Q. How many pairs of letters are there in the word “CASTRAPHONE” which have as many letters between them in the word as in the alphabet?

The correct answer is (D) 6.

Explanation:

To solve this problem, we need to identify all pairs of letters in the word “CASTRAPHONE” that have as many letters between them in the word as they do in the English alphabet.

First, let’s understand the condition: For any pair of letters, the number of letters between them in the word should be equal to the number of letters between them in the alphabet.

1. List the letters with their positions in the word and their positions in the alphabet:

Position (i) | Letter (L_i) | Alphabet Position (A_i)
1 | C | 3
2 | A | 1
3 | S | 19
4 | T | 20
5 | R | 18
6 | A | 1
7 | P | 16
8 | H | 8
9 | O | 15
10 | N | 14
11 | E | 5

2. Compare each pair of letters:

For each pair (i, j) where i < j, calculate:
– The number of letters between them in the word: delta_i_j = j – i
– The number of letters between them in the alphabet: delta_A_i_j = |A_i – A_j|

The pair satisfies the condition if delta_i_j = delta_A_i_j.

3. Identify the valid pairs:

Following this method, we find the following pairs satisfy the condition:
– Positions 3 and 4 (S and T)
– Positions 4 and 9 (T and O)
– Positions 4 and 10 (T and N)
– Positions 5 and 7 (R and P)
– Positions 8 and 11 (H and E)
– Positions 9 and 10 (O and N)

4. Count the valid pairs:

There are 6 pairs that meet the condition. Answer: 6