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A Learning Portal from Recruitment India

In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?

A.

9!/(4!*5!)

B.

4!*5!

C.

9!/4

D.

None of these

Answer with explanation

Answer: Option BExplanation

The word EDUCATION is a 9 letter word, with none of the letters repeating.

The vowels occupy 3, 5, 7^{th} and 8^{th} position in the word and the remaining 5 positions are occupied by consonants.

As the relative position of the vowels and consonants in any arrangement should remain the same as in the word EDUCATION, the vowels can occupy only the aforementioned 4 places and the consonants can occupy 1^{st}, 2^{nd}, 4^{th}, 6^{th} and 9^{th} positions.

The 4 vowels can be arranged in the 3^{rd}, 5^{th}, 7^{th} and 8^{th} position in 4! Ways.

Similarly, the 5 consonants can be arranged in 1^{st}, 2^{nd}, 4^{th}, 6^{th} and 9^{th} position in 5! Ways.

Hence, the total number of ways = 4! * 5!.

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In how many ways can you rearrange the word JUMBLE such that the rearranged word starts with a vowel?

A.

60

B.

120

C.

240

D.

360

Answer with explanation

Answer: Option CExplanation

JUMBLE is a six-lettered word. Since the rearranged word has to start with a vowel, the first letter can be either U or E. The balance 5 letters can be arranged in ^{5}P_{5} or 5! ways. Total number of words = 2 × 5! = 240.

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How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

A.

20

B.

15

C.

10

D.

5

Answer with explanation

Answer: Option AExplanation

Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.

The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.

The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.

Required number of numbers = (1 x 5 x 4) = 20.

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How many arrangements can be made out of the letters of the word ‘ENGINEERING’?

A.

277200

B.

182000

C.

924000

D.

734500

Answer with explanation

Answer: Option AExplanation

The word ‘ENGINEERING’ has 11 letters.

But in these 11 letters, ‘E’ occurs 3 times,’N’ occurs 3 times, ‘G’ occurs 2 times, ‘I’ occurs 2 times and rest of the letters are different.

Hence,number of ways to arrange these letters

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