$A$ solution of sodium in liquid ammonia is blue in colour due to

If ${}^n C_{r-1}=330$,${}^n C_r=462$,and ${}^n C_{r+1}=462$,then $r$ is equal to

Match the items of column $I$ with column $II$. Select the correct option from the following:

Column $I$	Column $II$
$(a)$ $XX$-$XO$ method of sex determination	$(i)$ Turner's syndrome
$(b)$ $XX$-$XY$ method of sex determination	$(ii)$ Female heterogametic
$(c)$ Karyotype-$45$	$(iii)$ Grasshopper
$(d)$ $ZW$-$ZZ$ method of sex determination	$(iv)$ Female homogametic

$A$ body of mass $5 \ kg$ makes an elastic collision with another body at rest and continues to move in the original direction after the collision with a velocity equal to $\frac{1}{10}$th of its original velocity. Then the mass of the second body is (in $kg$)

If $u=\log \left(x^3+y^3+z^3-3 x y z\right)$, then $(x+y+z)(u_x+u_y+u_z)$ is equal to

$100 \ mL$ of $0.6 \ M$ acetic acid is shaken with $2 \ g$ of activated charcoal. After adsorption,the final concentration of the solution becomes $0.5 \ M$. The amount of acetic acid adsorbed per gram of carbon is .......... $g$.