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Day 2: NDA Maths

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

  1. Question 1

    Probability. This type asked 7 times: NDA 1 2017, NDA 2 2017, NDA 1 2019, NDA 1 2020, NDA 2 2022, NDA 1 2025, NDA 2 2025. This one: NDA 2 2025

    119
    If P(A)=1/3P(A)=1/3, P(B)=1/2P(B)=1/2 and P(A∩B)=1/4P(A\cap B)=1/4, then what is the value of P(Aˉ∪B)P(\bar{A}\cup B)?

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  2. Question 2

    Binomial Distribution. This type asked 6 times: NDA 2 2017, NDA 1 2018, NDA 1 2021, NDA 1 2024, NDA 1 2026, NDA 2 2026. This one: NDA 2 2026

    103
    For a binomial distribution with mean 4 and standard deviation 3\sqrt{3}, what is the value of P(X=0)P(X = 0)?

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  3. Question 3

    Binomial Theorem. This type asked 6 times: NDA 1 2019, NDA 2 2019, NDA 2 2021, NDA 1 2022, NDA 1 2023, NDA 2 2026. This one: NDA 2 2026

    43
    Consider the following statements in respect of the expansion of (x2+x−2+2)4(x^2 + x^{-2} + 2)^4 : I. The number of terms in the expansion is 5. II. One of the coefficients in the expansion has a maximum value equal to 70. Which of the statements given above is/are correct?

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  4. Question 4

    Definite Integration. This type asked 6 times: NDA 1 2018, NDA 1 2021, NDA 2 2022, NDA 1 2024, NDA 2 2024, NDA 2 2026. This one: NDA 2 2026

    75
    If f(x+y)=f(x)+f(y)f(x + y) = f(x) + f(y), then what is ∫−11f(x) dx\int_{-1}^{1} f(x)\,dx equal to?

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  5. Question 5

    Matrices & Determinants. This type asked 6 times: NDA 1 2017, NDA 1 2019, NDA 2 2023, NDA 2 2025, NDA 1 2026, NDA 2 2026. This one: NDA 2 2026

    40
    Let A=(1−tan⁡θtan⁡θ1)A = \begin{pmatrix} 1 & -\tan\theta \\ \tan\theta & 1 \end{pmatrix} and B=(1tan⁡θ−tan⁡θ1)B = \begin{pmatrix} 1 & \tan\theta \\ -\tan\theta & 1 \end{pmatrix} If C=AB−1C = AB^{-1}, then what is det⁡(C)\det(C) equal to?

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