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Day 171: NDA Maths

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

  1. Question 1

    Application of Derivatives. Asked once: NDA 1 2022 (same type asked 5 times)

    76
    In which one of the following intervals is the function f(x)=x33−7x22+6x+5f(x)=\frac{x^3}{3}-\frac{7x^2}{2}+6x+5 decreasing?

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  2. Question 2

    Limits & Continuity. Asked once: NDA 1 2020 (same type asked 5 times)

    91
    Consider the following statements for f(x)=e−∣x∣f(x)=e^{-|x|}: 1. The function is continuous at x=0x=0. 2. The function is differentiable at x=0x=0. Which of the above statements is/are correct?

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  3. Question 3

    Matrices & Determinants. Asked once: NDA 1 2024 (same type asked 5 times)

    1
    Let AA and BB be matrices of order 3×33\times 3. If ∣A∣=122|A| = \dfrac{1}{2\sqrt{2}} and ∣B∣=1729|B| = \dfrac{1}{729}, then what is the value of ∣2B (adj(3A))∣\left|2B\,(\mathrm{adj}(3A))\right|?

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  4. Question 4

    Probability. Asked once: NDA 2 2023 (same type asked 5 times)

    105
    A, B, C, D are mutually exclusive and exhaustive. If 2P(A)=3P(B)=4P(C)=5P(D)2P(A)=3P(B)=4P(C)=5P(D), then what is 77P(A)77P(A) equal to?

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  5. Question 5

    Sequence & Series. Asked once: NDA 2 2021 (same type asked 5 times)

    10
    If 1b+c\frac{1}{b+c}, 1c+a\frac{1}{c+a}, 1a+b\frac{1}{a+b} are in HP, then which of the following is/are correct? 1. aa, bb, cc are in AP 2. (b+c)2(b+c)^{2}, (c+a)2(c+a)^{2}, (a+b)2(a+b)^{2} are in GP Select the correct answer using the code given below.

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