Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?

The area (in sq. units) of the region
A = {(x, y) : |x| + |y| $$ \le $$ 1, 2y² $$ \ge $$ |x|}

The position of a moving car at time t is
given by f(t) = at² + bt + c, t > 0, where a, b and c are real numbers greater than 1. Then the average speed of the car over the time interval [t₁ , t₂ ] is attained at the point :

Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is :