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Day 190: NDA Maths

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

  1. Question 1 (case study, 2 parts)

    Binomial Theorem. Asked once: NDA 2 2024 (same type asked 3 times)

    Let (8+37)20=U+V(8+3\sqrt{7})^{20}=U+V and (8−37)20=W(8-3\sqrt{7})^{20}=W, where UU is an integer and 0<V<10<V<1.
    45
    What is V+WV+W equal to?

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    46
    What is the value of (U+V)W(U+V)W?

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  2. Question 2

    Circles. Asked once: NDA 2 2017 (same type asked 3 times)

    58
    The equation of the circle which passes through the points (1,0)(1, 0), (0,−6)(0, -6) and (3,4)(3, 4) is

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  3. Question 3

    Complex Numbers. Asked once: NDA 1 2023 (same type asked 3 times)

    20
    If zz is a complex number such that z−1z+1\dfrac{z-1}{z+1} is purely imaginary, then what is ∣z∣|z| equal to?

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  4. Question 4 (case study, 2 parts)

    Differentiation. Asked once: NDA 2 2019 (same type asked 3 times)

    Directions for the following two (02) items : Read the following information and answer the two items that follow : Consider the equation xy=ex−yx^{y} = e^{x-y}.
    84
    What is dydx\dfrac{dy}{dx} at x=1x = 1 equal to ?

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    85
    What is d2ydx2\dfrac{d^{2}y}{dx^{2}} at x=1x = 1 equal to ?

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  5. Question 5

    Inverse Trigonometry. Asked once: NDA 2 2019 (same type asked 3 times)

    45
    What is tan⁡{2tan⁡−1(13)}\tan\left\{2\tan^{-1}\left(\dfrac{1}{3}\right)\right\} equal to ?

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