Circular Arrangement

Q. 2 girls and 4 boys are to be seated in a row in such a way that the girls do not sit together. In how many different ways can it be done?

1. 720
2. 480
3. 360
4. 240
5. None of these

Q.

Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?

1. 24

2. 32

3. 54

4. 32

5. 48

Q.

It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

1. None of these
2. 2880
3. 2480
4. 3680
5. 3280

Q.

The number of ways in which $6$ men and $5$ women can dine at a round table if no two women are to sit together is given by

1. $6!\times 5!$

2. $30$

3. $5!\times 4!$

4. $7!\times 5!$

Q. 4 boys and 3 girls are to be seated in a row in such a way that no 2 boys sit adjacent to each other. In how many different ways can it be done?

1. 5040
2. 30
3. 144
4. 72
5. None of these

Q. 5 people dine together at a round table. They dine together till each of them dines with different neighbours. Determine the number of days they dine together.

1. 12
2. 120
3. 24
4. 30
5. 7

Q. Find out the number of ways in which 18 flowers can be arranged in a necklace/garland.

1. 18!
2. 17!
3. 16!
4. ½(17!)
5. ½(18!)

Q.

The number of integer values of $\lambda$ such that the line x - 2y - 5 =0 passes through $\left(\lambda ,\left(\frac{\lambda -5}{2}\right)\right)$is

1. 1

2. 2

3. 4

4. Infinite

Q.

The number of integer values of $\lambda$ such that the line x - 2y - 5 =0 passes through $\left(\lambda ,\left(\frac{\lambda -5}{2}\right)\right)$is

1. 0

2. 1

3. 2

4. Infinite

5. 4

Q.

In how many ways can 4 men and their wives be made to stand in a line such that none of the 4 men stand next to his wife?

1. 40650

2. 40272

3. 40320

4. 39936