Explain the following in not more than two sentenses.

A solution of FeCl₃ in water gives a brown precipitate on standing.

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.

Given $$A = {\sin ^2}\theta + {\cos ^4}\theta $$ then for all real values of $$\theta $$

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