4
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:   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

Q:

In how many ways can letter of the word RAILINGS arrange so that R and S always come together?

A) 1260 B) 2520
C) 5040 D) 1080
 
Answer & Explanation Answer: C) 5040

Explanation:

The number of ways in which the letters of the word RAILINGS can be arranged such that R & S always come together is

 

Count R & S as only 1 space or letter so that RS or SR can be arranged => 7! x 2!

 

But in the word RAILINGS, I repeated for 2 times => 7! x 2!/2! = 7! ways = 5040 ways.

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7 3285
Q:

On the occasion of New Year, each student of a class sends greeting cards to the others. If there are 21 students in the class, what is the total number of greeting cards exchanged by the students?

A) 380 B) 420
C) 441 D) 400
 
Answer & Explanation Answer: B) 420

Explanation:

Given total number of students in the class = 21

 

So each student will have 20 greeting cards to be send or receive (21 - 1(himself))

 

Therefore, the total number of greeting cards exchanged by the students = 20 x 21 = 420.

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11 3891
Q:

How many more words can be formed by using the letters of the given word 'CREATIVITY'?

A) 851250 B) 751210
C) 362880 D) 907200
 
Answer & Explanation Answer: D) 907200

Explanation:

The number of letters in the given word CREATIVITY = 10

 

Here T & I letters are repeated

 

=> Number of Words that can be formed from CREATIVITY = 10!/2!x2! = 3628800/4 = 907200

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8 3629
Q:

If (1 × 2 × 3 × 4 ........ × n) = n!, then 15! - 14! - 13! is equal to ___?

A) 14 × 13 × 13! B) 15 × 14 × 14!
C) 14 × 12 × 12! D) 15 × 13 × 13!
 
Answer & Explanation Answer: D) 15 × 13 × 13!

Explanation:

15! - 14! - 13!

= (15 × 14 × 13!) - (14 × 13!) - (13!)

= 13! (15 × 14 - 14 - 1)

= 13! (15 × 14 - 15)

= 13! x 15 (14 - 1)

= 15 × 13 × 13!

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9 3507
Q:

To fill 8 vacancies there are 15 candidates of which 5 are from ST. If 3 of the vacancies are reserved for ST candidates while the rest are open to all, Find the number of ways in which the selection can be done ?

A) 7920 B) 74841
C) 14874 D) 10213
 
Answer & Explanation Answer: A) 7920

Explanation:

ST candidates vacancies can be filled by C35 ways = 10 

Remaining vacancies are 5 that are to be filled by 12 

=> C512= (12x11x10x9x8)/(5x4x3x2x1) = 792 

Total number of filling the vacancies = 10 x 792 = 7920

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10 3398
Q:

A,B,C,D,E,F,G and H are sitting around a circular table facing the centre but not necessarily in the same order. G sits third to the right of C. E is second to the right of G and 4th to the right of H. B is fourth to the right of C. D is not an immediate neighbour of E. A and C are immediate neighbours.

 Which of the following is/are correct ?

A) F is third to the left of B B) F is second to the right of B
C) B is an immediate neighbour of D D) All of the above
 
Answer & Explanation Answer: B) F is second to the right of B

Explanation:

From the given information, the circular arrangement is

EXP.

Here F is second to the right of B and the remaning all are wrong.

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6 3521
Q:

Nine different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, how many such words can be formed which have at least one letter repeated ?

A) 43929 B) 59049
C) 15120 D) 0
 
Answer & Explanation Answer: A) 43929

Explanation:

Number of words with 5 letters from given 9 alphabets formed = 95

 

Number of words with 5 letters from given 9 alphabets formed such that no letter is repeated is = 9P5

 

Number of words can be formed which have at least one letter repeated =  95 - 9P5

 

= 59049 - 15120

 

= 43929

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11 5058
Q:

In how many different ways can the letters of the word 'ABYSMAL' be arranged ?

A) 5040 B) 3650
C) 4150 D) 2520
 
Answer & Explanation Answer: D) 2520

Explanation:

Total number of letters in the word ABYSMAL are 7

 

Number of ways these 7 letters can be arranged are 7! ways

 

But the letter is repeated and this can be arranged in 2! ways

 

Total number of ways arranging ABYSMAL = 7!/2! = 5040/2 = 2520 ways.

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13 4093