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Day 333: NDA Maths

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

  1. Question 1

    Differentiation. Asked once: NDA 1 2021

    88
    What is the derivative of sin⁡(ln⁡x)+cos⁡(ln⁡x)\sin(\ln x)+\cos(\ln x) with respect to xx at x=ex=e?

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  2. Question 2

    Functions. Asked once: NDA 1 2023

    96
    If f(x)=x2+2f(x)=x^{2}+2 and g(x)=2x−3g(x)=2x-3, then what is (fg)(1)(fg)(1) equal to?

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  3. Question 3

    Limits & Continuity. Asked once: NDA 1 2021

    92
    If a differentiable function f(x)f(x) satisfies lim⁡x→−1f(x)+1x2−1=−32\lim_{x\to-1}\frac{f(x)+1}{x^2-1}=-\frac{3}{2}, then what is lim⁡x→−1f(x)\lim_{x\to-1}f(x) equal to?

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  4. Question 4 (case study, 2 parts)

    Lines. Asked once: NDA 1 2023

    Consider the following for the next two (02) items that follow: A quadrilateral is formed by the lines x=0x=0, y=0y=0, x+y=1x+y=1 and 6x+y=36x+y=3.
    55
    What is the equation of diagonal through origin?

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    56
    What is the equation of other diagonal?

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  5. Question 5

    Matrices & Determinants. Asked once: NDA 1 2025

    23
    If (x11)(123456789)(11x)=(45)\begin{pmatrix} x & 1 & 1 \end{pmatrix} \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \begin{pmatrix} 1 \\ 1 \\ x \end{pmatrix} = \begin{pmatrix} 45 \end{pmatrix} then which one of the following is a value of xx?

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