The function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x)=\frac{x}{x^2+1} \quad \forall x \in \mathbb{R}$ is
One-one and onto
Onto but not one-one
Neither one-one nor onto
One-one but not onto
$$ \begin{aligned} &\text { Consider two skew lines in 3D space. }\\ &M_1: \frac{x-1}{1}=\frac{2-y}{1}=\frac{z-5}{1} \text { and } M_2: \frac{x+3}{1}=\frac{y-7}{2}=\frac{z+4}{1} \end{aligned} $$
Let $L_1$ be the line of shortest distance (common perpendicular) between $M_1$ and $M_2$
If $L_2$ is a line parallel to the vector $\vec{b}=\hat{\jmath}+\hat{k}$,
Then the acute angle $\boldsymbol{\theta}$ between the lines $L_1$ and $L_2$ is:
$30^{\circ}$
$45^{\circ}$
$\cos ^{-1}\left(\frac{1}{3}\right)$
$60^{\circ}$
$$ \int \frac{d x}{x \sqrt{x^2+4}}= $$
$$ \frac{1}{4} \log \left|\frac{\sqrt{x^2+4}-2}{\sqrt{x^2+4}+2}\right|+C $$
$$ \frac{1}{4} \log \left|\frac{\sqrt{x^2+4}+2}{\sqrt{x^2+4}-2}\right|+C $$
$$ \frac{1}{2} \log \left|\frac{\sqrt{x^2+4}+2}{\sqrt{x^2+4}-2}\right|+C $$
$$ \frac{1}{2} \log \left|\frac{\sqrt{x^2+4}-2}{\sqrt{x^2+4}+2}\right|+C $$
Let $A$ and $B$ be two subsets of $\xi=\{\mathbf{1}, \mathbf{2}, \mathbf{3},-------, \mathbf{4 4}, \mathbf{4 5}\}$ such that
$A=\{x: x$ is divisible by 3 and 4$\}$
$B=\{x: x$ is a perfect square number $\}$
Then $n(B-A)$ equals
2
9
5
1
COMEDK Papers
All year-wise previous year question papers