If $y = \frac{3}{4} + \frac{3 \cdot 5}{4 \cdot 8} + \frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12} + \ldots \infty$,then:

If the number of $5$-element subsets of the set $A = \{a_1, a_2, \ldots, a_{20}\}$ of $20$ distinct elements is $k$ times the number of $5$-element subsets containing $a_4$,then $k$ is

${ }^{234}Th_{90}$ gets converted to ${ }^{206}Pb_{82}$ through a series of radioactive decay processes. The number of alpha and beta particles lost in this transformation respectively,are

An electronic transition in a hydrogen atom results in the formation of the $H_\alpha$ line of the hydrogen spectrum in the Lyman series. The energies associated with the electron in each of the orbits involved in the transition (in $kcal \ mol^{-1}$) are:

What are the metal ions present in carnallite?

$A$ vessel has $6 \ g$ of oxygen at pressure $P$ and temperature $400 \ K$. $A$ small hole is made in it so that oxygen leaks out. How much oxygen leaks out if the final pressure is $\frac{P}{2}$ and temperature is $300 \ K$ (in $g$)?