$n$ moles of an ideal gas at temperature $T$ (in kelvin) occupy $V \ L$ of volume,exerting a pressure of $P$ atmospheres. What is the concentration (in $mol / L$)?

Two ideal slits $S_1$ and $S_2$ are at a distance $d$ apart and are illuminated by light of wavelength $\lambda$ passing through an ideal source slit $S$ placed on the line through $S_2$ as shown. The distance between the plane of the slits and the source slit is $D$. $A$ screen is held at a distance $D$ from the plane of the slits. The minimum value of $d$ for which there is darkness at $O$ is

The final product $(III)$ obtained in the reaction sequence:
$CH_3CH_2COOH$ $\xrightarrow{PCl_3} I$ $\xrightarrow[AlCl_3]{C_6H_6} II$ $\xrightarrow[base, heat]{NH_2NH_2} III$ is

If the slope of one line of the pair of lines $2x^2 + hxy + 6y^2 = 0$ is thrice the slope of the other line,then $h =$

Two pendulums have time periods $T$ and $5T/4$. They start $SHM$ at the same time from the mean position. After how many oscillations of the smaller pendulum will they be again in the same phase?

If $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,then $\frac{b-d}{c-a}$ is equal to