JEE 2023 — Mathematics PYQ

Q: How do I solve JEE 2023 Mathematics questions?

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Question

JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is:

Choose the correct answer:

Explanation

Solution

1. Identify Letters: Word: ASSASSINATION (13 letters)

Vowels: A, A, I, I, A, O (6 total: 3A, 2I, 1O)
Consonants: S, S, S, S, N, T, N (7 total: 4S, 2N, 1T)

2. Grouping Vowels: Treat all 6 vowels as 1 single block. Total units = $7 \text{ consonants} + 1 \text{ block} = 8$ units.

Arrangement of 8 units: $\frac{8!}{4!2!1!}$
Arrangement within vowel block: $\frac{6!}{3!2!}$

3. Total Words:

\text{Total} = \frac{8!}{4!2!} \times \frac{6!}{3!2!} = \frac{40320}{48} \times \frac{720}{12} = 840 \times 60 = 50,400

Choose the correct answer:

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