The arrival of Babur in India in 1526 CE marked the establishment of the Mughal Empire. This dynasty was a direct continuation of the Timurid lineage, tracing its ancestry back to Timur from Central Asia. Therefore, statement 3 is correct.
Statement 1: The use of gunpowder and artillery was prevalent in India prior to Babur's arrival. Various Indian rulers, including the Bahmani Sultanate and the Delhi Sultanate, had employed gunpowder-based weapons and artillery since the 14th and 15th centuries. Babur's innovation was primarily in the tactical deployment of artillery, not its introduction. Thus, statement 1 is incorrect.
Statement 2: The architectural elements of the arch and dome were introduced into India much earlier by the Delhi Sultanate. Structures like the Qutub Minar complex, constructed in the 13th century, already feature prominent Islamic architectural styles incorporating arches and domes. Therefore, statement 2 is incorrect.