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

$X, Y, Z$ are the sets of all positive divisors of $10^{60}, 20^{50},$ and $30^{40}$ respectively. Find $n(X \cup Y \cup Z)$.

Let $A = \{1, 6, 11, 16, \dots\}$ and $B = \{9, 16, 23, 30, \dots\}$ be the sets consisting of the first $2025$ terms of two arithmetic progressions. Then $n(A \cup B)$ is

In a survey of $60$ people,it was found that $25$ people read newspaper $H$,$26$ read newspaper $T$,$26$ read newspaper $I$,$9$ read both $H$ and $I$,$11$ read both $H$ and $T$,$8$ read both $T$ and $I$,and $3$ read all three newspapers. Find the number of people who read exactly one newspaper.

In a survey of $600$ students in a school,$150$ students were found to be taking tea and $225$ taking coffee,$100$ were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

In a committee,$50$ people speak French,$20$ speak Spanish and $10$ speak both Spanish and French. How many speak at least one of these two languages?