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Which are not cleaved by $ HI{O_4} $ ?
 $ I $ : glycerol
 $ II $ : Glycol
 $ III $ : $ 1,3 $ -propanediol
 $ IV $ : methoxy- $ 2 $ -propanol
(A) $ I,II,III,IV $
(B) $ I,II $
(C) $ II,III $
(D) $ III,IV $

Answer
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Hint: Iodine in combination with oxygen forms oxyacids with different molecular formulas. One of them is periodic acid with a molecular formula of $ HI{O_4} $ . It cleaves $ 1,2 $ diols or the compounds consisting of hydroxyl groups attached to the adjacent carbon atoms.

Complete answer:
Glycerol is a polyhydroxy compound consisting of three hydroxyl groups attached to the three adjacent carbon atoms. The molecular formula of glycerol is $ {C_3}{H_8}{O_3} $ . The structure of glycerol is:
 $ C{H_2}\left( {OH} \right) - CH\left( {OH} \right) - C{H_2}\left( {OH} \right) $
As it consists of adjacent carbon with hydroxyl group it can be cleaved by periodic acid $ \left( {HI{O_4}} \right) $
Glycine is also a poly hydroxy compound consisting of two hydroxyl groups attached to the adjacent carbon atoms. Thus, it can also be cleaved by periodic acid $ \left( {HI{O_4}} \right) $ . The structure of glycol is:
 $ C{H_2}\left( {OH} \right) - C{H_2}\left( {OH} \right) $
 $ 1,3 $ -propanediol has the two hydroxyl groups attached to the carbon atoms present in one and three positions. Thus, it cannot be reduced by periodic acid $ \left( {HI{O_4}} \right) $
The structure of methoxy- $ 2 $ -propanol will be $ C{H_3} - CH\left( {OH} \right) - C{H_2}\left( {OC{H_3}} \right) $ . it does not have two adjacent carbon atoms with hydroxyl groups. Thus, it is not cleaved by periodic acid $ \left( {HI{O_4}} \right) $
Thus, $ 1,3 $ -propanediol and methoxy- $ 2 $ -propanol will not cleaved by $ HI{O_4} $
Thus, $ III $ and $ IV $ are not cleaved by $ HI{O_4} $
Option D is the correct one.

Note:
If the two hydroxyl groups are attached to the same carbon atoms. Then that compound can be known as a geminal diol. If the two hydroxyl groups are attached to the adjacent carbon atoms, then that compound is known as a vicinal diol. Periodic acid cleaves vicinal diols mainly.