Why is $7 \times 11 \times 13 + 13$ a composite number? Explain.

Prove that $\sqrt{3}$ is an irrational number.

The least number that is divisible by all the numbers from $1$ to $10$ (both inclusive) is

According to Euclid's division lemma,for given positive integers $a$ and $7$,there exist unique non-negative integers $q$ and $r$ such that $a = 7q + r$; where..........

The following real number is expressed in decimal form. Determine whether it is rational or not. If it is rational,express it in the form of $\frac{p}{q}$. $0.\overline{001}$

The following real number is expressed in decimal form: $0.05005000500005 \ldots$. Determine whether it is rational or irrational. If it is rational,express it in the form of $\frac{p}{q}$.