The remainder when $7^{84}$ is divided by $342$ is:

If $n=1+x$, where $x$ is the product of four consecutive positive integers, then which of the following is/are true?

$A. n$ is odd

$B. n$ is prime

$C. n$ is a perfect square

Let $S$ be the set of integers $x$ such that:

$\left(i\right) 100\le x\le 200$

$\left(ii\right) x$ is odd

$\left(iii\right) x$ is divisible by $3$ but not by $7$

How many elements does $S$ contain? 

Let $S$ be the set of prime numbers greater than or equal to $2$ and less than $100$. [ Multiply all elements of $S$.] With how many consecutive zeros will the product end?