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Q.

Letters of the word SUDESH can be arranged in

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a

24 ways when vowels and consonants occupy their respective places

b

240 ways when vowels do not occur together

c

120 ways when two vowels are together

d

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!)5!2!ways.

 A) (2!)5!2!=120

B) two vowels occupy  in alphabetical order 

Out of 6 letters two are vowels and two are identical

 B) 6!2!2!=180

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

and consonants can be arranged in 4!2!ways

 C) 4!2!(2!)=24

D) vowels do not occur together.

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

 D) 360120=240

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