`P` and `Q` are isomers of dicarboxylic acid `C_(4)H_(4)O_(4)`. Bothdecolorize `Br_(2)//H_(2)O`. On heating, `P` forms the cyclic anhydride. Upon treatment with dilute alkaline `KMnO_(4),P` as well as `Q` could produce one or more than one forms `S,T` and `U`.
Compounds formed from `P` and `Q` are, respectively

Options

A. optically inactive pair `(T,U)` and optically inactive `S`
B. optically active pair `(T,U)` and optically active `S`
C. optically inactive `S` and optically inactive pair `(T,U)`
D. optically active `S` and optically inactive pair `(T,U)`

Answer

C

Explanation

`DBE =(sum n(v-2))/(2)+1`
`=(4(4-2)+4(1-2)+4(2-2))/(2) +1=3`
Since it is deicarboxylic acid, and decolorizes `Br_(2)//H_(2)O`, the presence of `C=C` is confirmed
`HO_(2)C CH = CHCO_(2)H`

reaction with dilute alkaline `KMnO_(4)` causes syn hydroxylation: