Permutation of Distinct Objects - JEE Maths Free MCQ Test with solutions

Test: Permutation of Distinct Objects - Question 1

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

A.
144
B.
288
C.
12
D.
256

Detailed Solution: Question 1

Test: Permutation of Distinct Objects - 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.

A.
24
B.
48
C.
720
D.
120

Detailed Solution: Question 2

3 executives in 4 chairs = 4P3 ways
Total no. of ways = 2! * 4P3
=> 2*1*(4!/1!)
= 2*24
= 48

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Test: Permutation of Distinct Objects - 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

A.
164
B.
140
C.
112
D.
none of these

Detailed Solution: Question 3

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 ⁸C₆ = 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 = ²C₁ x ⁸C₅ =112 ways.
Therefore total number of ways is 28+ 112 = 140 ways,

Test: Permutation of Distinct Objects - Question 4

The number of ways in which 10 boys can be divided into 2 groups of 5, such that two tallest boys are in two different groups, is equal to

A.
70
B.
35
C.
252
D.
126

Detailed Solution: Question 4

Excluding the 2 tallest boys, we can divide the 8 boys into 2 groups of 4 each by
8!/4!4!2! ways.
The tallest boys can be assigned to the groups in 2 ways.
The desired number of ways are

Test: Permutation of Distinct Objects - Question 5

The number of ways of distributing eight identical rings to three different girls so that every girl gets at least one ring is

A.
21
B.
120
C.
⁸P₃
D.
⁸P₃−6

Detailed Solution: Question 5

The total no. of ways of dividing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is:

The number of ways =21.

Test: Permutation of Distinct Objects - Question 6

A.
8
B.
7
C.
3
D.
5

Detailed Solution: Question 6

7! /5! ×3!
=7×6×5! /5! ×3×2×1
=7

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Permutation of Distinct Objects - Free MCQ Practice Test with solutions,

MCQ Practice Test & Solutions: Test: Permutation of Distinct Objects (6 Questions)

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

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.

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

The number of ways in which 10 boys can be divided into 2 groups of 5, such that two tallest boys are in two different groups, is equal to

The number of ways of distributing eight identical rings to three different girls so that every girl gets at least one ring is

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