The ratio of the speed of sound to the average speed of an air molecule at $300 \,K$ and $1 \,atm$ pressure is close to

The coefficient of $x^n$ in $\frac{1-2x}{e^x}$ is:

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod perpendicular to its length. The acceleration of the centre of mass of the rod is:

In Young's double slit experiment,the phase difference between the light waves reaching the third bright fringe from the central fringe is $(\lambda = 6000 \ \mathring{A})$

Select the two correct statements out of the four $(i-iv)$ given below about the lac operon.
$i.$ Glucose or galactose may bind with the repressor and inactivate it.
$ii.$ In the absence of lactose,the repressor binds with the operator region.
$iii.$ The $z$-gene codes for permease.
$iv.$ This was elucidated by Francois Jacob and Jacques Monod.

$A$ capacitor of capacity $4 \mu F$ is charged to $80 \ V$ and another capacitor of capacity $6 \mu F$ is charged to $30 \ V$. When they are connected,the energy lost by the $4 \mu F$ capacitor is: (in $mJ$)