Three persons P, Q and R independently try to hit a target. I the probabilities of their hitting the target are $${3 \over 4},{1 \over 2}$$ and $${5 \over 8}$$ respectively, then the probability that the target is hit by P or Q but not by R is :

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teacher is :

The area (in sq. units) of the parallelogram whose diagonals are along the vectors $$8\widehat i - 6\widehat j$$ and $$3\widehat i + 4\widehat j - 12\widehat k,$$ is :

If two parallel chords of a circle, having diameter 4units, lie on the opposite sides of the center and subtend angles $${\cos ^{ - 1}}\left( {{1 \over 7}} \right)$$ and sec^$$-$$1 (7) at the center respectivey, then the distance between these chords, is :