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Day 45: NDA Maths

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

  1. Question 1

    Probability. Asked 2 times: NDA 2 2017*, NDA 1 2025 (* = numbers or wording changed that year)

    115
    If P(A)=13,P(B)=12P(A)=\frac{1}{3}, P(B)=\frac{1}{2} and P(A∩B)=14P(A\cap B)=\frac{1}{4}, then what is the value of P(B∣Ac)P(B|A^c)?

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  2. Question 2

    Functions. Asked 2 times: NDA 2 2022, NDA 2 2024

    71
    Let z=[y]z=[y] and y=[x]−xy=[x]-x, where [⋅][\cdot] is the greatest integer function. If xx is not an integer but positive, then what is the value of zz?

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  3. Question 3

    Limits & Continuity. Asked 2 times: NDA 1 2023*, NDA 2 2024 (* = numbers or wording changed that year)

    74
    Which one of the following is correct regarding lim⁡x→3∣x−3∣x−3\displaystyle\lim_{x\to3}\dfrac{|x-3|}{x-3}?

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  4. Question 4

    Probability. Asked 2 times: NDA 2 2018*, NDA 2 2024 (* = numbers or wording changed that year)

    104
    A, B, C are three mutually exclusive and exhaustive events associated with a random experiment. If 3P(B)=4P(A)3P(B)=4P(A) and 3P(C)=2P(B)3P(C)=2P(B), then what is P(A)P(A) equal to?

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  5. Question 5

    Functions. Asked 2 times: NDA 2 2022, NDA 2 2024

    73
    What is the minimum value of the function f(x)=log⁡10(x2+2x+11)f(x)=\log_{10}(x^2+2x+11)?

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