In the following common emitter circuit,if $\beta = 100$,$V_{CE} = 7 \, V$,$V_{BE} = \text{Negligible}$,and $R_C = 2 \, k\Omega$,then find $I_B$ in $mA$.

In the study of a transistor as an amplifier,if $\alpha = \frac{I_C}{I_E}$ and $\beta = \frac{I_C}{I_B}$,where $I_C, I_B$,and $I_E$ are the collector,base,and emitter currents,respectively,then:

In an $A.C.$ circuit,$V$ and $I$ are given by $V = 100 \sin(100t) \ V$ and $I = 100 \sin(100t + \frac{\pi}{3}) \ mA$. The power dissipated in the circuit is ...... $W$.

If a solid sphere and a solid cylinder of the same radius and density rotate about their own axes,which one will have a greater moment of inertia? (Assume $L=R$ for the cylinder)

Which of the following compounds is formed by the addition of a mineral acid to an aqueous solution of borax?

Match the thermodynamic processes taking place in a system with the correct conditions. In the table: $\Delta Q$ is the heat supplied,$\Delta W$ is the work done and $\Delta U$ is change in internal energy of the system.

Process	Condition
$(I)$ Adiabatic	$(A)$ $\Delta W = 0$
$(II)$ Isothermal	$(B)$ $\Delta Q = 0$
$(III)$ Isochoric	$(C)$ $\Delta U \neq 0, \Delta W \neq 0, \Delta Q \neq 0$
$(IV)$ Isobaric	$(D)$ $\Delta U = 0$