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

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

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?

Let the set $C=\left\{(x, y) \mid x^2-2^y=2023, x, y \in \mathbb{N}\right\}$. Then $\sum_{(x, y) \in C}(x+y)$ is equal to

The number of elements in the set $\left\{ n \in N : 10 \leq n \leq 100\right.$ and $3^{ n }-3$ is a multiple of $7\}$ is $........$.

$2n (A / B) = n (B / A)$ 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