A carbonyl compound P, which gives positive iodoform test, undergoes reaction with MeMgBr followed by dehydration to give an olefin Q. Ozonolysis of Q leads to a dicarbonyl compound R, which undergoes intramolecular aldol reaction to give predominantly S.

The structure of the product S is
Match each of the diatomic molecules in Column I with its property/properties in Column II:
| Column I | Column II | ||
|---|---|---|---|
| (A) | $${B_2}$$ | (P) | Paramagnetic |
| (B) | $${N_2}$$ | (Q) | Undergoes oxidation |
| (C) | $$O_2^ - $$ | (R) | Undergoes reduction |
| (D) | $${O_2}$$ | (S) | Bond order $$\ge$$ 2 |
| (T) | Mixing of $$s$$ and $$p$$ orbitals |
Match each of the compounds in Column I with its characteristic reaction(s) in Column II.
| Column I | Column II | ||
|---|---|---|---|
| (A) | $$C{H_3}C{H_2}C{H_2}CN$$ | (P) | Reduction with $$Pd - C/{H_2}$$ |
| (B) | $$C{H_3}C{H_2}OCOC{H_3}$$ | (Q) | Reduction with $$SnC{l_2}/HCl$$ |
| (C) | $$C{H_3} - CH = CH - C{H_2}OH$$ | (R) | Development of foul smell on treatment with chloroform and alcoholic KOH |
| (D) | $$C{H_3}C{H_2}C{H_2}C{H_2}N{H_2}$$ | (S) | Reduction with diisobutylaluminium hydride (DIBAL-H) |
| (T) | Alkaline hydrolysis |
Let $$z = x + iy$$ be a complex number where x and y are integers. Then the area of the rectangle whose vertices are the roots of the equation $$\overline z {z^3} + z{\overline z ^3} = 350$$ is
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