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1. A palindrome is a word which is similar if read from backwards. Eg ‘ARORA’. Find the number of such 5 letter palindromes.
- A. 676
- B. 676
- C. 676
- D. 676
Answer: Option B
Explanation:
The first letter can be chosen in 26 ways. Similarly, second letter can be chosen in 26 ways.
Hence, the first 2 letters can be chosen in 26 × 26 ways.
Also, the third letter can be chosen in 26 ways.
Hence, the first 3 letters can be chosen in 26 × 26 × 26 ways.
But the fourth letter should be similar to second letter. This can be done in just 1 way.
Similarly, fifth letter should be similar to first letter. This can be done only in 1 way.
Hence, number of words possible = 26 × 26 × 26 × 1 × 1
= 17576
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