UPSC 2015 CDS II Math Paper

21x+48y=5
⇒7x+16y=

5

3

Now, for any integral value of x and y, the LHS is an integer. But, RHS is not an integer.
So, the equation 21x+48y=5 has no solution in integers for x and y.
Thus, the number of pairs (x, y) satisfying the given equation is zero.