Let $A = \begin{bmatrix} a & 1 \\ 1 & b \end{bmatrix}$, where $a$ and $b$ are the roots of the equation $x^2 - 4x + 2 = 0$. If $A + A^{-1} = kI_2$, then the value of $k$ is ____

The domain of the function $f(x) = \sqrt{x - 1} + \sqrt{6 - x}$ is...

The domain of the function $f(x) = {}^{(10-x)}C_{(x-6)}$ is...

Let $[x]$ denotes the greatest integer less than or equal to x and $f(x) = [\tan^2 x]$, then which of the following is true ?