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Day 62: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

    Differentiation. This type asked 2 times: NDA 1 2020, NDA 1 2025. This one: NDA 1 2025

    Let (x+y)p+q=xpyq(x+y)^{p+q} = x^p y^q, where p,qp, q are positive integers.
    75
    The derivative of yy with respect to xx

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    76
    If p+q=10p + q = 10, then what is dydx\frac{dy}{dx} equal to?

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  2. Question 2 (case study, 2 parts)

    Functions. This type asked 2 times: NDA 2 2024, NDA 1 2025. This one: NDA 1 2025

    The function f(x)f(x) satisfies f(xy)=f(x)f(y)f\left(\dfrac{x}{y}\right) = \dfrac{f(x)}{f(y)} for all positive real values of xx and yy, and f(2)=3f(2) = 3.
    95
    What is f(16)f(16) equal to?

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    96
    What is f(1) f(4)f(1)\,f(4) equal to?

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  3. Question 3

    Lines. This type asked 2 times: NDA 1 2021, NDA 1 2025. This one: NDA 1 2025

    51
    Under what condition will the lines m2x+ny−1=0m^2 x + ny - 1 = 0 and n2x−my+2=0n^2 x - my + 2 = 0 be perpendicular?

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  4. Question 4

    Lines. This type asked 2 times: NDA 1 2024, NDA 1 2025. This one: NDA 1 2025

    54
    Let A(3,−1)A(3,-1) and B(1,1)B(1,1) be the end points of line segment AB. Let P be the middle point of the line segment AB. Let Q be the point situated at a distance 2\sqrt{2} units from P on the perpendicular bisector line of AB. What are the possible coordinates of Q?

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  5. Question 5

    Matrices & Determinants. This type asked 2 times: NDA 1 2017, NDA 1 2025. This one: NDA 1 2025

    26
    If f(θ)=(cos⁡θsin⁡θ−sin⁡θcos⁡θ)f(\theta) = \begin{pmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{pmatrix} then what is {f(π)}2\{f(\pi)\}^2 equal to?

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