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Day 143: NDA Maths

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

  1. Question 1

    Differentiation. Asked once: NDA 2 2023 (same type asked 2 times)

    66
    If f′(x)=cos⁡(ln⁡x)f'(x)=\cos(\ln x) and y=f ⁣(2x−3x)y=f\!\left(\frac{2x-3}{x}\right), then what is dydx\frac{dy}{dx} equal to?

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  2. Question 2

    Limits & Continuity. Asked once: NDA 2 2017 (same type asked 2 times)

    91
    Let gg be the greatest integer function. Then the function f(x)=(g(x))2−g(x2)f(x) = (g(x))^2 - g(x^2) is discontinuous at

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  3. Question 3

    Matrices & Determinants. Asked once: NDA 2 2023 (same type asked 2 times)

    7
    Let AA be a skew-symmetric matrix of order 3. What is the value of det⁡(4A4)−det⁡(3A3)+det⁡(2A2)−det⁡(A)+det⁡(−I)\det(4A^4) - \det(3A^3) + \det(2A^2) - \det(A) + \det(-I)?

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  4. Question 4

    Probability. Asked once: NDA 1 2023 (same type asked 2 times)

    117
    One bag contains 3 white and 2 black balls, another bag contains 2 white and 3 black balls. Two balls are drawn from the first bag and put into the second bag and then a ball is drawn from the second bag. What is the probability that it is white?

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  5. Question 5

    Probability. Asked once: NDA 1 2024 (same type asked 2 times)

    101
    A bag contains 5 black and 4 white balls. A man selects two balls at random. What is the probability that both of these are of the same colour?

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