The kinetic energy needed to project a body of mass $m$ from the earth's surface (radius $R$) to infinity is

For $k=1, 2, 3$,the box $B_k$ contains $k$ red balls and $(k+1)$ white balls. Let $P(B_1)=\frac{1}{2}$,$P(B_2)=\frac{1}{3}$,and $P(B_3)=\frac{1}{6}$. $A$ box is selected at random and a ball is drawn from it. If a red ball is drawn,then the probability that it has come from box $B_2$ is:

The method of zone refining of metals is based on the principle of:

At $T \text{ K}$,the ratio of kinetic energies of $4 \text{ g}$ of $H_{2(g)}$ and $8 \text{ g}$ of $O_{2(g)}$ is

The equation of a straight line,perpendicular to $3x - 4y = 6$ and forming a triangle of area $6$ sq. units with the coordinate axes,is

One mole of the complex compound $Co(NH_3)_5Cl_3$ gives $3$ moles of ions on dissolution in water. One mole of the same complex reacts with two moles of $AgNO_3$ solution to yield two moles of $AgCl_{(s)}$. The structure of the complex is :-