The correct answer is: Only assumption II is implicit.
The statement says that Sachin wrote to his brother at Bangalore to collect personally the application form from the University for the Post-graduation Course in Mathematics. This does not necessarily mean that the University may issue application forms to a person other than the prospective student. It is possible that the University only issues application forms to the prospective student, but Sachin wants his brother to collect the form on his behalf.
However, the statement does imply that Sachin’s brother may receive the letter well before the last date of collecting application forms. This is because Sachin would not have asked his brother to collect the form if he did not think that his brother would be able to do so on time.
Therefore, only assumption II is implicit in the statement.