At what time between 1'O clock and 2'O clock the hands of the clock are opposite to each other.

The minute hand to coincide with the hour hand it should trace at first 5 minute spaces and then the hands of the clocks to be opposite to each other minute hand should trace 30 minute spaces i.e. totally it should gain 5 + 30 = 35 minute spaces to be opposite to that of hour hand.
We know that, Minute hand gains 55 minute spaces over hour hand in 1 hour. Therefore, Minute hand gain 40 minute spaces over hand in 35 x (60/55) = 38(2/11).
Hence the hand of the clock will minutes be opposite to each at 38 (2/11) past 1'O clock. Therefore, Correct option is B.