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Day 352: NDA Maths

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

  1. Question 1

    Limits & Continuity. Asked once: NDA 2 2017

    85
    If f(x)=x(x−x+1)f(x) = x(\sqrt{x} - \sqrt{x+1}), then f(x)f(x) is

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  2. Question 2

    Lines. Asked once: NDA 1 2020

    58
    If the foot of the perpendicular drawn from the point (0,k)(0,k) to the line 3x−4y−5=03x-4y-5=0 is (3,1)(3,1), then what is the value of kk?

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  3. Question 3

    Matrices & Determinants. Asked once: NDA 2 2023

    15
    If ∣x2+3xx−1x+3x+1−2xx−4x−3x+43x∣=ax4+bx3+cx2+dx+e\begin{vmatrix}x^2+3x & x-1 & x+3\\x+1 & -2x & x-4\\x-3 & x+4 & 3x\end{vmatrix} = ax^4+bx^3+cx^2+dx+e, then what is the value of ee?

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  4. Question 4

    Probability. Asked once: NDA 1 2023

    103
    A biased coin with the probability of getting head equal to 14\frac{1}{4} is tossed five times. What is the probability of getting tail in all the first four tosses followed by head?

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  5. Question 5

    Sequence & Series. Asked once: NDA 1 2018

    1
    If n∈Nn \in N, then 121n−25n+1900n−(−4)n121^{n} - 25^{n} + 1900^{n} - (-4)^{n} is divisible by which one of the following?

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