Given that the determinant of the matrix $$\left[ {\matrix{ 1 & 3 & 0 \cr 2 & 6 & 4 \cr { - 1} & 0 & 2 \cr } } \right]$$ is $$-12$$, the determinant of the matrix $$\left[ {\matrix{ 2 & 6 & 0 \cr 4 & {12} & 8 \cr { - 2} & 0 & 4 \cr } } \right]$$ is

Which one of the following describes the relationship among the three vectors, $$\widehat i + \widehat j + \widehat k,\,\,2\widehat i + 3\widehat j + \widehat k$$ and $$5\widehat i + 6\widehat j + 4\widehat k?$$

$$\mathop {Lt}\limits_{x \to 0} {{x - \sin x} \over {1 - \cos x}}$$ is

The integral $$\,\,\oint\limits_C {\left( {ydx - xdy} \right)\,\,} $$ is evaluated along the circle $${x^2} + {y^2} = {1 \over 4}\,$$ traversed in counter clockwise direction. The integral is equal to