Question

The coefficient of \( x^2 \) in the expansion of the determinant \( \begin{vmatrix} x^2 & x^3+1 & x^5+2 \\ x^3+3 & x^2+x & x^3+x^4 \\ x+4 & x^3+x^5 & 2^3 \end{vmatrix} \) is:

• A. $-10$
• B. $-8$
• C. $-2$
• D. $-6$
• E. $8$

Hint:

To find the coefficient of $x^n$ in a determinant, you can differentiate the determinant $n$ times using the rule of differentiating rows/columns and evaluate at $x=0$, then divide by $n!$.

Answer 1

The Correct Option is A