CUET UG 2025 — General Test Quantitative Reasoning

The word DOCUMENT has the following letters:

Vowels: O, U, E (3 vowels)

Consonants: D, C, M, N, T (5 consonants)

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Since all vowels must come together, treat the vowels (O, U, E) as one single block.

This gives:

1 vowel block (OUE) + 5 consonants (D, C, M, N, T) = 6 units to arrange

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The 6 units can be arranged in:

$$6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1$$6!=6×5×4×3×2×1

$= 720$=720 ways

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Within the vowel block, the 3 vowels can be arranged among themselves in:

$$3! = 3 \times 2 \times 1$$3!=3×2×1

$= 6$=6 ways

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Total arrangements = (Ways to arrange the 6 units) $\times$× (Ways to arrange vowels within the block)

Total $= 6! \times 3!$=6!×3!

$$= 720 \times 6$$=720×6

$$= 4320$$=4320

Therefore, the letters of DOCUMENT can be arranged in 4320 ways with all vowels together.