Delhi Sultanate

In 1206, Shahabuddin Ghori appointed Qutb-ud-din Aibak as his Naib-us-Sultanate in India at a grand darbar at Lahore, which was attended by a large majority of the nobles and dignitaries of his kingdom. It was at this occasion that Shahabuddin Ghori bestowed upon Qutb-ud-din the title of Aibak, meaning Axis of the Faith.

Statement 1 is wrong: Prithvi Raj III, commonly known as Prithviraj Chauhan (1149-1192 CE), was a king of the Hindu Kshatriya Chauhan (Chauhamana) dynasty.
Statement 2 is correct: Prithviraj Chauhan defeated the Muslim ruler Shahabuddin Muhammad Ghori in the First Battle of Tarain in 1191.

Aram Shah succeeded Aibak but was faced by a rebellious Iltutmish in battle. Aram was beaten in the battle and Shams-ud-din Iltutmish, another ex-slave and an outstanding ruler of Turkic ancestry who was married to Aibak's daughter, succeeded him as Sultan of Delhi.
The surviving sons of the Sultan were incapable of the task of administration. In 1236 Iltutmish, on his death-bed, nominated his daughter Raziya as his heiress.

Sultan Qutb-ud-din Aibak was the first Muslim Emperor of India who ruled from his capital in Delhi, where he built Qutub Minar and the Quwwat Al Islam Mosque.
He was a central Asian Turkish warrior by descendency, the first Sultan of Delhi and founder of the Slave Dynasty (also known as the Ghulam Dynasty) of India.
Sultan Qutbuddin died accidentally in 1210, while he was playing a game of polo in Lahore on horseback.

Jalal-ud-din Firuz Khilji was founder of the Khilji dynasty.
The most distinguishing part of Ala-ud-din's reign was the fact that he repeatedly defeated the Mongol invaders. Not only did he defeat them, but also raided their strongholds. So much was his fear that the Mongols spared India after that.

In 1398, Timur Lang invaded India on the pretext that the Muslim sultans of Delhi were too tolerant of their Hindu subjects.
After defeating the armies of Nasiruddin Mahmud of Tughlaq dynasty on 15 December 1398, Timur entered Delhi on 18 December, 1398, and the city was sacked, destroyed and left in ruins, and over 100, 000 war prisoners were killed as well.

Muhammad- Bin- Tughlaq transferred his capital from Delhi to Devagiri. The plan proved disastrous due to Mongol Attack on North. And since this happened in summer, many people died because of inadequate water supply arrangements in Daulatabad; after only two years, the capital had to be shifted back again to Delhi, again at great loss, and it was said that Delhi was a ghost town for years after the move back. "When I entered Delhi, it was almost like a desert", wrote the famed North African travel writer, Ibn Battuta.

Ghiyas-ud-Din Tughluq, real name Ghazi Malik (died in February 1325), was the founder and the first ruler of the Turkic Muslim Tughluq dynasty in India, who reigned over Sultanate of Delhi (1320 - 1325).
Muhammad Shah Tughluq was the title conferred on Ghazi Malik by his son Fakhr Malik.
Ghiyas-ud-Din was succeeded by his son Muhammad bin Tughluq.

Slave dynasty - Founded by Qutb-ud-din Aibak in1206
Khilji dynasty - Founded by Jalal ud din Firoz Khilji in 1290
Tughlaq dynasty - Founded by Ghiyas-ud-Din Tughluq in 1320
Sayyid dynasty - Founded by Khizr Khan in 1414
Lodi dynasty - Founded by Bahlul Lodi in 1451

The Delhi Sultanate is the only Indo-Islamic Empire to have enthroned female ruler in India. Razia Sultana (1236-1240) is the example for this fact.
Qutb-ud-din Aibak was a former slave (Mamluk) of Muhammad of Ghor.

The rise of Persian speaking people to the throne naturally resulted in the spread of the Persian language in India. It was the official language and soon literary works in the language began to appear.
Sanskrit continued to remain an important language of the time, and despite the increasingly influence of Persian, it was able to hold its ground. There was also significant amount of work taking place in regional languages.

Assertion is wrong: Actually it is not the First Battle of Tarain but the Second one is regarded by the historians as the turning point of Indian History.
Reason is correct: After the Second Battle of Tarain, the Muslim power was strongly founded in Northern India. After defeating Prithvîrâj Chauhân, Shahabuddin Ghori marched onwards unchallenged towards Ajmer and soon established Ghorid control in northern and central India.

The correct sequence is:
Change of Capital - Token Currency - Plan to invade Khorasan - Establishment of Swargdwari

After the overthrow of Razia Sultana he made rapid strides in the subsequent reigns. He was initially the Prime Minister of Sultan Nasir ud din Mahmud from 1246 to 1266 and married his daughter, but Balban declared himself the Sultan of Delhi after sultan Nasir ud din Mahmud's death because Sultan Nasir ud din Mahmud had no male heir.

The assertion that the Sultanate ushered in a period of Indian cultural renaissance is true - this period saw significant cultural flowering. The reason is also true - the Indo-Muslim fusion created lasting syncretic traditions in architecture (Indo-Islamic style), music (Qawwali, development of Hindustani classical), literature (early Urdu, Persian works), religion (Bhakti-Sufi movements), and clothing. The fusion directly caused and explains the cultural renaissance mentioned in the assertion.