Let $A =\{ x \in R :| x +1|<2\}$ and $B=\{x \in R:|x-1| \geq 2\}$. Then which one of the following statements is NOT true ?

If $X = \{ {4^n} - 3n - 1:n \in N\} $ and $Y = \{ 9(n - 1):n \in N\} ,$ then $X \cup Y$ is equal to

Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers satisfying the condition $x^2-y^2=12345678$. Then,

Suppose ${A_1},\,{A_2},\,{A_3},........,{A_{30}}$ are thirty sets each having $5$ elements and ${B_1},\,{B_2}, ......., B_n$ are $n$ sets each with $3$ elements. Let $\bigcup\limits_{i = 1}^{30} {{A_i}} = \bigcup\limits_{j = 1}^n {{B_j}} = S$ and each elements of $S$ belongs to exactly $10$ of the $A_i's$ and exactly $9$ of the $B_j's$. Then $n$ is equal to

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

Let $\mathrm{A}=\{\mathrm{n} \in[100,700] \cap \mathrm{N}: \mathrm{n}$ is neither a multiple of $3$ nor a multiple of 4$\}$. Then the number of elements in $\mathrm{A}$ is