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Day 27: NDA Maths

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

  1. Question 1

    Complex Numbers. This type asked 3 times: NDA 1 2023, NDA 1 2024, NDA 1 2026. This one: NDA 1 2026

    4
    Let Z1Z_1 and Z2Z_2 be complex numbers such that 3Z14Z2\dfrac{3Z_1}{4Z_2} is purely imaginary. What is ∣Z1+Z2Z1−Z2∣\left|\dfrac{Z_1+Z_2}{Z_1-Z_2}\right| equal to?

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  2. Question 2 (case study, 2 parts)

    Differentiation. This type asked 3 times: NDA 2 2019, NDA 1 2022, NDA 1 2026. This one: NDA 1 2026

    For the next two (02) items that follow: Let (ey)x−y=0(e^y)^x-y=0, where y is a function of x whose domain is (0,10].
    81
    What is dydx\dfrac{dy}{dx} equal to?

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    82
    What is dydx\dfrac{dy}{dx} equal to, given that y=y0y=y_0 when x=1x=1?

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  3. Question 3

    Inverse Trigonometry. This type asked 3 times: NDA 2 2019, NDA 1 2024, NDA 1 2026. This one: NDA 1 2026

    35
    What is tan⁡ ⁣[2tan⁡−112−π4]\tan\!\left[2\tan^{-1}\dfrac{1}{2}-\dfrac{\pi}{4}\right] equal to?

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  4. Question 4

    Matrices & Determinants. This type asked 3 times: NDA 2 2023, NDA 2 2024, NDA 1 2026. This one: NDA 1 2026

    20
    If Mk=(kk−1k−1k)M_k=\begin{pmatrix}k & k-1\\k-1 & k\end{pmatrix} where kk is a natural number, then what is ∣M1∣+∣M2∣+∣M3∣+…+∣M50∣|M_1|+|M_2|+|M_3|+\ldots+|M_{50}| equal to?

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  5. Question 5

    Sequence & Series. This type asked 3 times: NDA 2 2024, NDA 1 2025, NDA 1 2026. This one: NDA 1 2026

    1
    Let p, q and r be three unequal numbers such that p, q and r are in AP. If (q−p)(q-p), (r−q)(r-q) and pp are in GP, then (p+q):(q+r):(r+p)(p+q):(q+r):(r+p) equals

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