Pakistan and the Mughal Empire are Muslim in governance. The Mughal empire was established in 1526 by the ruler Babur and declined in the 19th century as the British acquired more and more territory in India. Pakistan was established after Indian Independence in 1947 as a nation that South Asian Muslims could call a homeland.
Perhaps the major similarity between the two is political instability. In its decline, the Mughal Empire went through a series of weak rulers with short terms. The last powerful Mughal ruler was Aurangzeb, who died in 1707 after tyrannically ruling India for fifty years. He so thoroughly kept others from gaining power that no one was able to fully take control of the empire after his death, and the Mughal rulers who succeeded him had short terms that often ended in conflict. Moreover, the Mughals lost territory to the British, who consolidated their rule over India.
Like Mughal India, Pakistan has had considerable political instability. In the late 1970's, Prime Minister Zulfikar Ali Bhutto was arrested and executed in 1979. After this coup Pakistan was ruled by a military general, Zia al-Haq, who ruled until his death in a plane crash in 1988. Pakistan has ranged between democratically elected rulers at times, such as Benazir Bhutto (Zulfikar Ali Bhutto's daughter) and Nawaz Sharif, and has had other military coups, such as when Pervez Musharraf took power in 1999. Also, Pakistan has lost territory like the Mughal Empire. The country we know as Bangladesh used to be part of Pakistan, and seceded in 1971.