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Day 8: NDA Maths

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

  1. Question 1

    Complex Numbers. This type asked 5 times: NDA 1 2020, NDA 1 2021, NDA 1 2022, NDA 2 2023, NDA 2 2024. This one: NDA 2 2024

    9
    If Z=13∣i2i12i3i2313∣=x+iyZ=\frac{1}{3}\begin{vmatrix}i & 2i & 1 \\ 2i & 3i & 2 \\ 3 & 1 & 3 \end{vmatrix} = x + iy where i=−1i=\sqrt{-1}, then what is the modulus of ZZ?

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  2. Question 2

    Functions. This type asked 5 times: NDA 1 2017, NDA 2 2017, NDA 1 2019, NDA 2 2022, NDA 2 2024. This one: NDA 2 2024

    93
    Let f(t)=ln⁡ ⁣(t+1+t2)f(t)=\ln\!\left(t+\sqrt{1+t^2}\right) and g(t)=tan⁡(f(t))g(t)=\tan(f(t)). Consider the following statements: A. f(t)f(t) is an odd function. B. g(t)g(t) is an odd function. Which of the statements given above is/are correct?

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  3. Question 3

    Differential Equations. This type asked 5 times: NDA 2 2017, NDA 2 2018, NDA 1 2019, NDA 1 2021, NDA 1 2024. This one: NDA 1 2024

    72
    The differential equation representing the curve y=ex(acos⁡x+bsin⁡x)y=e^x(a\cos x+b\sin x), where aa and bb are arbitrary constants, is

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  4. Question 4 (case study, 2 parts)

    Limits & Continuity. This type asked 5 times: NDA 2 2019, NDA 1 2021, NDA 2 2021, NDA 1 2023, NDA 2 2023. This one: NDA 2 2023

    Let f(x)=x−3∣x−3∣+a; x<3f(x)=\frac{x-3}{|x-3|}+a;\ x<3, a−b; x=3a-b;\ x=3, x−3∣x−3∣+b; x>3\frac{x-3}{|x-3|}+b;\ x>3. f(x)f(x) is continuous at x=3x=3.
    59
    What is the value of aa?

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    60
    What is the value of bb?

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  5. Question 5

    Differentiation. This type asked 5 times: NDA 2 2019, NDA 1 2020, NDA 1 2021, NDA 2 2021, NDA 1 2023. This one: NDA 1 2023

    92
    What is the derivative of sin⁡2x\sin^{2}x with respect to cos⁡2x\cos^{2}x?

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