Re: Mrs. Shobha is leaving to Delhi this evening/by this evening.
both are okay, but they have different meanings.
"Mrs. Shoba is leaving to Delhi by this evening"
::means that she is leaving no later than, or before this evening - maybe she will leave in the morning or the afternoon.
"Mrs. Shoba is leaving to Delhi this evening" means that she will leave at that time, and no other time.