The number of tetrahedral voids present in $0.5 \text{ mole}$ of $HCP$ crystal structure is:

If the plane $3x - 2y - z - 18 = 0$ meets the coordinate axes at $A$,$B$,and $C$,then the centroid of $\triangle ABC$ is:

For $|x| < \frac{1}{5}$,the coefficient of $x^3$ in the expansion of $\frac{1}{(1-5 x)(1-4 x)}$ is

Suppose $\overrightarrow{a}=\lambda \hat{i}-7 \hat{j}+3 \hat{k}$ and $\overrightarrow{b}=\lambda \hat{i}+\hat{j}+2 \lambda \hat{k}$. If the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is greater than $90^{\circ}$,then $\lambda$ satisfies the inequality

Identify $A$ and $B$ in the following reaction:
$A \xrightarrow[\Delta]{aq. NaOH} C_2H_5OH \xleftarrow{AgOH} B$

If you suspect a major deficiency of antibodies in a person,to which of the following would you look for confirmatory evidence?