2
Q:

There are 4 books on fairy tales, 5 novels and 3 plays. In how many ways can you arrange these so that books on fairy tales are together, novels are together and plays are together and in the order, books on fairytales, novels and plays ?

A) 12400 B) 17820
C) 17280 D) 12460

Answer:   C) 17280



Explanation:

There are 4 books on fairy tales and they have to be put together. They can be arranged in 4! ways.

 

Similarly, there are 5 novels.They can be arranged in 5! ways.

 

And there are 3 plays.They can be arranged in 3! ways.

 

So, by the counting principle all of them together can be arranged in 4!´5!´3! ways = 17280

Q:

There are 5 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next two have 6 choices each?

A) 1112 B) 2304
C) 1224 D) 2426
 
Answer & Explanation Answer: B) 2304

Explanation:

Number of questions = 5
Possibilities of choices for each question 1 to 5 respectively = 4, 4, 4, 6, 6


Reuired total number of sequences

= 4 x 4 x 4 x 6 x 6

= 2304.

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5 185
Q:

How many numbers of five digits can be formed by using the digits 1, 0, 2, 3, 5, 6 which are between 50000 and 60000 without repeating the digits?

A) 120 B) 240
C) 256 D) 360
 
Answer & Explanation Answer: A) 120

Explanation:

Required number of 5 digit numbers can be formed by using the digits 1, 0, 2, 3, 5, 6 which are between 50000 and 60000 without repeating the digits are 

5 x 4 x 3 x 2 x 1 = 120.

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3 220
Q:

What is the value of 100P2 ?

A) 10000 B) 9900
C) 8900 D) 7900
 
Answer & Explanation Answer: B) 9900

Explanation:

Here in 100P2, P says that permutations and is defined as in how many ways 2 objects can be selected from 100 and can be arranged.

 

That can be done as,

 

100 P2  = 100!/(100 - 2)!

= 100 x 99 x 98!/98!

= 100 x 99 

= 9900.

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1 762
Q:

In how many different ways can the letters of the word 'THERAPY' be arranged so that the vowels always come together?

A) 720 B) 1440
C) 1800 D) 3600
 
Answer & Explanation Answer: B) 1440

Explanation:

Given word is THERAPY.

Number of letters in the given word = 7

Number of vowels in the given word = 2 = A & E

Required number of different ways, the letters of the word THERAPY arranged such that vowels always come together is

6! x 2! = 720 x 2 = 1440.

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6 474
Q:

In how many different ways the letters of the word 'TRANSFORMER' can be arranged such that 'N' and 'S' always come together?

A) 112420 B) 85120
C) 40320 D) 1209600
 
Answer & Explanation Answer: D) 1209600

Explanation:

Given word is TRANSFORMER.

Number of letters in the given word = 11 (3 R's)

 

Required, number of ways the letters of the word 'TRANSFORMER' can be arranged such that 'N' and 'S' always come together is

10! x 2!/3!

= 3628800 x 2/6

= 1209600

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3 516
Q:

In how many ways the letters of the word 'CIRCUMSTANCES' can be arranged such that all vowels came at odd places and N always comes at end?

A) 1,51,200 ways. B) 5,04,020 ways
C) 72,000 ways D) None of the above
 
Answer & Explanation Answer: A) 1,51,200 ways.

Explanation:

In circumcstances word there are 3C's, 2S's, I, U,R, T, A, N, E

Total = 13 letters

But last letter must be N

Hence, available places = 12

In that odd places = 1, 3, 5, 7, 9, 11

Owvels = 4

This can be done in 6P4 ways 

Remaining 7 letters can be arranged in 7!/3! x 2! ways

 

Hence, total number of ways = 6P4 x 7!/3! x 2! = 360 x 5040/12 = 1,51,200 ways.

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2 617
Q:

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

A) 720 B) 5040
C) 360 D) 180
 
Answer & Explanation Answer: A) 720

Explanation:

The number of letters in the given word RITUAL = 6

Then, 

Required number of different ways can the letters of the word 'RITUAL' be arranged = 6!

=> 6 x 5 x 4 x 3 x 2 x 1 = 720

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3 579
Q:

How many four digits numbers greater than 6000 can be made using the digits 0, 4, 2, 6 together with repetition.

A) 64 B) 63
C) 62 D) 60
 
Answer & Explanation Answer: B) 63

Explanation:

Given digits are 0, 4, 2, 6

Required 4 digit number should be greater than 6000.

So, first digit must be 6 only and the remaining three places can be filled by one of all the four digits.

This can be done by

1x4x4x4 = 64

Greater than 6000 means 6000 should not be there.

Hence, 64 - 1 = 63.

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8 908