$A$ nuclear fuel rod generates energy at a rate of $5 \times 10^8 \,W/m^3$. It is in the shape of a cylinder of radius $4.0 \,mm$ and length $0.20 \,m$. $A$ coolant of specific heat $4 \times 10^3 \,J \cdot kg^{-1} \cdot K^{-1}$ flows past it at a rate of $0.2 \,kg/s$. The temperature rise in this coolant is approximately ............ $^{\circ}C$.

Fast neutrons can easily be slowed down by

Match the $\text{LIST-I}$ with $\text{LIST-II}$:

$A. \text{ } _0^1 n + { }_{92}^{235} U \rightarrow { }_{54}^{140} Xe + { }_{38}^{94} Sr + 2_0^1 n$	$I. \text{ Chemical reaction}$
$B. \text{ } 2H_2 + O_2 \rightarrow 2H_2O$	$II. \text{ Fusion with } +ve \ Q \text{ value}$
$C. \text{ } _1^2 H + _1^2 H \rightarrow _2^3 He + _0^1 n$	$III. \text{ Fission}$
$D. \text{ } _1^1 H + _1^3 H \rightarrow _1^2 H + _1^2 H$	$IV. \text{ Fusion with } -ve \ Q \text{ value}$

Choose the correct answer from the options given below:

The isotope ${}_{5}^{12}B$ having a mass $12.014 \text{ u}$ undergoes $\beta$-decay to ${}_{6}^{12}C$. ${}_{6}^{12}C$ has an excited state of the nucleus $({}_{6}^{12}C^*)$ at $4.041 \text{ MeV}$ above its ground state. If ${}_{5}^{12}B$ decays to ${}_{6}^{12}C^*$, the maximum kinetic energy of the $\beta$-particle in units of $\text{MeV}$ is ($1 \text{ u} = 931.5 \text{ MeV}/c^2$, where $c$ is the speed of light in vacuum).

If $200 \, MeV$ of energy is released per fission,how many fissions per second must occur in a $1000 \, kW$ reactor?

If the binding energy per nucleon of deuteron $({ }_1 H^2)$ is $1.15 \text{ MeV}$ and an $\alpha$-particle has a binding energy of $7.1 \text{ MeV}$ per nucleon,then the energy released per nucleon in the given reaction is ${ }_1 H^2 + { }_1 H^2 \rightarrow { }_2 He^4 + Q$. (in $\text{ MeV}$)