CAT Exam Model Paper 4 with solutions for free online practice

${\mathit{x}}^2-3{\mathit{y}}^2=1376$
As we can see L.H.S. is definitely a multiple of 3 and in R.H.S. 1376 leaves a remainder of 2 when divided by 3.
There are three possibilities for x in R.H.S:
(i) If x is multiple of 3, so is x${}^2$, and R.H.S. will leave a remainder of 1 when divided by 3
(ii) If x is of the form 3m + 1, x${}^2$will be of the form 3n + 1 and R.H.S will leave a remainder of 2. m, n ∈ N
(iii) If x is of the form 3m + 2, x${}^2$ will be of the form 3n + 1 and R.H.S. will leave a remainder of 2. m, n ∈ N
So R.H.S. can never be a multiple of 3, while L.H.S. is always a multiple of 3. Hence no real solution exists.