Question

If $$f(x) = \begin{vmatrix} 2 \cos^4 x & 2 \sin^4 x & 3 + \sin^2 2x \\ 3 + 2 \cos^4 x & 2 \sin^4 x & \sin^2 2x \\ 2 \cos^4 x & 3 + 2 \sin^4 x & \sin^2 2x \end{vmatrix}$$ then $\frac{1}{5} f'(0)$ is equal to

• A. 0
• B. 1
• C. 2
• D. 6

Answer 1

The Correct Option is A

By simplifying the determinant using row operations:

$R_2 \rightarrow R_2 - R_1$,    $R_3 \rightarrow R_3 - R_1$

we find that $f(x)$ is constant. Therefore, $f'(x) = 0$.

Thus,

$$\frac{1}{5} f'(0) = 0$$