The correct option is option 3, which states that statements 1 and 2 are correct. Let`s dissect each option to better understand why this is the correct answer.

Option 1 states that statement 1 is correct. Statement 1 mentions that Akbar strengthened his control on the nobility and army by introducing the mansabdari system. This is true. The mansabdari system was a hierarchical ranking system introduced by Akbar, whereby every officer was assigned a rank or mansab. By implementing this system, Akbar was able to maintain control over the nobility and the army as he could appoint and promote officers based on their loyalty and competence.

Option 2 states that statement 2 is correct, which states that under the mansabdari system, every officer was assigned a rank or mansab. This is also true. The mansabdari system was designed to assign a specific rank to each officer, based on their military capabilities and administrative responsibilities. This rank or mansab determined their salary, the number of troops they commanded, and their overall status within the Mughal administration.

Option 3 correctly identifies that both statements 1 and 2 are correct.

Option 4, on the other hand, states that statement 1 and 3 are correct