In a common emitter configuration with suitable bias, it is given that $${R_L}$$ is the load resistance and $${R_{BE}}$$ is small signal dynamic resistance (input side). Then, voltage gain, current gain and power gain are given, respectively, by :

$$\beta $$ is curret gain, $${{\rm I}_B},{{\rm I}_C}$$ and $${{\rm I}_E}$$ are respectively base, collector and emitter currents.

In a screw gauge, $$5$$ complete rotations of the screw cause it to move a linear distance of $$0.25$$ $$cm.$$ There are $$100$$ circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of $$4$$ main scale divisions and $$30$$ circular scale divisions. Assuming negligible zero error, the thickness of the wire is :

The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in $$15$$ $$s$$ and (ii) the time at which the car will catch up with the scooter are, respectively.

A charge $$Q$$ is placed at a distance $$a/2$$ above the center of the square surface of edge a as shown in the figure.


The electric flux through the square surface is