Let $A = \{x:x \in R,\,|x|\, < 1\}\,;$ $B = \{x:x \in R,\,|x - 1| \ge 1\}$ and $A \cup B = R - D,$then the set $D$ is

If $\mathrm{S}=\{\mathrm{a} \in \mathrm{R}:|2 \mathrm{a}-1|=3[\mathrm{a}]+2\{\mathrm{a}\}\}$, where $[\mathrm{t}]$ denotes the greatest integer less than or equal to $t$ and $\{t\}$ represents the fractional part of $t$, then $72 \sum_{\mathrm{a} \in \mathrm{S}} \mathrm{a}$ is equal to....................

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

Let $a>0, a \neq 1$. Then, the set $S$ of all positive real numbers $b$ satisfying $\left(1+a^2\right)\left(1+b^2\right)=4 a b$ is

Consider the two sets :

$A=\{m \in R:$ both the roots of $x^{2}-(m+1) x+m+4=0$ are real $\}$ and $B=[-3,5)$

Which of the following is not true?

If $X = \{ {8^n} - 7n - 1:n \in N\} $ and $Y = \{ 49(n - 1):n \in N\} ,$ then