The decomposition of N₂O₅ according to the equation:
2N₂O₅ (g) $$\to$$ 4NO₂(g) + O₂(g)
is a first order reaction. After 30 min. from the start of the decomposition in a closed vessel, the total pressure developed is found to be 284.5 mm of Hg and on complete decomposition, the total pressure is 584.5 mm of Hg. Calculate the rate constant of the reaction.

Write the IUPAC name for the following :

The value of
$$\sin {\pi \over {14}}\sin {{3\pi } \over {14}}\sin {{5\pi } \over {14}}\sin {{7\pi } \over {14}}\sin {{9\pi } \over {14}}\sin {{11\pi } \over {14}}\sin {{13\pi } \over {14}}$$ is equal to ______.

If $$\exp \,\,\,\left\{ {\left( {\left( {{{\sin }^2}x + {{\sin }^4}x + {{\sin }^6}x + \,\,\,..............\infty } \right)\,In\,\,2} \right)} \right\}$$ satiesfies the equation $${x^2} - 9x + 8 = 0,$$ find the value of $${{\cos x} \over {\cos x + \sin x}},\,0 < x < {\pi \over 2}.$$