Compound A is a light green crystalline solid. It gives the following tests :

(i) It dissolves in dilute sulphuric acid. No gas is produced.

(ii) A drop of KMnO₄ is added to the above solution. The pink colour disappears.

(iii) Compound A is heated strongly. Gases B and C, with pungent smell, come out. A brown residue D is left behind.

(iv) The gas mixture (B and C) is passed into a dichromate solution. The solution turns green.

(v) The green solution from step (iv) gives a white precipitate E with a solution of barium nitrate.

(vi) Residue D from step (iii) is heated on charcoal in a reducing flame. It gives a magnetic substance E.

Name the compounds A, B, C, D and E.

The probability that an event $$A$$ happens in one trial of an experiment is $$0.4.$$ Three independent trials of the experiment are performed. The probability that the event $$A$$ happens at least once is

Two events $$A$$ and $$B$$ have probabilities $$0.25$$ and $$0.50$$ respectively. The probability that both $$A$$ and $$B$$ occur simultaneously is $$0.14$$. Then the probability that neither $$A$$ nor $$B$$ occurs is

The equation $$\,2{\cos ^2}{x \over 2}{\sin ^2}x = {x^2} + {x^{ - 2}};\,0 < x \le {\pi \over 2}$$ has