Who was the last Mughal Ruler of India?

Bahadur Shah II

The correct answer is Option 2 - Bahadur Shah II

The last Mughal ruler of India was Bahadur Shah II, also known as Zafar.

The Mughal rulers in order are:

Babur (1526-1530)
Humayun (1530-1540, 1555-1556)
Akbar (1556-1605)
Jahangir (1605-1627)
Shah Jahan (1628-1658)
Aurangzeb (1658-1707)
Bahadur Shah I (1707-1712)  
Muhammad Shah I (1719-1748)
Ahmad Shah Bahadur (1748-1754)
Alamgir II (1754-1759)
Jahan Shah (1759-1760)
Shah Alam II (1760-1806)
Akbar Shah II (1806-1837)
Muhammad Shah II (1837-1840)
Bahadur Shah II (1840-1857) (answer)