List of top Mathematics Questions on Properties of Determinants asked in KCET

The value of determinant $\begin{vmatrix}a-b&b+c&a\\ b-a&c+a&b\\ c-a&a+b&c \end{vmatrix}$ is

$\begin{vmatrix} {Sin \alpha}&{ \cos\alpha} &Sin ({\alpha+ \delta })\\ {Sin \beta}&{ Cos \beta}& Sin ({\beta+\delta}) \\ {Sin \gamma}&{ Cos \gamma}&Sin ({\gamma+\delta})\\ \end{vmatrix} $ is equal to

If $\omega$ is a complex cube-root of unity then, $\begin{vmatrix} {1}&{\omega} &{\omega^2}\\ {\omega}&{\omega^2}& {1} \\ {\omega^2}&{1}&{\omega}\\ \end{vmatrix} $ is equal to

Let \(f(x)=\begin{vmatrix}cosx &x& 1\\ 2sinx &x& 2x \\ sinx& x& x\end{vmatrix}\).Then \(\lim\limits_{x \to 0}\frac{f(x)}{x^2}\)=