Choose the grammatically correct sentence:

The correct answer is Option (1) → Kavya taught herself to swim by watching videos during the summer holidays.

Reflexive pronoun for the same person:

A reflexive pronoun is used when the doer and the receiver are the same person. Kavya did the teaching, and Kavya was also the one taught. So “herself” is right. The sentence has no other error.

Why the Other Options are Incorrect?

Option 2: Mrs Rao invited my parents and myself to her son’s wedding in Udaipur. — Incorrect. The given sentence says “invited my parents and myself”. This is wrong: “myself” needs “I” as the subject of the same sentence. Here the subject is Mrs Rao, so the plain object form “me” is needed.
Corrected: Mrs Rao invited my parents and me to her son’s wedding in Udaipur.

Option 3: Them mangoes on the top shelf are from my uncle’s farm. — Incorrect. The given sentence says “Them mangoes”. This is wrong: “them” cannot come before a noun to point to it. Use “those”.
Corrected: Those mangoes on the top shelf are from my uncle’s farm.

Option 4: Him and his cousins played carrom till late at night. — Incorrect. The given sentence says “Him and his cousins played”. This is wrong: the subject needs the subject form “he”, not the object form “him”.
Corrected: He and his cousins played carrom till late at night.