If $\left|\begin{array}{lll}x & 3 & 6 \\ 3 & 6 & x \\ 6 & x & 3\end{array}\right|=\left|\begin{array}{lll}2 & x & 7 \\ x & 7 & 2 \\ 7 & 2 & x\end{array}\right|=\left|\begin{array}{lll}4 & 5 & x \\ 5 & x & 3 \\ x & 4 & 5\end{array}\right|=0$ then x is equal to

-9

By circulant determinant property a + b + c = 0

⇒ x + 3 + 6 = x + 2+ 7

= x + 4 + 5 = 0 ⇒ x = -9

Hence (2) is the correct answer.