If a, b, c are distinct,
Question:

If $a, b, c$ are distinct, then the value of $x$ satisfying $\left|\begin{array}{ccc}0 & x^{2}-a & x^{3}-b \\ x^{2}+a & 0 & x^{2}+c \\ x^{4}+b & x-c & 0\end{array}\right|=0$ is

(a) $c$

(b) $a$

(c) $b$

(d) 0

Solution:

(d) 0

When we put $x=0$ in the given matrix, then it turns out to be the skew symmetric matrix of order 3 and the determinant of the skew symmetric matrix of odd order is always 0 .