Question

We are required to form different words with the help of letter of the word $INTEGER$. Let $m_1$ be the number of words in which $I$ and $N$ are never together and $m_2$ be the number of words which start with $I$ and end with $R$, then $m_1/m_2$ is given by

• A. $90$
• B. $30$
• C. $60$
• D. $180$

Answer 1

The correct option is B $30$

All possible words are $\frac{7!}{2!}$ = $2520$
If I and N are always together(two ways IN or NI),
= $\frac{2.6!}{2!}=720$
So, $m_1=1800$
If it is starting with I and ends with R,
$m_2=\frac{5!}{2}=60$
So, $\frac{m_1}{m_2}=30$