The most learned medieval Muslim ruler who was well versed in various branches of learning including astronomy, mathematics and medicine was

Sikandar Lodi
Iltutmish
Muhammad bin Tughlaq
Alauddin Khalji

The correct answer is: C. Muhammad bin Tughlaq

Muhammad bin Tughlaq was a 14th-century Turkic ruler of the Tughlaq dynasty who ruled over the Delhi Sultanate. He was a brilliant military strategist and administrator, but he was also known for his eccentricity and cruelty. He was a patron of the arts and sciences, and he established several universities and libraries. He was also a scholar himself, and he was well-versed in various branches of learning, including astronomy, mathematics, and medicine.

Sikandar Lodi was a 16th-century Afghan ruler who founded the Lodi dynasty. He was a successful military commander, and he expanded the Lodi Empire to include much of northern India. He was also a patron of the arts and sciences, and he built several mosques and tombs.

Iltutmish was a 13th-century Turkic ruler who founded the Delhi Sultanate. He was a successful military commander, and he expanded the Delhi Sultanate to include much of northern India. He was also a patron of the arts and sciences, and he built several mosques and tombs.

Alauddin Khalji was a 13th-century Turkic ruler who ruled over the Delhi Sultanate. He was a successful military commander, and he expanded the Delhi Sultanate to include much of northern India. He was also a patron of the arts and sciences, and he built several mosques and tombs.

However, among these four rulers, Muhammad bin Tughlaq was the most learned. He was a scholar himself, and he was well-versed in various branches of learning, including astronomy, mathematics, and medicine.