The % yield of ammonia as a function of time in the reaction

N₂(g) + 3H₂(g) $$\rightleftharpoons$$ 2NH₃(g), $$\Delta$$H < 0 at (P, T₁) is given below:

If this reactions is conducted at (P, T₂), with T₂ > T₁, the % yield of ammonia as a function of time is represented by

The number of distinct solutions of the equation

$${5 \over 4}{\cos ^2}\,2x + {\cos ^4}\,x + {\sin ^4}\,x + {\cos ^6}\,x + {\sin ^6}\,x\, = \,2$$

in the interval $$\left[ {0,\,2\pi } \right]$$ is

Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of $${m \over n}$$ is

Let $$P$$ and $$Q$$ be distinct points on the parabola $${y^2} = 2x$$ such that a circle with $$PQ$$ as diameter passes through the vertex $$O$$ of the parabola. If $$P$$ lies in the first quadrant and the area of the triangle $$\Delta OPQ$$ is $${3\sqrt 2 ,}$$ then which of the following is (are) the coordinates of $$P$$?