The compressibility factor for an ideal gas is

During the estimation of oxalic acid against $KMnO_4$,the self-indicator is:

$A$ body is projected vertically from the surface of the earth of radius $R$ with a velocity equal to half of the escape velocity. The maximum height reached by the body is

Compound $A$ $(C_3H_6O)$ undergoes the following reactions to form $B$ and $C$. Identify $A$,$B$,and $C$.

Bulk of carbon dioxide $(CO_2)$ released from body tissues into the blood is present as

The line $x=\frac{\pi}{4}$ divides the area of the region bounded by $y=\sin x$,$y=\cos x$ and the $x$-axis $(0 \leq x \leq \frac{\pi}{2})$ into two regions of areas $A_1$ and $A_2$. Then $A_1 : A_2$ equals (in $: 1$)