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Day 231: NDA Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Definite Integration. Asked once: NDA 1 2017 (same type asked 4 times)

    90
    If f(x)f(x) and g(x)g(x) are continuous functions satisfying f(x)=f(a−x)f(x)=f(a-x) and g(x)+g(a−x)=2g(x)+g(a-x)=2, then what is ∫0af(x)g(x) dx\int_0^a f(x)g(x)\,dx equal to?

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  2. Question 2

    Inverse Trigonometry. Asked once: NDA 1 2018 (same type asked 4 times)

    44
    What is tan⁡−1 ⁣(14)+tan⁡−1 ⁣(35)\tan^{-1}\!\left(\frac{1}{4}\right) + \tan^{-1}\!\left(\frac{3}{5}\right) equal to?

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  3. Question 3

    Complex Numbers. Asked once: NDA 1 2017 (same type asked 4 times)

    3
    The value of i2n+i2n+1+i2n+2+i2n+3i^{2n} + i^{2n+1} + i^{2n+2} + i^{2n+3}, where i=−1i = \sqrt{-1}, is

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  4. Question 4

    Probability. Asked once: NDA 2 2021 (same type asked 4 times)

    120
    Seven white balls and three black balls are randomly placed in a row. What is the probability that no two black balls are placed adjacently?

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  5. Question 5

    Complex Numbers. Asked once: NDA 1 2017 (same type asked 4 times)

    6
    The value of (−1+i32)n+(−1−i32)n\left(\dfrac{-1+i\sqrt{3}}{2}\right)^n + \left(\dfrac{-1-i\sqrt{3}}{2}\right)^n, where nn is not a multiple of 3 and i=−1i = \sqrt{-1}, is

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