Let $f:R \to R$ be defined by $f(x) = 2x + |x|$,then $f(2x) + f(-x) - f(x) = $

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

The domain of the function $\sqrt{\log \left( \frac{5x - x^2}{6} \right)}$ is

Consider the two sets:
$A = \{m \in R : \text{both the roots of } x^{2} - (m+1)x + m+4 = 0 \text{ are real}\}$ and $B = [-3, 5)$.
Which of the following is not true?

Let $n(U) = 700, n(A) = 200, n(B) = 300$ and $n(A \cap B) = 100,$ then $n(A^c \cap B^c) = $

Let $A = \{1, 2, 3\}$. The total number of distinct relations that can be defined over $A$ is