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Day 232: NDA Maths

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

  1. Question 1

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

    66
    If y=sec⁡−1 ⁣(x+1x−1)+sin⁡−1 ⁣(x−1x+1)y = \sec^{-1}\!\left(\dfrac{x+1}{x-1}\right) + \sin^{-1}\!\left(\dfrac{x-1}{x+1}\right), then dydx\dfrac{dy}{dx} is equal to

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  2. Question 2

    Probability. Asked once: NDA 2 2019 (same type asked 3 times)

    102
    A bag contains 20 books out of which 5 are defective. If 3 of the books are selected at random and removed from the bag in succession without replacement, then what is the probability that all three books are defective ?

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  3. Question 3

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

    23
    If y=x+x2+x3+…y = x + x^2 + x^3 + \ldots up to infinite terms, where x<1x < 1, then which one of the following is correct?

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  4. Question 4

    Lines. Asked once: NDA 1 2018 (same type asked 8 times)

    52
    What is the angle between (m2−mn)y=(mn+n2)x+n3(m^2-mn)y=(mn+n^2)x+n^3 and (mn+m2)y=(mn−n2)x+m3(mn+m^2)y=(mn-n^2)x+m^3, where m>nm>n?

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  5. Question 5

    Matrices & Determinants. Asked once: NDA 2 2017 (same type asked 8 times)

    3
    The matrix AA has xx rows and x+5x+5 columns. The matrix BB has yy rows and 11−y11-y columns. Both ABAB and BABA exist. What are the values of xx and yy respectively?

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