Final answer:
a. Ajai Singh.
The son of Banda Singh Bahadur from his first wife was Ajai Singh. Banda Singh Bahadur is a notable figure in Sikh history who fought against Mughal rule, and Guru Tegh Bahadur, whom Aurangzeb executed, was a leader of the Sikh faith.
Step-by-step explanation:
The son of Banda Singh Bahadur from his first wife was named Ajai Singh. The multiple-choice options provided include Ajai Singh, Gajinder Singh, Ranjit Singh, and Harbhajan Singh, with Ajai Singh being the correct answer. Banda Singh Bahadur was a significant figure in Sikh history, known for his valiant struggle against Mughal rule in India, which follows the execution of Guru Tegh Bahadur who was a leader of the Sikh religion by the Mughal emperor Aurangzeb.