If $\begin{bmatrix} 2 & 1 & -1 \\ -1 & 2 & 1 \\ 1 & -1 & 2 \end{bmatrix} \begin{bmatrix} a \\ b \\ c \end{bmatrix} = \begin{bmatrix} 4 \\ 0 \\ -2 \end{bmatrix}$ then the distance of point $P(a, b, c)$ from the plane $2x + y + 2z = 10$ is

If $\cot(\cos^{-1} x) = \sec\left(\tan^{-1} \dfrac{a}{\sqrt{b^2 - a^2}}\right)$, then the value of $x$ is

If $g(x) = x^2 + x - 2$ and $\dfrac{1}{2}(g \circ f)(x) = 2x^2 - 5x + 2$ then $f(x)$ is equal to

Let the function f be defined by $f(x) = \dfrac{x - |x|}{x}$, for $x \neq 0$ and $f(0) = 2$ then f is