(N/A) Bayer's test (Test for unsaturation):
$KMnO_4$ (Potassium permanganate) is a purple-coloured solution. When alkenes react with cold,dilute alkaline $KMnO_4$ solution,the purple colour disappears,and a vicinal diol is formed. This process is known as hydroxylation.
Example: $CH_2=CH_2 + H_2O + [O] \xrightarrow{dil. KMnO_4, 273K} CH_2(OH)-CH_2(OH)$ (Ethane$-1,2-$diol).
$(b)$ Oxidation with strong oxidizing agents:
When alkenes are treated with strong oxidizing agents like acidic $KMnO_4$ or $K_2Cr_2O_7$ at high temperatures,the double bond is cleaved to form ketones or carboxylic acids,depending on the structure of the alkene.
Example: $CH_3-CH=CH-CH_3 \xrightarrow{KMnO_4/H^+} 2CH_3COOH$ (Ethanoic acid).