In the nuclear fission of one nucleus of $U^{235}$, the energy released is $188 \text{ MeV}$. The energy released in the nuclear fission of $235 \text{ g}$ of $U^{235}$ is nearly (Avogadro number $= 6.02 \times 10^{23} \text{ mol}^{-1}$)

$A$ heavy nucleus $N$,at rest,undergoes fission $N \rightarrow P+Q$,where $P$ and $Q$ are two lighter nuclei. Let $\delta=M_N-M_P-M_Q$,where $M_P, M_Q$ and $M_N$ are the masses of $P, Q$ and $N$,respectively. $E_P$ and $E_Q$ are the kinetic energies of $P$ and $Q$,respectively. The speeds of $P$ and $Q$ are $v_P$ and $v_Q$,respectively. If $c$ is the speed of light,which of the following statement$(s)$ is(are) correct?
$(A)$ $E_P+E_Q=c^2 \delta$
$(B)$ $E_P=\left(\frac{M_P}{M_P+M_Q}\right) c^2 \delta$
$(C)$ $\frac{v_P}{v_Q}=\frac{M_Q}{M_P}$
$(D)$ The magnitude of momentum for $P$ as well as $Q$ is $c \sqrt{2 \mu \delta}$,where $\mu=\frac{M_P M_Q}{M_P+M_Q}$

The energy released by the fission of a single uranium nucleus is $200 \,MeV$. The number of fissions of uranium nucleus per second required to produce $16 \,MW$ of power is (Assume efficiency of the reactor is $50\%$).

Find the value of $x$ and $y$ in the following nuclear reaction:
${}_{92}^{235} U + {}_{0}^{1} n \rightarrow {}_{x}^{133} Sb + {}_{41}^{y} Nb + 4 {}_{0}^{1} n$

How long can an electric lamp of $100\; W$ be kept glowing by the fusion of $2.0\; kg$ of deuterium? Take the fusion reaction as $_{1}^{2} H + _{1}^{2} H \rightarrow _{2}^{3} He + n + 3.27\; MeV$.

Suppose India had a target of producing by $2020\; AD$, $200,000\; MW$ of electric power, ten percent of which was to be obtained from nuclear power plants. Suppose we are given that, on an average, the efficiency of utilization (i.e., conversion to electric energy) of thermal energy produced in a reactor was $25\%$. How much amount of fissionable uranium would our country need per year by $2020$? Take the heat energy per fission of $^{235}_{92}U$ to be about $200\; MeV$.