Statement 1 is incorrect. The United East India Company of the Netherlands (VOC) was formed in 1602. The Gajapati dynasty, which ruled the Odisha region, had declined significantly by 1541 (the last ruler being Kakharua Deva). Therefore, the Dutch could not have received land grants from Gajapati rulers. They typically acquired land from local rulers like the Nayakas or the Golconda Sultanate on the east coast.

Statement 2 is correct. Alfonso de Albuquerque captured Goa in 1510 from the Bijapur Sultanate (Adil Shahis). This victory established the Portuguese as a formidable regional power.

Statement 3 is correct. In 1639, Francis Day of the English East India Company obtained a lease for a strip of land in Madras from the Nayaka of Chandragiri (Damarla Venkatapathy), who was a representative/vassal of the declining Vijayanagara Empire.

In medieval India, the term "Fanam" referred to a unit of currency, particularly a gold coin used in South India, especially in regions like the Vijayanagara Empire, the Nayakas of Madurai, and the various states of the Deccan. The Fanam was often minted in small denominations and was widely used for trade and commerce in the region.

Statement 1 is Incorrect: The first Mongol invasion of India occurred in 1221 CE under Genghis Khan during the reign of Shamsuddin Iltutmish, not Jalal-ud-din Khalji. Jalal-ud-din Khalji ruled much later, from 1290 to 1296 CE.

Statement 2 is Correct: During the reign of Ala-ud-din Khalji (1296–1316 CE), the Mongols invaded several times. In 1303 CE, a Mongol army of about 120,000 horsemen led by Targhi marched up to Delhi and besieged the city, forcing Ala-ud-din to take shelter in the Siri Fort.

Statement 3 is Incorrect: Muhammad-bin-Tughlaq defeated the Mongols (led by Tarmashirin) early in his reign. Instead of losing territory, he took steps to secure the frontier and even planned a 'Khurasan expedition' to mobilize against Mongol territories, though it was later abandoned.

The Sayyids were claimed to descend from the Prophet through his daughter Fatima. They commanded special respect in Muslim society. Even Timur protected the life of Sayyids during his invasion of India, although his policy was one of general slaughter.

The Sayyids put on a pointed cap (kulah) and they were known as KulahDaran during the Delhi Sultanate.

Pair 1 is correctly matched. Nannuka was the founder of the Chandela dynasty.

Pair 2 is incorrectly matched. Jayashakti belonged to the Chandel dynasty, not the Paramara dynasty.

Pair 3 is correctly matched. Nagabhata II was indeed a ruler of the Gurjara-Pratihara dynasty.

Pair 4 is incorrectly matched. Bhoja belonged to the Paramara dynasty, not the Rashtrakuta dynasty.