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PDF Editor FAQ

What is the unit digit in the product of (4387) ²⁴³×(621) ¹²⁴?

Answer: 3Briefly the unit digit (UD) of a product is the product of the UDs of the numbers being multiplied.For example:12*13=156 and so UD(156)=UD(12)*UD(13)=2*3=6UD(4387^243) = UD(7^243) = UD((7^4)^60 * 7^3)= UD(7^3) = 3 … because UD(7^4)=1.UD(621^124) = UD(621)^124 = 1^124 = 1So desired answer is 3 * 1 = 3.

What is the Mughal empire?

The period between 1526 to 1857 in India's history is known as the Mughal period. The Mughal Empire was a Muslim dynasty that ruled Northern India and parts of present day Pakistan and Afghanistan. The empire was established by Zahir-ud-din Muhammad Babur, a descendant of Timur and Genghis Khan, in 1526, which lasted until 1857.One of the Gunpowder empires.The government structure was absolute monarchy.Agra, Fatehpur Sikri, Lahore and Shahjahanabad were the capitals of the empire.Persian was the official language of the Mughals.The Mughal Empire was interrupted for a brief time from 1540 to 1555 by the Sur dynasty (Sher Shah Suri and his successors). Humayun, son of Babur, however, defeated Sher Shah’s successor and re-established the Mughal empire in 1555.However, soon after the death of Humayun, the Hindu King Hemu occupied Delhi and Agra. In the second battle of Panipat (5 Nov 1556), Akbar’s general defeated Hemu and the Mughal empire was once again re-established.The rulers were:1. Zahir-ud-din Muhammad "Babur" (1526-1530)2. Nasir-ud-din Muhammad "Humayun" (1530-1540 & 1555-1556)3. Jalal-ud-din Muhammad "Akbar (1556-1605)4. Nur-ud-din Muhammad Salim "Jahangir" (1605-1627)5. Shahab-ud-din Muhammad Khurram "Shah Jahan" (1628-1658)6. Muhi-ud-din Mohammad "Aurangzeb" (1658-1707)7. Qutb-ud-din Muazzam Bahadur "Shah Alam" (1707-1712)8. Muizz-ud-din Muhammad "Jahandar Shah" (1712-1713)9. Muin-ud-din Muhammad "Farrukh-Siyar" (1713-1719)10. Shams-ud-din Muhammad "Rafi-ud-Darajat" (1719)11. Rafi-ud-din Muhammad Rafi-ud-Daulah "Shah Jahan II" (1719)12. Nasir-ud-din Roshan Akhtar “Muhammad Shah" (1719-1748)13. Mujahid-ud-din Muhammad "Ahmad Shah" (1748-1754)14. Aziz-ud-din "Alamgir II" (1754-1759)15. Jalal ud-din Ali Gauhar "Shah Alam II" (1759-1806)16. Muin-ud-din Muhammad "Akbar Shah II" (1806-1837)17. Siraj-ud-din Muhammad "Bahadur Shah Zafar" (1837-1857)Akbar was the greatest ruler of the Mughal Empire. Aurangzeb was last of the great Mughals, and the empire reached its greatest extent under him. However, the empire began to decline after his death. The Mughal rulers after him were weak rulers. That's why there are called the later Mughals. Bahadur Shah Zafar was the last ruler of the Mughal dynasty.

Who was the longest serving king of the Delhi Sultanate?

Let’s look at the longest serving Sultan of each of the five dynasties of the Delhi Sultanate. At the end, we can look at the longest serving Sultan overall during the three century rule of the Delhi Sultanate.Mamluk DynastyShams-ud-Din Iltutmish ( 1211 – 1236) - 25 years.Khalji DynastyAlauddin Khalji (1296 – 1316) - 20 yearsTughlaq DynastyFiroz Shah Tughlaq (1351 – 1388) - 37 yearsSayyid DynastyMubarak Shah (1421 – 1434) - 13 yearsLodi DynastyBahlul Khan Lodi (1451 – 1489)- 38 yearsOverallThe longest ruling Sultans of the Delhi Sultanate are:Bahlul Khan Lodi - 38 yearsFiroz Shah Tughlaq - 37 yearsMuhammad bin Tughluq - 26 yearsHowever the person who was in power in the Delhi Sultan for the longest time was Ghiyas ud din Balban. Balban ruled as a Sultan from 1266 to 1287, a period of 21 years. However Balban also ruled as the vizier of his predecessor, Nasir ud din Mahmud. Nasir ud din Mahmud was a pious man and had no interest in ruling. The actual ruler of the Sultanate was Balban. This was from 1246 to 1266, a period of 20 years. However during his time as vizier, he was dismissed for one year. This means that he was vizier of the Sultanate for 19 years. So Ghiyas ud din Balban ruled the Delhi Sultanate in total for 40 years.Interestingly, this is still less than the rule of the Mughal Emperors Akbar and Aurangzeb. Both ruled approximately 49 years. Akbar ruled for longer, 49 years and 8 months.

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