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1.

At time t = 0, N₁ nuclei of decay constant λ₁ and N₂ nuclei of decay constant λ₂ are mixed. The decay rate of the mixture is:
1. $-N_1{N}_2{e}^{-\left({\lambda }_1+{\lambda }_2\right)t}$ $$
2. $-\left(\frac{N_1}{N_2}\right)$ $e^{{}^{-\left({\lambda }_1+{\lambda }_2\right)t}}$ $$
3. $-\left(N_1{\lambda }_1{e}^{-{\lambda }_{1}t}\right)$ $+$ $N_2{\lambda }_2{e}^{-{\lambda }_{2}t}$ $$
4. $-N_1{\lambda }_1{N}_2{\lambda }_2{e}^{{}^{-\left({\lambda }_1+{\lambda }_2\right)t}}$

2.

A nucleus ${}_n{}^{m}X$ emits one $\alpha$ and two $\beta -$particles. The resulting nucleus is
1. ${}_n{}^{m-4}X$ 
2. ${}_{n-2}{}^{m-4}X$   
3. ${}_{n-4}{}^{m-4}X$ 
4. None of these

3. If the nuclear force between two protons, two neutrons and between a proton and a neutron is denoted by \(F_{pp} ,F_{nn}\) and \(F_{pn}\) respectively, then:
1. \(F_{p p} \approx F_{n n} \approx F_{p n}\)
2. \(F_{p p} \neq F_{n n}\) and \(F_{p n} = F_{n n}\)
3. \(F_{p p} = F_{n n} = F_{p n}\)
4. \(F_{p p} \neq F_{n n} \neq F_{p n}\)

4.

Which of the following is used as a moderator in nuclear reactors? 
1. Plutonium 
2. Cadmium 
3. Heavy water
4. Uranium 

5. In a fission reaction,
\(^{236}_{92}\mathrm{U}\rightarrow ~^{117}\mathrm{X}~+~^{117}\mathrm{Y}~+~^1_0n~+~^1_0n,\) the binding energy per nucleon of \(\mathrm{X}\) and \(\mathrm{Y}\) is \(8.5\) MeV whereas that of \(^{236}\mathrm{U}\) is \(7.6\) MeV. The total energy liberated will be about:
1. \(2000\) MeV
2. \(200\) MeV
3. \(2\) MeV 
4. \(1\) keV

6.

$m_p$ denotes the mass of a proton and  $m_n$ that of a neutron. A given nucleus of binding energy BE, contains Z protons and N neutrons. The mass m (N, Z) of the nucleus is given by 
1. m(N, Z) = N$m_n$+Z$m_p$- BE$c^2$
2. m(N, Z) = N$m_n$ + Z$m_p$ + BE$c^2$
3. m(N, Z) = N$m_n$ + Z$m_p$ - BE / $c^2$
4. m(N, Z) = N$m_n$ + Z$m_p$ + BE / $c^2$

7.

The rate of disintegration of a fixed quantity of a radioactive substance can be increased by:
1. increasing the temperature.
2. increasing the pressure.
3. chemical reaction.
4. it is not possible.

8.

The nucleus ${}_6{}^{12}C$ absorbs an energetic neutron and emits a beta particle $\left({\beta }^{-}\right)$. The resulting nucleus is 
1. ${}_7{}^{14}C$
2. ${}_7{}^{13}N$ 
3. ${}_5{}^{13}B$ 
4. ${}_6{}^{13}C$

9.

The numbers of nuclei of a radioactive substance at time t = 0 are 1000 and 900 at time t = 2 sec. Then the number of nuclei at time t = 4 sec will be:
1. 800
2. 810 
3. 790 
4. 700

10.

A and B are two radioactive substances whose half-lives are 1 and 2 years respectively. Initially 10 g of A and 1 g of B is taken. The time (approximate) after which they will have the same quantity remaining is:
1. 6.62 yr
2. 5 yr   
3. 3.2 yr 
4. 7 yr

11.

In a radioactive decay process, the negatively charged emitted $\beta$-particles are:

1.	The electrons present inside the nucleus.
2.	The electrons produced as a result of the decay of neutrons inside the nucleus.
3.	The electrons produced as a result of collisions between atoms.
4.	The electrons orbiting around the nucleus.

12.

A nucleus ruptures into two nuclear parts which have their velocity ratio equal to 2:1. What will be the ratio of their nuclear size (nuclear radius) ? 
1. $2^{1/3} : 1$ 
2. $1 : 2^{1/3}$ 
3. $3^{1/2} : 1$
4. $1 : 3^{1/2}$

13.

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then,
(1) the helium nucleus has more kinetic energy than the thorium nucleus
(2) the helium nucleus has less momentum than the thorium nucleus
(3) the helium nucleus has more momentum than the thorium nucleus
(4) the helium nucleus has less kinetic energy than the thorium nucleus

14.

The decay constant of a radio isotope is $\mathrm{\lambda }.$ If ${\mathrm{A}}_1$ and ${\mathrm{A}}_2$ are its activities at times ${\mathrm{t}}_1$ and ${\mathrm{t}}_2$ respectively, the number of nuclei which have decayed during the time $({\mathrm{t}}_1-{\mathrm{t}}_2)\; is:$
1. ${\mathrm{A}}_1{\mathrm{t}}_1-{\mathrm{A}}_2{\mathrm{t}}_2$                                       
2. ${\mathrm{A}}_1-{\mathrm{A}}_2$
3. $\frac{({\mathrm{A}}_1-{\mathrm{A}}_2)}{\mathrm{\lambda }}$                                         
4. $\mathrm{\lambda }({\mathrm{A}}_1-{\mathrm{A}}_2)$ 

15. If an electron and a positron annihilate, then the energy released is:
1. \(3.2\times 10^{-13}~\text{J}\)
2. \(1.6\times 10^{-13}~\text{J}\)
3. \(4.8\times 10^{-13}~\text{J}\)
4. \(6.4\times 10^{-13}~\text{J}\)