You are given 8 metallic plates, Any two plates arc to be separated from each other so that capacitance of the capacitor formed by them is 1 μF. What is the maximum capacitance one can obtain with them

The plates can be connected as shown in fig. to give maximum capacitance. It is obvious from the figure that the combination is equivalent to 7 capacitors in parallel. As the capacitance of each capacitor is 1 μF and hence the total capacitance is 7 μF.