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Day 214: NDA Maths

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

  1. Question 1

    Functions. Asked once: NDA 2 2017 (same type asked 5 times)

    72
    The function f(x)=∣x∣−x3f(x) = |x| - x^3 is

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  2. Question 2

    Limits & Continuity. Asked once: NDA 1 2021 (same type asked 5 times)

    93
    If the function f(x)={a+bx,x<15,x=1b−ax,x>1f(x)=\begin{cases}a+bx, & x<1\\5, & x=1\\b-ax, & x>1\end{cases} is continuous, then what is the value of (a+b)(a+b)?

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  3. Question 3

    Differentiation. Asked once: NDA 1 2020 (same type asked 5 times)

    94
    What is the derivative of tan⁡−1x\tan^{-1}x with respect to cot⁡−1x\cot^{-1}x?

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  4. Question 4

    3D Geometry. Asked once: NDA 2 2017 (same type asked 4 times)

    43
    If α\alpha, β\beta and γ\gamma are the angles which the vector OP→\overrightarrow{OP} (OO being the origin) makes with the positive direction of the coordinate axes, then which of the following are correct? 1. cos⁡2α+cos⁡2β=sin⁡2γ\cos^2\alpha + \cos^2\beta = \sin^2\gamma 2. sin⁡2α+sin⁡2β=cos⁡2γ\sin^2\alpha + \sin^2\beta = \cos^2\gamma 3. sin⁡2α+sin⁡2β+sin⁡2γ=2\sin^2\alpha + \sin^2\beta + \sin^2\gamma = 2 Select the correct answer using the code given below.

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  5. Question 5

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

    99
    Geometrically Re(z2−i)=2\text{Re}(z^2-i)=2, where i=−1i=\sqrt{-1} and Re is the real part, represents

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