1) If $f(x)=\begin{vmatrix}\cos x & 1 & 0 \\1 & 2\cos x & 1 \\0 & 1 & 2\cos x \end{vmatrix}$ $\int_{0}^{\pi/2}f(x)dx$ is equal to A) $\frac{1}{4}$ B) $-\frac{1}{3}$ C) $\frac{1}{2}$ D) 1 Answer: Option BExplanation:f(x)= 4cos3 x - cos x - 2cos x = cos 3x (Expansion of determinant) $\therefore\int_{0}^{\pi/2}f(x)dx =\frac{\sin3x}{3}]^{{\pi/2}}_{0}=-\frac{1}{3}$
