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This mock test of Test: Permutations Distinct Objects for JEE helps you for every JEE entrance exam.
This contains 10 Multiple Choice Questions for JEE Test: Permutations Distinct Objects (mcq) to study with solutions a complete question bank.
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QUESTION: 1

In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate.

Solution:

Let the Arrangement be,

**B G B G B G B**

4 boys can be seated in 4! Ways.

Girl can be seated in 3! Ways.

Required number of ways,

= 4!*3! = 144.

QUESTION: 2

In how many ways 2 directors and 3 executives can be arranged for a meeting? If there are 6 chairs available two on one side and remaining four on the other side of the table and the two directors has to be together on one side and the executives on the other side.

Solution:

3 executives in 4 chairs = 4P3 ways

Total no. of ways = 2! * 4P3

=> 2*1*(4!/1!)

= 2*24

= 48

QUESTION: 3

A lady arranges a dinner party for 6 guests .The number of ways in which they may be selected from among 10 friends if 2 of the friends will not attend the party together is

Solution:

Let the friends be A,B,C,D,E,F,G,H,I,J and assume A and B will not battend together

**Case 1 :** Both of them will not attend the party : Now we have to select the 6 guests from the remaing 8 members

Then no of ways is ^{8}C_{6} = 28 ways.

**Case 2 :** Either of them are selected for the party :Now we have to select the 5 guests from the remaing 8 members and one from A and B

Then the no of ways = ^{2}C_{1} x ^{8}C_{5} =112 ways.

Therefore total number of ways is 28+ 112 = 140 ways,

QUESTION: 4

What is the value of ^{n}p_{o}

Solution:

nP0

= n!/(n-0)!

=> n!/n! = 1

QUESTION: 5

Find the value of n if ^{n}P_{1} = 10

Solution:

nPr = 10

nPr = n!/(n-r)!

10 = n!/(n-1)!

10 = [n!.(n-1)!]/(n-1)!

n! = 10

QUESTION: 6

Number of signals that can be made using 2 flags out of given 4 flags.

Solution:

No. of ways of selecting two flags out of four = 4C2

So, total possible different signals generated = 4C2×2!

⟹ 6×2=12

QUESTION: 7

What is the value of ^{n}p_{n}

Solution:

nPn

= n!/(n-n)!

= n!

QUESTION: 8

Solution:
7! /5! Ã—3!

=7Ã—6Ã—5! /5! Ã—3Ã—2Ã—1

=7

=7Ã—6Ã—5! /5! Ã—3Ã—2Ã—1

=7

QUESTION: 9

5 singers are to be given performance in a concert. How many ways can they be arranged in a order

Solution:

5P5 ⇒ 5!/(5-5)!

= 5!/0!

= 5!/1 ⇒ 5!

= 120 ways

QUESTION: 10

What is the value of 0!

Solution:

The value of 0! = 1

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