The interval for which ${\sin ^{ - 1}}\sqrt x + {\cos ^{ - 1}}\sqrt x = \frac{\pi }{2}$ holds is:

$2n (A \setminus B) = n (B \setminus A)$ and $5n (A \cap B) = n (A) + 3n (B)$,where $P \setminus Q = P \cap Q^C$. If $n (A \cup B) \leq 10$,then the value of $\frac{n(A) \cdot n(B) \cdot n(A \cap B)}{8}$ is:

Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$, then

If the sets $A$ and $B$ are defined as $A = \{ (x, y) : y = \frac{1}{x}, x \in R, x \neq 0 \}$ and $B = \{ (x, y) : y = -x, x \in R \}$,then:

If $A = \{x : x = \frac{n-1}{n+1}, n \in W\}$ and $\{n \leq 10\}$,point out the correct statement from the following:

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