Evaluate $$\int {{{{x^2}dx} \over {{{\left( {a + bx} \right)}^2}}}} $$

Two fair dice are tossed. Let $$x$$ be the event that the first die shows an even number and $$y$$ be the event that the second die shows an odd number. The two events $$x$$ and $$y$$ are:

Six boys and six girls sit in a row randomly. Find the probability that
(i) the six girls sit together
(ii) the boys and girls sit alternately.

The dispalcement x of particle moving in one direction, under the action of a constant force is related to the time t by the equation $$t = \sqrt x + 3$$
where x is in meters and t in seconds. Find

(i) The displacement of the particle when its velocity is zero, and

(ii) The work done by the force in the first 6 seconds.