Explanation:

 Statement 1: TaapakaAnnamacarya (or Annamayya) was a 15th-century Hindu saint and is the earliest known Indian musician to compose songs called sankirtanas in praise of the god Venkateswara, a form of Vishnu. Hence S1 is incorrect.
Statement 2: Tyagaraja took music training from SontiVenkataramayya. But that didn’t stop him from taking musical inspirations from various earlier poets. He was an ardent devotee of lord Rama. In his praise and honour he wrote numerous musical operas, and about twenty four thousand songs, a claim that has been speculated among music historians. Hence, S2 is correct.
Statement 3: Tyagaraja was born on 14th May 1767 in the village of Thiruvayaru in the Thanjavur district of Tamil Nadu whereas Ta??apakaAnnamacarya (or Annamayya) (22 May 1408 – 4 April 1503) was a 15th-century Hindu saint. Hence, statement 3 is incorrect.
Statement 4: TaapakaAnnamacarya (or Annamayya) (22 May 1408 – 4 April 1503) was a 15th-century Hindu saint and is the earliest known Indian musician to compose songs called sankirtanas in praise of the god Venkateswara, a form of Vishnu. Hence, S4 is correct.