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 :

In a test an examine either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he make a guess is $$1/3$$ and the probability that he copies the answer is $$1/6$$. The probability that his answer is correct given that he copied it, is $$1/8$$. Find the probability that he knew the answer to the questions given that he correctly answered it.

Given that $$\overrightarrow a = \left( {1,1,1} \right),\,\,\overrightarrow c = \left( {0,1, - 1} \right),\,\overrightarrow a .\overrightarrow b = 3$$ and $$\overrightarrow a \times \overrightarrow b = \overrightarrow c ,$$ then $$\overrightarrow b \, = $$.........