A.

1

The multiplication factor (k) is an important reactor parameter and is the ratio of number of neutrons present at the beginning of a particular generation to the number present at the beginning of the next generation. It is a measure of the growth rate of the neutrons in the reactor. For k =l, the operation of the reactor is said to be critical.

 Note: If k becomes greater than one, the reaction rate and the reactor power increase exponentially. Unless the factor k is brought down very close to unity, the reactor will become supercritical and can even explode.

D.

colour changes to red and also intensity gets reduced

As batteries wear out, temperature of filament of flash light attains lesser value, therefore intensity of radiation reduces. Also dominating wavelength (λ_m ) in spectrum, which is the red colour, increases.

D.

None all have same wavelength

On the basis of dual nature of light, Lious de-Broglie suggested that the dual nature is not only of light, but each moving material particle has the dual nature.

He assumed a wave to be associated with each moving material particle which is called the matter wave. The wavelength of this wave is determined by the momentum of the particle. If p is the momentum of the particle, the wavelength of the wave associated with it is

                                     $\mathrm{\lambda } = \frac{\mathrm{h}}{\mathrm{p}}$ 

Where h is Planck's constant.

Since it is given that alpha, beta and gamma rays carry same momentum, so they will have same wavelength.

C.

1 : 4

Total number of nuclei remained after n half- lives is 

             N = N_o ${\left(\frac{1}{2}\right)}^{\mathrm{n}}$

Total time given = 80 min

Number of half-lives of A, n_A = $\frac{80 \min }{20 \min }$

                                           = 4

Number of half-lives of B, n_B = $\frac{80 \min }{40 \min }$

                                           = 2

Number of nuclei remains undecayed

                    $\mathrm{N} ={\mathrm{N}}_{\mathrm{o}} {\left(\frac{1}{2}\right)}^{\mathrm{n}}$

Where N_o is initial number of nuclei.

            $\therefore \frac{{\mathrm{N}}_{\mathrm{A}}}{{\mathrm{N}}_{\mathrm{B}}} = \frac{{\displaystyle {\left(\frac{1}{2}\right)}^{{\mathrm{n}}_{\mathrm{A}}}}}{{\displaystyle {\left(\frac{1}{2}\right)}^{{\mathrm{n}}_{\mathrm{B}}}}}$

            $$\begin{gathered} \Rightarrow \frac{ {\mathrm{N}}_{\mathrm{A}}}{{\mathrm{N}}_{\mathrm{B}}} = \frac{{\left({\displaystyle \frac{1}{2}}\right)}^4}{{\left({\displaystyle \frac{1}{2}}\right)}^2} \\ =\frac{{\displaystyle \frac{1}{16}}}{{\displaystyle \frac{1}{4}}} \end{gathered}$$

               $\Rightarrow \frac{{\mathrm{N}}_{\mathrm{A}}}{{\mathrm{N}}_{\mathrm{B}}} = \frac{1}{4}$

A.

Two images are formed

Since, lens is made of two layers of different refractive indices, for a given wavelength of light it will have two focal lengths or will form two images at two different points as there are μ's is

                $\frac{1}{\mathrm{f}} \propto \left(\mathrm{\mu } - 1\right)$