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Day 311: NDA Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Differentiation. Asked once: NDA 2 2022

    90
    If ddx ⁣(1+x4+x81−x2+x4)=ax+bx3\frac{d}{dx}\!\left(\frac{1+x^4+x^8}{1-x^2+x^4}\right) = ax+bx^3, then which one of the following is correct?

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  2. Question 2

    Functions. Asked once: NDA 1 2024

    35
    Let A={1,2,3,4,5}A=\{1,2,3,4,5\} and B={6,7}B=\{6,7\}. What is the number of onto functions from AA to BB?

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  3. Question 3

    Indefinite Integration. Asked once: NDA 2 2019

    82
    What is ∫dxx(1+ln⁡x)n\displaystyle\int \dfrac{dx}{x(1 + \ln x)^{n}} equal to (n≠1)(n \neq 1) ?

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  4. Question 4

    Inverse Trigonometry. Asked once: NDA 1 2017

    47
    Let xx, yy, zz be positive real numbers such that xx, yy, zz are in GP and tan⁡−1x\tan^{-1}x, tan⁡−1y\tan^{-1}y and tan⁡−1z\tan^{-1}z are in AP. Then which one of the following is correct?

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  5. Question 5 (case study, 2 parts)

    Limits & Continuity. Asked once: NDA 2 2023

    Let f(x)=ax−1+bx−12f(x)=\dfrac{a^{x-1}+b^{x-1}}{2} and g(x)=x−1g(x)=x-1.
    53
    What is lim⁡x→1f(x)−1g(x)\lim_{x\to1}\frac{f(x)-1}{g(x)} equal to?

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    54
    What is lim⁡x→1f(x)1/g(x)\lim_{x\to1}f(x)^{1/g(x)} equal to?

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