The correct answer is B. Ajmer Singh.
Ajmer Singh was the ruler of Kutlehr during the first-Anglo-Sikh War. He expelled the Sikhs from his state in 1845.
The other options are incorrect.
A. Bidhi Pal was the ruler of Kutlehr before Ajmer Singh. He was not involved in the first-Anglo-Sikh War.
C. Narain Pal was the ruler of Kutlehr after Ajmer Singh. He was not involved in the first-Anglo-Sikh War.
D. Shamsher Singh was not the ruler of Kutlehr during the first-Anglo-Sikh War. He was the ruler of Kutlehr after Narain Pal.