NIMCET 2009 — Reasoning PYQ

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Question

NIMCET 2009 — Reasoning PYQ

NIMCET | Reasoning | 2009

All the letters of the word ‘INDIA are permuted in all possible ways and the words so formed are written as in dictionary then the 58th word in the list is

Choose the correct answer:

Explanation

1. Analyze the Letters:

The word is INDIA.

Total letters: $5$
Repeated letters: $I$ appears $2$ times.
Letters in alphabetical order: A, D, I, I, N

2. Finding words starting with 'A':

If 'A' is fixed at the first position, we arrange the remaining letters (D, I, I, N):

\text{Number of words} = \frac{4!}{2!} = \frac{24}{2} = 12

(Total count so far: 12)

3. Finding words starting with 'D':

If 'D' is fixed at the first position, we arrange the remaining letters (A, I, I, N):

\text{Number of words} = \frac{4!}{2!} = \frac{24}{2} = 12

(Total count so far: 12 + 12 = 24)

4. Finding words starting with 'I':

If 'I' is fixed at the first position, we arrange the remaining letters (A, D, I, N). Since only one 'I' remains, there are no duplicates to divide by:

\text{Number of words} = 4! = 24

(Total count so far: 24 + 24 = 48)

5. Finding words starting with 'N':

We need the $58^{th}$ word. We have reached $48$ . We need $10$ more words starting with 'N'.

Words starting with 'NA': Fix 'N' and 'A', arrange (D, I, I):

$\text{Number of words} = \frac{3!}{2!} = 3$

(Total count: 48 + 3 = 51)
Words starting with 'ND': Fix 'N' and 'D', arrange (A, I, I):

$\text{Number of words} = \frac{3!}{2!} = 3$

(Total count: 51 + 3 = 54)
Words starting with 'NI': Fix 'N' and 'I', arrange (A, D, I):
- Alphabetical order of these words:
  
  55. NIADI
  
  56. NIAID
  
  57. NIDAI
  
  58. NIDIA

Final Answer:

The $58^{th}$ word is NIDIA.

Correct Option: (c)