Q:
If it is possible to make a meaningful word with the first, the seventh, the ninth and the tenth letters of the word RECREATIONAL, using each letter only once, which of the following will be the third letter of the word? If more than one such word can be formed, give ‘X’ as the answer. If no such word can be formed, give ‘Z’ as the answer.
Answer & Explanation Answer: D] R
Explanation:
The first, the seventh, the ninth and the tenth letters of the word RECREATIONAL are R, T, O and N respectively. Meaningful word from these letters is only TORN. The third letter of the word is ‘R’.
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Text Solution
3604807205040
Answer : C
Solution : The word 'LEADING ' has 7
different letters.
when the vowels EAI are always together , they can be supposed to form one letter.
then , we have to arrange the letters LNDG [EAI] .
Now , 5[4+1=5] letters can be arranged in 5! = 120 ways . the vowels [EAI] can be arranged among themselves in 3! = 6 ways.
`therefore ` Required number of ways `=[120 xx6]= 720`
1. | In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together? | |||||||
Answer: Option C Explanation: The word 'LEADING' has 7 different letters. When the vowels EAI are always together, they can be supposed to form one letter. Then, we have to arrange the letters LNDG [EAI]. Now, 5 [4 + 1 = 5] letters can be arranged in 5! = 120 ways. The vowels [EAI] can be arranged among themselves in 3! = 6 ways. Required number of ways = [120 x 6] = 720. |
2. | From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? | |||||||||||||||||||||||||||||||||||||
Answer: Option D Explanation: We may have [3 men and 2 women] or [4 men and 1 woman] or [5 men only].
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3. | In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together? | |||||||||||
Answer: Option D Explanation: In the word 'CORPORATION', we treat the vowels OOAIO as one letter. Thus, we have CRPRTN [OOAIO]. This has 7 [6 + 1] letters of which R occurs 2 times and the rest are different.
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged Required number of ways = [2520 x 20] = 50400. |
4. | In how many ways can the letters of the word 'LEADER' be arranged? | |||||||||||
Answer: Option C Explanation: The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
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5. | Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? | |||||||||||||||||||||||||||
Answer: Option C Explanation: Number of ways of selecting [3 consonants out of 7] and [2 vowels out of 4]
Number of groups, each having 3 consonants and 2 vowels = 210. Each group contains 5 letters.
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