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SBI PO Prelims 8 Mar 2025 Shift 3 Paper

Question : 89 of 100

Marks: +1, -0

How many pairs of letters are there in the word “TRANSMISSION” which have as many letters between them as in the English alphabetical series (both in forward and backward direction)?

One
Two
Three
Four
More than Four

Validate

Solution:

Concept:

We count pairs of letters in the word where the number of letters between them equals the number of positions between them in the alphabet, considering both forward and backward order.

Explanation:

Write the word with positions and alphabet positions:

1\text{:T}(20),\;2\text{:R}(18),\;3\text{:A}(1),\;4\text{:N}(14),\;5\text{:S}(19),\;6\text{:M}(13),\;7\text{:I}(9),\;8\text{:S}(19),\;9\text{:S}(19),\;10\text{:I}(9),\;11\text{:O}(15),\;12\text{:N}(14).

For a pair

(i,j)

with

i < j

, the="" condition="" is=""

j-i="|\text{alpha}(j)-\text{alpha}(i)|

.Check all possible pairs:

- N (pos 4) and S (pos 9):

9-4=5

and

|19-14|=5

- I (pos 7) and N (pos 12):

12-7=5

and

|14-9|=5

- O (pos 11) and N (pos 12):

12-11=1

and

|14-15|=1

- M (pos 6) and I (pos 10):

10-6=4

and

|9-13|=4

No other pair satisfies the condition.

Thus there are four such pairs.

Answer:

Four

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