Between 2 & 3 o'clock what is the time when the hour and minute hand are in the same position ?

Let the time when the hour and the minute hand are in the
same position between 2 o'clock and 3 o'clock be at T minutes past
2.

The hour hand moves 360/12 = 30 degrees in an hour. At
2, the hour hand makes an angle of 60 degrees with the line pointing towards
12.

At T past 2, the angle made by the hour hand with line
pointing towards 12 is 30 + (30/60)*T. The angle made by the minute hand is
(360/60)*T

As the two have to be at the same position, 30 +
T/2 = (360/60)*T

=> 30 + T/2 =
6T

=> 11T/2 =
30

=> T =
60/11

=> T =
5.45

The time when the two hands are at the
same position is 5.45 minutes past 2.