A cone made of conducting material is given a charge $ Q $. $ \sigma_1, \sigma_2, \sigma_3 $ and $ \sigma_4 $ are charge densities at four points $ P, Q, R $ and $ S $. $ P $ is at the vertex of the cone and $ Q, R, S $ are at the periphery of the base. Choose the correct option. 
The variations of resistivity \( \rho \) with absolute temperature \( T \) for three different materials X, Y, and Z are shown in the graph below. Identify the materials X, Y, and Z. 
What are the charges stored in the \( 1\,\mu\text{F} \) and \( 2\,\mu\text{F} \) capacitors in the circuit once current becomes steady? 
Which one among the following compounds will most readily be dehydrated under acidic condition?

Manufacturers supply a zener diode with zener voltage \( V_z=5.6\,\text{V} \) and maximum power dissipation \( P_{\max}=\frac14\,\text{W} \). This zener diode is used in the circuit shown. Calculate the minimum value of the resistance \( R_s \) so that the zener diode will not burn when the input voltage is \( V_{in}=10\,\text{V} \). 
Two charges \( +q \) and \( -q \) are placed at points \( A \) and \( B \) respectively which are at a distance \( 2L \) apart. \( C \) is the midpoint of \( AB \). The work done in moving a charge \( +Q \) along the semicircle CSD (\( W_1 \)) and along the line CBD (\( W_2 \)) are 
A piece of granite floats at the interface of mercury and water. If the densities of granite, water and mercury are \( \rho, \rho_1, \rho_2 \) respectively, the ratio of volume of granite in water to that in mercury is 