The correct answer is (a) Balaji Vishwanath.
Balaji Vishwanath was the first Peshwa of the Maratha Empire. He was the son of Dadoji Kondadev, a Brahmin minister in the court of Shahaji Bhosale, the father of Shivaji Maharaj. Balaji Vishwanath was appointed as the Peshwa in 1680, after the death of his father. He was a brilliant administrator and diplomat, and he played a key role in expanding the Maratha Empire. He also established the Peshwa as the virtual ruler of the Maratha Empire, with the Maratha king becoming a non-entity.
Baji Rao I was the second Peshwa of the Maratha Empire. He was the son of Balaji Vishwanath. Baji Rao I was a great military commander, and he led the Maratha army to many victories. He also expanded the Maratha Empire to its greatest extent. However, he was not as successful as his father in establishing the Peshwa as the virtual ruler of the Maratha Empire.
Balaji Rao II was the third Peshwa of the Maratha Empire. He was the grandson of Balaji Vishwanath. Balaji Rao II was a weak and indecisive ruler, and he was unable to prevent the decline of the Maratha Empire. He was eventually overthrown by his cousin, Raghunathrao.
Madhavrao I was the fourth Peshwa of the Maratha Empire. He was the son of Balaji Rao II. Madhavrao I was a capable ruler, and he tried to revive the Maratha Empire. However, he was unsuccessful, and the Maratha Empire continued to decline after his death.
In conclusion, the correct answer is (a) Balaji Vishwanath. Balaji Vishwanath was the first Peshwa of the Maratha Empire, and he played a key role in expanding the Maratha Empire and establishing the Peshwa as the virtual ruler of the Maratha Empire.