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

Let $S=\{1,2,3, \ldots \ldots, n\}$ and $A=\{(a, b) \mid 1 \leq$ $a, b \leq n\}=S \times S$. A subset $B$ of $A$ is said to be a good subset if $(x, x) \in B$ for every $x \in S$. Then, the number of good subsets of $A$ is

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

Let $S=\{4,6,9\}$ and $T=\{9,10,11, \ldots, 1000\}$. If

$A=\left\{a_{1}+a_{2}+\ldots+a_{k}: k \in N, a_{1}, a_{2}, a_{3}, \ldots, a_{k} \in S\right\}$ then the sum of all the elements in the set $T - A$ is equal to $......$

Let $S = \{1, 2, 3, ….., 100\}$. The number of non-empty subsets $A$ of $S$ such that the product of elements in $A$ is even is

Let $S = \{ x \in R:x \ge 0$ and $2\left| {\sqrt x - 3} \right| + \sqrt x \left( {\sqrt x - 6} \right) + 6 = 0\} $ then $S:$ . . .