The major product of the reaction of $2-$butene with cold alkaline $KMnO_4$ is:

Compound$(s)$ that on hydrogenation produce$(s)$ optically inactive compound$(s)$ is (are)

$1-$Propanol can be prepared from propene by

Cyclopentene on treatment with alkaline $KMnO_4$ gives

Taking into account the stability of various cycloalkanes and carbocations,as well as the rules governing mechanisms of carbocation rearrangements,what is the most likely product of this reaction?

Product $(A)$ will be