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The given question checks knowledge about Indian cultural history related to music, mentioning Tyagaraja and Annamacharya. Let`s scrutinize each option.
Statement 1: Most of Tyagaraja`s compositions are indeed devotional songs but they are mostly dedicated to Lord Rama, not Lord Krishna.
Statement 2: Tyagaraja, one of the trinities of Carnatic music, did innovate and create new ragas, thus this statement is correct.
Statement 3: Tyagaraja (1767–1847) and Annamacharya (1408–1503) are not contemporaries as they lived in different periods.
Statement 4: Annamacharya`s compositions, known as Sankirtanas or Kirtanas, are indeed in praise of Lord Venkateshwara, making this statement correct too.
When we examine the information above, it`s clear that statements 2 and 4 are the only correct ones, rendering option 2 as the correct answer.