A palindrome is a word that reads the same backwards and forwards. For example, the word LEVEL is a palindrome. If we are allowed to construct words that need not have a meaning, then in how many different ways can we construct a five-letter palindrome using English alphabets?

Correct option is C

Solution:

Palindromes
A palindrome reads the same forward and backward.
For a 5-letter palindrome, the structure is:

_ _ _ _ _
Where:

1st = 5th letter

2nd = 4th letter

3rd is in the middle

So the structure is like this: A B C B A

So only 3 positions (A, B, C) are independent. Once you fix the first 3 letters, the remaining two are automatically fixed.

Choices per letter:
We have 26 English alphabets, so:

A (1st and 5th position): 26 choices

B (2nd and 4th position): 26 choices

C (middle letter): 26 choices

Total number of 5-letter palindromes:
= 26 × 26 × 26
= 26³
Final Answer:
S. Ans. (c) 26 × 26 × 26