If in order to pass the exam, a minimum of 105 marks are needed in History,…

To determine how many students passed the History exam, we need to calculate the actual marks obtained by each student and compare them to the passing threshold of 105 marks. The maximum marks for History are 175.

Calculation of Marks in History
To find the actual marks for each student, we use the formula:
Actual Marks = (Percentage / 100) * Maximum Marks

Ram: (54 / 100) * 175 = 94.5 marks

Mohan: (51 / 100) * 175 = 89.25 marks

Shyam: (75 / 100) * 175 = 131.25 marks

Comparison with Passing Threshold
The passing threshold is 105 marks.

Ram: 94.5 < 105 (Fail)

Mohan: 89.25 < 105 (Fail)

Shyam: 131.25 > 105 (Pass)

Only Shyam scored above the minimum of 105 marks required to pass.

Conclusion
There is 1 student (Shyam) who passed the History exam. Therefore, Option 2 is the correct answer.