A voltmeter with internal resistance of $x \Omega$ can be used to measure upto 20 V . In order to increase its measuring range to 30 V , the required modification is to $\_\_\_\_$ .

Two 4 bits binary numbers, $A=1101$ and $B=1010$ are given in the inputs of a logic circuit shown in figure below. The output $(Y)$ will be :

A rod of length 10 cm lies along the principle axis of a concave mirror of focal length 10 cm as shown in figure. The length of the image is $\_\_\_\_$ cm.

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed $v$. If $x$ is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to $x^\alpha$, where $\alpha$ is $\_\_\_\_$ .