° and 60° respectively. Let PQ = a and QR = b.
    39
    What is PN equal to?

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    40
    What is MN equal to?

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  5. Question 5

    Indefinite Integration. Asked once: NDA 2 2026

    71
    What is ∫x1−x3 dx\int \frac{\sqrt{x}}{\sqrt{1 - x^3}}\,dx equal to?

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