It is given that the number of rectangles formed in chess board (Let having size \(n \times n\)) is 1296
\(\begin{aligned}
& \therefore \quad{ }^{n+1} C_2 \times{ }^{n+1} C_2=1296 \\
& \Rightarrow \quad\left(\frac{n(n+1)}{2}\right)^2=1296=(36)^2 \\
& \Rightarrow \quad \frac{n(n+1)}{2}=36 \Rightarrow n(n+1)=72 \Rightarrow n=8 \\
\end{aligned}\)
So, number of squares of any sizes are
\(\begin{aligned}
& n^2+(n-1)^2+(n-2)^2+\ldots \ldots .+1^2 \\
& =1^2+2^2+3^2+\ldots \ldots+8^2 \\
& =\frac{8 \times 9 \times 17}{6}=4 \times 3 \times 17=12 \times 17=204
\end{aligned}\)
Hence, option (c) is correct.