If $f(x) = \frac{x - |x|}{|x|}$,then $f(-1) = $

Let $P = \{ \theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta \}$ and $Q = \{ \theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta \}$ be two sets. Then

Let $A = \{a, b, c\}$ and $B = \{1, 2, 3, 4\}$. Then the number of elements in the set $C = \{f : A \rightarrow B \mid 2 \in f(A) \text{ and } f \text{ is not one-one}\}$ is

If $(1, 3), (2, 5)$ and $(3, 3)$ are three elements of $A \times B$ and the total number of elements in $A \times B$ is $6$,then the remaining elements of $A \times B$ are

The domain of the function $f(x) = \frac{1}{\sqrt{|x| - x}}$ is

Domain of the function $\frac{\sqrt{1 + x} - \sqrt{1 - x}}{x}$ is