PYQ Vault

Day 296: NDA Maths

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

  1. Question 1

    Conics. Asked once: NDA 1 2020

    55
    In the parabola y2=xy^2=x, what is the length of the chord passing through the vertex and inclined to the x-axis at an angle θ\theta?

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  2. Question 2

    Definite Integration. Asked once: NDA 1 2018

    81
    What is ∫1exln⁡x dx\int_{1}^{e}x\ln x\,dx equal to?

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  3. Question 3

    Differential Equations. Asked once: NDA 2 2018

    88
    The equation of the curve passing through the point (−1,−2)(-1,-2) which satisfies dydx=−x2−1x3\frac{dy}{dx}=-x^2-\frac{1}{x^3}, is

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  4. Question 4

    Differentiation. Asked once: NDA 1 2023

    94
    What is the derivative of cosec⁡(x∘)\cosec(x^{\circ})?

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  5. Question 5

    Functions. Asked once: NDA 2 2024

    Let f(x)=[x]2−[x2]f(x)=[x]^2-[x^2], where [⋅][\cdot] denotes the greatest-integer function.
    83
    What is f(0.999)+f(1.001)f(0.999)+f(1.001) equal to?

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