NIMCET 2011 — Mathematics PYQ

Solution

1. Analyze the word "DETAIL":

• Total number of letters = $6$

• Vowels: E, A, I (Total = $3$)

• Consonants: D, T, L (Total = $3$)

2. Identify the positions:

Since there are $6$ letters, there are $6$ available positions:

• Odd positions: $1,3,5$ (Total = $3$ positions)

• Even positions: $2,4,6$ (Total = $3$ positions)

3. Arrange the Vowels:

The problem states that vowels must occupy only the odd positions. There are $3$ vowels and $3$ odd positions.

The number of ways to arrange $3$ vowels in $3$ positions is:

4. Arrange the Consonants:

The remaining $3$ positions (the even ones) will be occupied by the $3$ consonants.

The number of ways to arrange $3$ consonants in the remaining $3$ positions is:

5. Calculate the Total Number of Ways:

To get the total arrangements, we multiply the possibilities for vowels and consonants:

Correct Option: (b) $36$