Letters of the word SUDESH can be arranged in

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24 ways when vowels and consonants occupy their respective places

240 ways when vowels do not occur together

120 ways when two vowels are together

180 ways when two vowels occupy in alphabetical order

answer is A, B, C, D.

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Detailed Solution

A)(UE),S,S,D,H can be arranged in $(2!) \frac{5!}{2!}$ ways.

$A) (2!) \frac{5!}{2!}$ =120

B) two vowels occupy in alphabetical order

Out of 6 letters two are vowels and two are identical

$B) \frac{6!}{2! 2!}$ =180

C) Vowels U,E can be arranged in 2! ways

and consonants can be arranged in $\frac{4!}{2!}$ ways

$C) \frac{4!}{2!} (2!)$ =24

D) vowels do not occur together.

Total arrangements- number of arrangements in which vowels come together -

$D) 360 - 120$ =240

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