Write the main product of the given reactions:
$1$. $CH_3-CH=CH-CH_3 \xrightarrow[cold, Na_2CO_3]{KMnO_4}$
$2$. $2,3-$Dimethylbut$-2-$ene $\xrightarrow{Baeyer\ test}$

(N/A) The reaction of alkenes with cold,dilute alkaline $KMnO_4$ solution (Baeyer's reagent) is known as the Baeyer's test. This reaction results in the syn-hydroxylation of the double bond to form vicinal diols.
$1$. For $CH_3-CH=CH-CH_3$ (But$-2-$ene):
$CH_3-CH=CH-CH_3 + [O] + H_2O \xrightarrow{cold, alkaline\ KMnO_4} CH_3-CH(OH)-CH(OH)-CH_3$ (Butane$-2,3-$diol).
$2$. For $2,3-$Dimethylbut$-2-$ene:
$(CH_3)_2C=C(CH_3)_2 + [O] + H_2O \xrightarrow{Baeyer\ test} (CH_3)_2C(OH)-C(OH)(CH_3)_2$ ($2,3-$Dimethylbutane$-2,3-$diol).