Answer: $C$
Determinant comes out to be $0$. So, rank cannot be $3$. The minor $\begin{bmatrix} 3 & 5 \\[0.3em] 1 & 1 \\[0.3em] \end{bmatrix}$ $!=0$. So, rank is $2.$
(or)
if we do elementary row operations on the given matrix then we get
As the number of non zero row is $2$,then the rank of the matrix is also $2.$