51.

A radioactive nucleus is being produced  at  a constant  rate  $\mathrm{\alpha }$  per  second. Its  decay  constant  is  λ. If N₀ are the  number  of  nuclei  at  time  t = 0, then the maximum number of  nuclei possible are

• N₀  +  $\frac{\mathrm{\alpha }}{\mathrm{\lambda }}$

• N₀

• $\frac{\mathrm{\lambda }}{\mathrm{\alpha }}$ + N₀

• $\frac{\mathrm{\alpha }}{\mathrm{\lambda }}$

In a concave mirror, an object is placed at a distance  d₁  from  the focus  and  the image is formed  at  a distance d₂ from the focus. Then the focal length of the mirror is

• $\sqrt{{\mathrm{d}}_1 {\mathrm{d}}_2}$

• d₁ d₂ 

• (d₁ + d₂ )/ 2

• $\sqrt{\raisebox{1ex}{${\mathrm{d}}_1$}\!\left/ \!\raisebox{-1ex}{${\mathrm{d}}_2$}\right.}$

A short linear object, of length l, lies along  the  axis  of  a  concave  mirror, of focal length f, at a distance d from the pole of the mirror. The  size  of  the  image  is  then (nearly)  

• $- \frac{\mathrm{l} \mathrm{f}}{\mathrm{d} - \mathrm{f}}$

• $\frac{\mathrm{d} - \mathrm{f}}{\mathrm{l} \mathrm{f}}$

• $\mathrm{l} \frac{{\mathrm{f}}^2}{{\left(\mathrm{d} - \mathrm{f}\right)}^2}$

• $\frac{{\left(\mathrm{d} - \mathrm{f}\right)}^2}{{\mathrm{f}}^2} \mathrm{l}$

Assertion:  A  total  reflecting  prism  is  used  to erect  the  inverted  image  without deviation. 

Reason:  Rays  of  light  incident  parallel  to  base  of  prism  emerge  out  as  parallel rays.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false.

Assertion: The  edges  of  the  images  of  white  object  formed  by  a  concave  mirror  on  the  screen  appear white. 

Reason:  Concave  mirror  does  not  suffer  chromatic aberration.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false

Assertion:  A photon has no rest mass, yet it carries definite momentum.

Reason:  Momemtum of photon is due to its energy and hence its equivalent mass.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false

Assertion:  A photocell is called an electric eye. 

Reason:  When light is incident on some semiconductor its electrical resistance is reduced.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion 

• If assertion is true but reason is false

• If both assertion and reason are false

Assertion: Nuclei  having mass  number  about  60 are  most stable. 

Reason:  When  two  or  more  light  nuclei  are  combined  into  a  heavier  nucleus, then the binding  energy  per  nucleon  will increase.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false

Assertion:  In  a  common-emitter  amplfier,  the  load  resistance  of  the  output  circuit is 1000  times  the load  resistance of  the  input  circuit. If  $\mathrm{\alpha }$ = 0.98, then  voltage  gain  is 49 x 10³.

Reason:  $\mathrm{\alpha } = \frac{\mathrm{\alpha }}{1 - \mathrm{\beta }}$ ( symbols have  their  usual  meaning ).

• If  both  assertion  and  reason  are  true  and  reason is the  correct  explanation  of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false

Assertion:  Most  amplifiers  use  common  emitter  circuit configuration. 

Reason:  Its input resistance is comparatively higher.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false