$A$ monoatomic gas is suddenly compressed to $(1/8)^{\text{th}}$ of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is (given $\gamma = 5/3$).

In the electrolytic extraction of $Al$,molten cryolite $(Na_3AlF_6)$ is used because it .......

When substance $A$ reacts with water,it produces a combustible gas $B$ and a solution of substance $C$ in water. When another substance $D$ reacts with solution $C$,it produces the same gas $B$ even when reacting with dilute sulfuric acid at room temperature. $A$ imparts a golden yellow color to the non-luminous flame of a Bunsen burner. What are $A$,$B$,$C$,and $D$ respectively?

If $\log 2=a, \log 3=b, \log 7=c$ and $6^x=7^{x+4}$,then $x$ is equal to:

$A$ mass $m$ moving horizontally (along the $x-$ axis) with velocity $v$ collides and sticks to a mass of $3m$ moving vertically upward (along the $y-$ axis) with velocity $2v$. The final velocity of the combination is

The coefficient of $x^{24}$ in the expansion of $(1+x^2)^{12}(1+x^{12})(1+x^{24})$ is