$A$ vessel contains hydrogen and nitrogen gases in the ratio $2:3$ by mass. If the temperature of the mixture of the gases is $30^{\circ} C$, then the ratio of the average kinetic energies per molecule of hydrogen and nitrogen gases is $($Molecular mass of hydrogen $=2$ and molecular mass of nitrogen $=28)$

The number of integer values of $m$, for which the $x$-coordinate of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is also an integer, is

Consider the following statements about manganate and permanganate ions. Identify the correct statements:
$(A)$ The geometry of both manganate and permanganate ions is tetrahedral.
$(B)$ The oxidation states of $Mn$ in manganate and permanganate are $+7$ and $+6$, respectively.
$(C)$ Oxidation of $Mn(II)$ salt by peroxodisulphate gives manganate ion as the final product.
$(D)$ Manganate ion is paramagnetic and permanganate ion is diamagnetic.
$(E)$ Acidified permanganate ion reduces oxalate, nitrite and iodide ions.
Choose the correct answer from the options given below:

$A$ metal $M$ which is not affected by strong acids like conc. $HNO_3$,conc. $H_2SO_4$ and conc. solutions of alkalies like $NaOH$,$KOH$ forms $MCl_3$ which finds use for toning in photography. The metal $M$ is

In a series resonant $LCR$ circuit,the voltage across $R$ is $100\,V$ and $R = 1\,k\Omega$ with $C = 2\,\mu F$. The resonant frequency $\omega$ is $200\,rad/s$. At resonance,the voltage across $L$ is:

Explain the structures of diborane and boric acid.