$A$ body of mass $5\, kg$ moving with a velocity $10\, m/s$ collides with another body of mass $20\, kg$ at rest and comes to rest. The velocity of the second body after the collision is ......... $m/s$.

In a galvanometer,$5 \%$ of the total current in the circuit passes through it. If the resistance of the galvanometer is $G$,the shunt resistance $S$ connected to the galvanometer is

The area (in sq. units) of the parallelogram whose diagonals are along the vectors $8 \hat{i}-6 \hat{j}$ and $3 \hat{i}+4 \hat{j}-12 \hat{k}$ is:

The reaction of propane with bromine in the presence of $UV$ light predominantly forms

At the temperature $T$ $(K)$ for the reaction $X_2O_{4(l)} \rightarrow 2XO_{2(g)}$,$\Delta U = x \ kJ \ mol^{-1}$ and $\Delta S = y \ J \ K^{-1} \ mol^{-1}$. The Gibbs energy change for the reaction is (Assume $XO_2$ is an ideal gas):

The ratio of the specific heat capacities of a gas is $1.5$. When the gas undergoes an adiabatic process,its volume is doubled and pressure becomes $P_1$. When the gas undergoes an isothermal process,its volume is doubled and pressure becomes $P_2$. If $P_1 = P_2$,the ratio of the initial pressures of the gas when it undergoes adiabatic and isothermal processes is