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Q:

Out of seven consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed ?

A) 25200	B) 25000
C) 25225	D) 24752

Answer & Explanation Answer: A) 25200

Explanation:

Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) =( $C_{3}^{7} \times C_{2}^{4}$ ) = 210.

Number of groups, each having 3 consonants and 2 vowels =210

Each group contains 5 letters.

Number of ways of arranging 5 letters among themselves = 5! = 120.

Required number of words = (210 x 120) = 25200.

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Filed Under: Permutations and Combinations
Exam Prep: CAT , Bank Exams
Job Role: Bank PO , Bank Clerk

Q:

In how many ways the letters of the word 'DESIGN' can be arranged so that no consonant appears at either of the two ends?

A) 240	B) 72
C) 48	D) 36

Answer & Explanation Answer: C) 48

Explanation:

DESIGN = 6 letters

No consonants appear at either of the two ends.

= $2 x 4 P_{4}$ = 2 x 4 x 3 x 2 x 1= 48

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Filed Under: Permutations and Combinations
Exam Prep: CAT , Bank Exams , AIEEE
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Q:

In How many ways can the letters of the word 'CAPITAL' be arranged in such a way that all the vowels always come together?

A) 360	B) 720
C) 120	D) 840

Answer & Explanation Answer: A) 360

Explanation:

CAPITAL = 7

Vowels = 3 (A, I, A)

Consonants = (C, P, T, L)

5 letters which can be arranged in $5 P_{5} = 5!$

Vowels A,I = $\frac{3!}{2!}$

No.of arrangements = 5! x $\frac{3!}{2!}$ =360

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Filed Under: Permutations and Combinations
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk

Q:

Explain in your words about Channel of communication, Skipper and Sundry Services.

Answer

Channel of communication : It is a floe of communication within a department.

Skipper : This term is used for the status of a room, which indicates that a guest has left the hotel room without arranging to settle his or her account.

Sundry Services :These are the extra services, which are provided to the guests. For e.g. message, handling of guests.

Workspace

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Subject: Hospitality

Q:

How many such pairs of letters are there in the word ORDINAL each of which has as many letters between them in the word as in the English alphabet?

A) None	B) One
C) Two	D) Three

Answer & Explanation Answer: D) Three

Explanation:

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Filed Under: Verbal Reasoning - Mental Ability
Exam Prep: Bank Exams
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Q:

How many such pairs of letters are there in the word ELEVATION each of which have as many letters between them in the word as they have between them in the English Alphabet?

A) One	B) Two
C) Three	D) More than three

Answer & Explanation Answer: C) Three

Explanation:

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Filed Under: Verbal Reasoning - Mental Ability
Exam Prep: Bank Exams
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Q:

How many arrangements can be made out of the letters of the word COMMITTEE, taken all at a time, such that the four vowels do not come together?

A) 216	B) 45360
C) 1260	D) 43200

Answer & Explanation Answer: D) 43200

Explanation:

There are total 9 letters in the word COMMITTEE in which there are 2M's, 2T's, 2E's.

The number of ways in which 9 letters can be arranged = $\frac{9!}{2! \times 2! \times 2!}$ = 45360

There are 4 vowels O,I,E,E in the given word. If the four vowels always come together, taking them as one letter we have to arrange 5 + 1 = 6 letters which include 2Ms and 2Ts and this be done in $\frac{6!}{2! \times 2!}$ = 180 ways.

In which of 180 ways, the 4 vowels O,I,E,E remaining together can be arranged in $\frac{4!}{2!}$ = 12 ways.

The number of ways in which the four vowels always come together = 180 x 12 = 2160.

Hence, the required number of ways in which the four vowels do not come together = 45360 - 2160 = 43200

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Q:

In the below word how many words are there in which R and W are at the end positions?

RAINBOW

A) 120	B) 180
C) 210	D) 240

Answer & Explanation Answer: D) 240

Explanation:

When R and W are the first and last letters of all the words then we can arrange them in 5!ways. Similarly When W and R are the first and last letters of the words then the remaining letters can be arrange in 5! ways.

Thus the total number of permutations = 2 x 5! = 2 x 120 = 240

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Filed Under: Permutations and Combinations

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