In the following reaction,$X$ and $Y$ respectively are:
$C_2H_5OH \xrightarrow{KMnO_4 / H^{+}} X$
$X \xrightarrow[H_2SO_4 / \Delta]{Y} CH_3COOC_2H_5$

The period of $f(x)=\cos \left(\frac{x}{3}\right)+\sin \left(\frac{x}{2}\right)$ is (in $\pi$)

Viruses behave as non-living entities because outside the host cell they:

In the following common emitter circuit,if $\beta = 100$,$V_{CE} = 7\,V$,$V_{BE} = 0$,and $R_C = 2\,k\Omega$,then find the value of $I_B$ in $mA$.

Two persons $A$ and $B$ are located in the $X-Y$ plane at the points $(0,0)$ and $(0,10)$ respectively. (The distances are measured in $MKS$ units). At time $t=0$,they start moving simultaneously with velocities $\overrightarrow{v}_A = 2\hat{j} \text{ m/s}$ and $\overrightarrow{v}_B = 2\hat{i} \text{ m/s}$ respectively. The time after which $A$ and $B$ are at their closest distance is