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Day 258: NDA Maths

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

  1. Question 1 (case study, 2 parts)

    Circles. Asked once: NDA 2 2024

    A triangle ABCABC is inscribed in the circle x2+y2=100x^2+y^2=100. BB and CC have coordinates (6,8)(6,8) and (−8,6)(-8,6) respectively.
    61
    What is ∠BAC\angle BAC equal to?

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    62
    What are the coordinates of AA?

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  2. Question 2

    Complex Numbers. Asked once: NDA 1 2026

    5
    If α\alpha, β\beta, γ\gamma are cube roots of −8-8, then what is α2p2+β2q2+γ2r2β2p2+γ2q2+α2r2\dfrac{\alpha^2p^2+\beta^2q^2+\gamma^2r^2}{\beta^2p^2+\gamma^2q^2+\alpha^2r^2} equal to?

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  3. Question 3

    Conics. Asked once: NDA 2 2024

    60
    Consider the points P(4k,4k)P(4k,4k) and Q(4k,−4k)Q(4k,-4k) lying on the parabola y2=4kxy^2=4kx. If the vertex is AA, then what is ∠PAQ\angle PAQ equal to?

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  4. Question 4

    Definite Integration. Asked once: NDA 1 2024

    77
    Let p=∫abf(x) dxp=\displaystyle\int_a^b f(x)\,dx and q=∫ab∣f(x)∣ dxq=\displaystyle\int_a^b|f(x)|\,dx. If f(x)=e−xf(x)=e^{-x}, then which one of the following is correct?

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  5. Question 5

    Differential Equations. Asked once: NDA 1 2023

    95
    A solution of the differential equation (dydx)2−xdydx=0\left(\dfrac{dy}{dx}\right)^{2}-x\dfrac{dy}{dx}=0 is

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