# Problem Solving Practice Test 2

Question 1

6 students of nursery class are playing a game. They are standing in a circle and have to pass a ball among themselves. How many such passes are possible?

1. 32760
2. 15625
3. 30
4. 36
5. 46656

Question 2

There are 5 boys standing in a row and 5 girls are to be paired with them for a group dance competition in a school. In how many ways can the girls be made to stand?

1. 360
2. 120
3. 540
4. 720
5. 180

Question 3

In the editorial groupâ€™s photograph of a school all the 5 teachers are to be seated in the front row. Four girls are to be in the second row and six boys in the third row. If the principal has a fixed seat in the first row, then how many arrangements are possible?

1. 237144
2. 251820
3. 502340
4. 72000
5. 2073600

Question 4

In how many ways can 8 people be seated at a round table?

1. 5040
2. 40320
3. 2520
4. 4914
5. 378

Question 5

Sunita wants to make a necklace. She has 8 beads. How many different choices does she have?

1. 2400
2. 1200
3. 600
4. 250
5. 100

Question 6

From city A to B there are 3 different roads. From B to C there are 5. From C to D there are 2. Laxman has to go from city A to D attending some work in city B and C on the way and has to come back in the reverse order. In how many ways can he complete his journey if he has to take a different while coming back than he did while going?

1. 250
2. 90
3. 100
4. 870
5. 900

Question 7

Neetu has five identical beads each of nine different colours. She wants to make a necklace such that the beads of the same colour always come together. How many different arrangements can she have?

1. 2534
2. 1500
3. 56321
4. 42430
5. 20160

Question 8

On a chess board one white square is chosen at random. In how many ways can a black square be chosen such that it does not lie in the same row as the white square?

1. 1450
2. 2920
3. 3105
4. 2002
5. 1400

Question 9

How many necklaces can be made using at least 5 from 8 beads of different colours?

1. 230
2. 2952
3. 5904
4. 7695
5. 5130

Question 10

Find the possible values of n if 30 P(n,6) = P(n+2,7).

1. 10,15
2. 6,7
3. 4,25
4. 9,10
5. 8,19

Question 11

Using all the prime numbers less than 10 how many four-digit even numbers can be made if repetition is not allowed?

1. 8
2. 4
3. 2
4. 6
5. 3

Question 12

There are 15 points in a plane, out of which 6 are collinear. How many pentagons can be drawn with these points?

1. 3006
2. 3003
3. 2997
4. 3005
5. 3009

Question 13

If P(n-1,3):P(n,3) = 1:9, find n.

1. 6
2. 7
3. 8
4. 9
5. 4

Question 14

How many four-digit numbers are there with distinct digits?

1. 6547
2. 10000
3. 3600
4. 4536
5. 5040