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Day 175: NDA Maths

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

  1. Question 1

    Limits & Continuity. Asked once: NDA 2 2021 (same type asked 5 times)

    75
    Let f(x)={1+x2k,0<x<2kx,2≤x<4f(x)=\begin{cases}1+\frac{x}{2k},&0<x<2\\kx,&2\le x<4\end{cases}. If lim⁡x→2f(x)\lim_{x\to2}f(x) exists, then what is the value of kk?

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  2. Question 2

    Differentiation. Asked once: NDA 1 2021 (same type asked 5 times)

    91
    What is the derivative of exe^x with respect to xex^e?

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  3. Question 3

    3D Geometry. Asked once: NDA 1 2020 (same type asked 4 times)

    63
    If a line has direction ratios ⟨a+b,b+c,c+a⟩\langle a+b, b+c, c+a\rangle, then what is the sum of the squares of its direction cosines?

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  4. Question 4

    Complex Numbers. Asked once: NDA 2 2021 (same type asked 4 times)

    14
    If z=x+iyz=x+iy, where i=−1i=\sqrt{-1}, then what does the equation zzˉ+∣z∣2+4(z+zˉ)−48=0z\bar{z}+|z|^{2}+4(z+\bar{z})-48=0 represent?

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  5. Question 5

    Differential Equations. Asked once: NDA 1 2022 (same type asked 4 times)

    80
    What does the equation xdydx−2y=0x\frac{dy}{dx}-2y=0 represent?

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