The total number of students in $\text{Year 2} = 60 \text{(pass)} + 5 \text{(fail)} = 65$
The number of students, who failed in the exam in $\text{Year 1}$, and appeared in $\text{Year 2} = 10$
$\therefore$ The total number of students in $\text{Year 2}$ who appeared for the first time $ = 65 – 10 = 55$
Similarly, the total number of students in $\text{Year 3} = 50 \text{(pass)} + 3 \text{(fail)} = 53$
The number of students, who failed in the exam in $\text{Year 2}$, and appeared in $\text{Year 3} = 5$
$\therefore$ The total number of students in $\text{Year 3}$ who appeared for the first time $ = 53-5 = 48$
So, the correct answer is $(D).$