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Day 92: NDA Maths

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

  1. Question 1

    Definite Integration. Asked once: NDA 2 2024 (same type asked 6 times)

    Let f(t)=ln⁡ ⁣(t+1+t2)f(t)=\ln\!\left(t+\sqrt{1+t^2}\right) and g(t)=tan⁡(f(t))g(t)=\tan(f(t)).
    94
    What is ∫−ππg(t) dt\displaystyle\int_{-\pi}^{\pi}g(t)\,dt equal to?

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  2. Question 2

    Matrices & Determinants. Asked once: NDA 1 2026 (same type asked 6 times)

    17
    If A is a square matrix such that ∣A∣=−2|A|=-2, then ∣AAT∣|AA^T|, where ATA^T is the transpose of A, is equal to

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  3. Question 3

    Probability. Asked once: NDA 2 2021 (same type asked 6 times)

    104
    A problem is given to three students AA, BB and CC, whose probabilities of solving the problem independently are 12\frac{1}{2}, 34\frac{3}{4} and pp respectively. If the probability that the problem can be solved is 2932\frac{29}{32}, then what is the value of pp?

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  4. Question 4

    Probability. Asked once: NDA 1 2025 (same type asked 6 times)

    117
    If two fair dice are tossed, then what is the probability that the sum of the numbers on the faces of the dice is strictly greater than 7?

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  5. Question 5

    Sequence & Series. Asked once: NDA 1 2023 (same type asked 6 times)

    18
    In an AP, the first term is xx and the sum of the first nn terms is zero. What is the sum of next mm terms?

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