Option $A$ is correct.
Questions says the MST of graph $G$ contain an edge $e$ which is a maximum weight edge in $G$. Need to choose the answer which is always true to follow the above constraint.
Option B says that if edge $e$ is in MST then for sure there is a cycle having all edges of maximum weight. But it is not true always because when there is only n-1 edges( but no cycle) in graph then also maximum edge has to be taken for MST.
Option C says otherwise. That if e is in MST then it cannot be in any cycle that is wrong as if there is a cycle with all maximum edges then also e will be in MST
Option D says all edges should be of same weight same explanation if there are $n-1$ distinct edges( but no cycle) in $G$ then have to take all edges including maximum weight edge.
And at last option A says if e is in MST then for sure there is a cut-set ( A subset of Edge set of G whose removal disconnects the graph) in $G$ having all edges of maximum weight. And it is true.
Because then only we maximum weight edges has to be taken in MST.
For eg. If there are $n-1$ edges (but no cycle) then if edge e is not taken in the MST then MST will not be connected.