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Day 115: NDA Maths

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

  1. Question 1

    Binomial Theorem. Asked once: NDA 1 2025 (same type asked 3 times)

    22
    If k<(2+1)3<k+2k < (\sqrt{2}+1)^3 < k+2, where kk is a natural number, then what is the value of kk?

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  2. Question 2 (case study, 2 parts)

    Circles. Asked once: NDA 2 2021 (same type asked 3 times)

    Direction: Consider the following for the next two (02) items that follow. A circle is passing through the points (5, -8), (-2, 9) and (2, 1).
    51
    What are the coordinates of the centre of the circle?

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    52
    If rr is the radius of the circle, then which one of the following is correct?

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  3. Question 3

    Complex Numbers. Asked once: NDA 1 2024 (same type asked 3 times)

    9
    Let z1z_1 and z2z_2 be two complex numbers such that ∣z1+z2z1−z2∣=1\left|\dfrac{z_1+z_2}{z_1-z_2}\right|=1, then what is Re ⁣(z1z2)+1\text{Re}\!\left(\dfrac{z_1}{z_2}\right)+1 equal to?

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  4. Question 4

    Differentiation. Asked once: NDA 1 2022 (same type asked 3 times)

    69
    If xyyx=1x^y y^x=1, then what is dydx\frac{dy}{dx} at (1,1)(1,1) equal to?

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  5. Question 5

    Inverse Trigonometry. Asked once: NDA 1 2024 (same type asked 3 times)

    42
    What is 15+cot⁡2 ⁣(π4−2cot⁡−13)\sqrt{15+\cot^2\!\left(\dfrac{\pi}{4}-2\cot^{-1}3\right)} equal to?

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