Explanation:

Correct Answer is (b).There are two errors in the bold part of the given sentence.
First, the main verb of the sentence must be singular as the subject 'The government' is singular in number.
Secondly, usage of perfect infinitive right after the main verb is erroneous. The perfect infinitive often refers to things that might have happened in the past.
We form the perfect infinitive with 'to have + the -ed form of a verb'. But here, past participle form of the verb 'launch' is not used.
Ex. He pretended to have lost her number and so had been unable to contact her.
The correct sentence will therefore be:The Government claims to have launched the first ever laboratory for DNA profiling of the criminals in the premises of the Central Forensic Sciences Laboratory in Chandigarh.
Hence, Option B is the right choice among the given options.