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Day 109: NDA Maths

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

  1. Question 1 (case study, 2 parts)

    Functions. Asked once: NDA 2 2019 (same type asked 4 times)

    Directions for the following two (02) items : Read the following information and answer the two items that follow : Let f(x)=x2f(x) = x^{2}, g(x)=tan⁡xg(x) = \tan x and h(x)=ln⁡xh(x) = \ln x.
    79
    For x=π2x = \dfrac{\sqrt{\pi}}{2}, what is the value of [h∘(g∘f)](x)[h \circ (g \circ f)](x) ?

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    80
    What is [f∘(f∘f)](2)[f \circ (f \circ f)](2) equal to ?

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  2. Question 2

    Lines. Asked once: NDA 2 2017 (same type asked 4 times)

    56
    The equation of the line passing through the point (2,3)(2, 3) and the point of intersection of lines 2x−3y+7=02x - 3y + 7 = 0 and 7x+4y+2=07x + 4y + 2 = 0 is

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  3. Question 3

    Differentiation. Asked once: NDA 1 2019 (same type asked 4 times)

    71
    What is the derivative of sec⁡2(tan⁡−1x)\sec^2(\tan^{-1}x) with respect to x?

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  4. Question 4

    Trigonometric Equations. Asked once: NDA 1 2020 (same type asked 4 times)

    43
    If cot⁡α\cot\alpha and cot⁡β\cot\beta are the roots of the equation x2−3x+2=0x^2-3x+2=0, then what is cot⁡(α+β)\cot(\alpha+\beta) equal to?

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  5. Question 5

    Limits & Continuity. Asked once: NDA 2 2018 (same type asked 4 times)

    73
    Consider the function f(x)={sin⁡2x5xif x≠0215if x=0f(x) = \begin{cases} \frac{\sin 2x}{5x} & \text{if } x \neq 0 \\ \frac{2}{15} & \text{if } x = 0 \end{cases}. Which one of the following is correct in respect of the function?

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