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Day 236: NDA Maths

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

  1. Question 1

    Statistics. Asked once: NDA 2 2019 (same type asked 5 times)

    104
    Arithmetic mean of 10 observations is 60 and sum of squares of deviations from 50 is 5000. What is the standard deviation of the observations ?

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  2. Question 2

    Complex Numbers. Asked once: NDA 1 2020 (same type asked 5 times)

    46
    What is the modulus of the complex number cos⁡θ+isin⁡θcos⁡θ−isin⁡θ\frac{\cos\theta+i\sin\theta}{\cos\theta-i\sin\theta}, where i=−1i=\sqrt{-1}?

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  3. Question 3

    Inverse Trigonometry. Asked once: NDA 2 2017 (same type asked 4 times)

    35
    The value of sin⁡−1 ⁣(35)+tan⁡−1 ⁣(17)\sin^{-1}\!\left(\dfrac{3}{5}\right) + \tan^{-1}\!\left(\dfrac{1}{7}\right) is equal to

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  4. Question 4

    Differentiation. Asked once: NDA 2 2017 (same type asked 4 times)

    82
    If y=cos⁡−1 ⁣(2x1+x2)y = \cos^{-1}\!\left(\dfrac{2x}{1+x^2}\right), then dydx\dfrac{dy}{dx} is equal to

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  5. Question 5

    Sequence & Series. Asked once: NDA 2 2017 (same type asked 3 times)

    15
    The value of the product 612×614×618×6116×…6^{\frac{1}{2}} \times 6^{\frac{1}{4}} \times 6^{\frac{1}{8}} \times 6^{\frac{1}{16}} \times \ldots up to infinite terms is

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