An $\alpha$-particle of energy $E$ is liberated during the decay of a nucleus of mass number $236$. The total energy released in this process is

$A$ $^{235}U$ nuclear reactor generates energy at a rate of $3.70 \times 10^7 \text{ J/s}$. Each fission liberates $185 \text{ MeV}$ of useful energy. If the reactor has to operate for $144 \times 10^4 \text{ s}$, the mass of the fuel needed is (Assume Avogadro's number $= 6 \times 10^{23} \text{ mol}^{-1}$, $1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$) (in $\text{ kg}$)

In a nuclear reactor,the fuel is consumed at the rate of $1 \times 10^{-3} \text{ g s}^{-1}$. The power generated in kW is

The binding energy of deuteron $_1^2H$ is $1.112 \, MeV$ per nucleon and an $\alpha$-particle $_2^4He$ has a binding energy of $7.047 \, MeV$ per nucleon. Then in the fusion reaction $_1^2H + _1^2H \to _2^4He + Q$,the energy $Q$ released is ........ $MeV$.

Which of the following statement$(s)$ is/are correct?
$(1)$ The rest mass of a stable nucleus is less than the sum of the rest masses of its constituent nucleons.
$(2)$ The rest mass of a stable nucleus is greater than the sum of the rest masses of its constituent nucleons.
$(3)$ Nuclear fusion involves the fusion of two light nuclei to form a heavier nucleus.
$(4)$ Nuclear fission involves the release of energy by the splitting of a heavy nucleus.

In a reactor, $2 \, kg$ of ${ }_{92} U ^{235}$ fuel is fully used up in $30$ days. The energy released per fission is $200 \, MeV$. Given that the Avogadro number, $N_A = 6.023 \times 10^{26} \, \text{per kilo mole}$ and $1 \, eV = 1.6 \times 10^{-19} \, J$. The power output of the reactor is close to $..... \, MW$.