Aspire Faculty ID #16491 · Topic: NIMCET 2009 · Just now
NIMCET 2009

All the letters of the word 'INDIA' are permuted… the 58th word in dictionary order is?

Solution

Word: INDIA
Letters in alphabetical order: A, D, I, I, N (5 letters)

Number of permutations starting with each leading letter:

● Starting with A:
Remaining: D, I, I, N → total = 4! / 2! = 12 words

● Starting with D:
Remaining: A, I, I, N → again 12 words
Cumulative: 24 words

● Starting with I (first I):
Remaining: A, D, I, N → 4 letters all different = 24 words
Cumulative: 48 words

Next block starts with I again (second I):
We need the 58th word → 58 − 48 = 10th word in this block.

Now list 4-letter permutations of A, D, I, N:

Alphabetical order: A, D, I, N

Block starting with I gives words:

I A D N

I A N D

I A I N

I A N I

I D A N

I D N A

I D I A

I I A D

I I A N

I I D A → This is the 10th.

So final word = NIIDA? No, because leading letter should be I?
Wait: The initial letter of the block is N, not I — Let's correct.

We already used A (12), D (12), I (24).
Next letter in order is N.

So 48 words before N.
We need 58 → 10th under “N…”.

Remaining letters: A, D, I, I
Sorted: A, D, I, I

10th permutation of A, D, I, I is IDIA → attach N at start:

Correct word = NIDIA
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