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Day 181: NDA Maths

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

  1. Question 1

    Complex Numbers. Asked once: NDA 1 2018 (same type asked 4 times)

    35
    What is ∑n=211(in+in+1)\sum_{n=2}^{11}(i^n + i^{n+1}), where i=−1i = \sqrt{-1}?

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  2. Question 2

    Conics. Asked once: NDA 1 2019 (same type asked 4 times)

    53
    The sum of the focal distances of a point on an ellipse is constant and equal to the

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  3. Question 3

    Definite Integration. Asked once: NDA 2 2018 (same type asked 4 times)

    82
    What is ∫28∣x−5∣ dx\int_2^8 |x-5|\,dx equal to?

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  4. Question 4

    Inverse Trigonometry. Asked once: NDA 1 2022 (same type asked 4 times)

    37
    If 3sin⁡−1x+cos⁡−1x=π3\sin^{-1}x+\cos^{-1}x=\pi, then what is xx equal to?

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  5. Question 5

    Probability. Asked once: NDA 2 2018 (same type asked 4 times)

    101
    If two dice are thrown and at least one of the dice shows 5, then the probability that the sum is 10 or more is

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