Institution: জাতীয় কবি কাজী নজরুল ইসলাম বিশ্ববিদ্যালয় (JKKNIU) Exam: গ ইউনিট || জাতীয় কবি কাজী নজরুল ইসলাম বিশ্ববিদ্যালয় || 2013
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

The question 'যদি x' translates to "if x," which implies that the answer must logically stem from a relationship or expression involving 'x.' Among the options provided, option B, 'a+x', stands out as the correct choice because it directly incorporates 'x' in a straightforward manner.

Option A, 'a+x>b+y', presents a comparative expression but does not solely define or express 'x' and its implications. This makes it less relevant as a direct answer to the question.

Option C, 'ax=by', introduces a proportional relationship but is more complex and indirect regarding 'x', making it a potential distractor. Finally, option D, 'a=y', offers a relationship between 'a' and 'y' without addressing 'x' at all.

Choosing 'a+x' signifies that we are forming a new expression by adding 'x' to 'a', directly reflecting the implications of 'x' in a clear and concise manner. This choice emphasizes the importance of 'x' in determining the value of the overall expression, hence aligning with the initial condition presented by 'যদি x'.