Identify the sentence which is grammatically correct.

Correct option is C

The correct option is (c).

Option (c) is grammatically correct because it uses a comma before the coordinating conjunction but to join two independent clauses, and it also ends with a proper full stop.

Step-by-step reasoning:

• First clause: She likes to dance (independent clause).
• Second clause: she doesn't like to sing (independent clause).
• When two independent clauses are joined by but, a comma is commonly used before but in standard exam-style punctuation.
• Option (c) correctly uses: , but and ends with a period.

Why other options are incorrect:

• (a) Incorrect punctuation: placing a comma after but is wrong; the comma (if used) should come before but, not after it.
• (b) Missing comma and missing final punctuation; in objective exams, the standard correct form prefers the comma and proper ending.
• (d) Incorrect use of semicolon: a semicolon generally joins two independent clauses without a conjunction, or it can be used with conjunctive adverbs. Using ; but is considered incorrect in standard exam usage.

Information booster: A semicolon is properly used like: She likes to dance; she doesn't like to sing. If but is used, the common pattern is: ..., but ...

So the correct answer is (c)