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Day 206: NDA Maths

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

  1. Question 1

    Probability. Asked once: NDA 1 2021 (same type asked 2 times)

    120
    If AA and BB are two events such that P(A)=34P(A)=\frac{3}{4} and P(B)=58P(B)=\frac{5}{8}, then consider the following statements: 1. The minimum value of P(A∪B)P(A\cup B) is 34\frac{3}{4}. 2. The maximum value of P(A∩B)P(A\cap B) is 58\frac{5}{8}. Which of the above statements is/are correct?

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  2. Question 2

    Binomial Theorem. Asked once: NDA 1 2021 (same type asked 2 times)

    46
    What is C(n,1)+C(n,2)+⋯+C(n,n)C(n,1)+C(n,2)+\cdots+C(n,n) equal to?

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  3. Question 3

    Complex Numbers. Asked once: NDA 1 2019 (same type asked 2 times)

    11
    The common roots of the equations z3+2z2+2z+1=0z^3 + 2z^2 + 2z + 1 = 0 and z2017+z2018+1=0z^{2017} + z^{2018} + 1 = 0 are

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  4. Question 4

    Binomial Theorem. Asked once: NDA 1 2018 (same type asked 2 times)

    3
    In the expansion of (1+x)43(1+x)^{43}, if the coefficients of (2r+1)th(2r+1)^{\text{th}} and (r+2)th(r+2)^{\text{th}} terms are equal, then what is the value of rr (r≠1)(r \ne 1)?

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  5. Question 5

    Indefinite Integration. Asked once: NDA 2 2017 (same type asked 2 times)

    88
    ∫(ln⁡x)−1 dx−∫(ln⁡x)−2 dx\displaystyle\int (\ln x)^{-1}\,dx - \int (\ln x)^{-2}\,dx is equal to

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