For an intrinsic semiconductor $$\left(\mathrm{n}_{\mathrm{h}}\right.$$ and $$\mathrm{n}_{\mathrm{e}}$$ are the number of holes per unit volume and number of electrons per unit volume respectively)

A $$5.0 \mathrm{~V}$$ stabilized power supply is required to be designed using a $$12 \mathrm{~V}$$ DC power supply as input source. The maximum power rating of zener diode is $$2.0 \mathrm{~W}$$. The minimum value of resistance $$R_{\mathrm{s}}$$ in $$\Omega$$ connected in series with zener diode will be

A jar '$$\mathrm{P}$$' is filled with gas having pressure, volume and temperature $$\mathrm{P}, \mathrm{V}, \mathrm{T}$$ respectively. Another gas jar $$Q$$ filled with a gas having pressure $$2 \mathrm{P}$$, volume $$\frac{\mathrm{V}}{4}$$ and temperature $$2 \mathrm{~T}$$. The ratio of the number of molecules in jar $$\mathrm{P}$$ to those in jar $$Q$$ is

The magnetic flux through a loop of resistance $$10 ~\Omega$$ varying according to the relation $$\phi=6 \mathrm{t}^2+7 \mathrm{t}+1$$, where $$\phi$$ is in milliweber, time is in second at time $$\mathrm{t}=1 \mathrm{~s}$$ the induced e.m.f. is