How many automobile license plates can be made, if each plate contains two different letters followed by three different digits?

How many licence plates may be made using either two distinct letters followed by four digits or two digits followed by 4 distinct letters where all digits and letters are distinct?

How many five-digit numbers can be made having exactly two identical digits?

How many different signals can be given using any number of flags from 5 flags of different colors?

(i) A mobile phone has a passcode of 6 digits. What is the maximum number of attempts one makes to retrieve the passed. (ii) Given four flags of different colours, how many different signals can be generated if each signal requires the use three flags, One below the other?

In how many ways 10 different balls can be put in 2 difference boxes ?

How many different diagonal matrices of order n can be formed which are involuntary ?

Figure shows a capacitor made of two circular plates each of radius 12 cm and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15 A. a. Calculate the capacitance and the rate of change of potential difference between the plates. b. Obtain the displacement current across the plates. c. Is Kirchhoff's first rule (junction rule) valid at each plate of the capacitor ?