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# Problem Solving Practice Test 5

**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? **

- 32760
- 15625
- 30
- 36
- 46656

**Correct Answer : B **

**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?**

- 360
- 120
- 540
- 720
- 180

**Correct Answer : B **

**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?**

- 237144
- 251820
- 502340
- 72000
- 2073600

**Correct Answer : E **

**Question 4**

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

- 5040
- 40320
- 2520
- 4914
- 378

**Correct Answer : A **

**Question 5**

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

- 2400
- 1200
- 600
- 250
- 100

**Correct Answer : B **

**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?**

- 250
- 90
- 100
- 870
- 900

**Correct Answer : D **

**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?**

- 2534
- 1500
- 56321
- 42430
- 20160

**Correct Answer : E **

**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?**

- 1450
- 2920
- 3105
- 2002
- 1400

**Correct Answer : D **

**Question 9**

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

- 230
- 2952
- 5904
- 7695
- 5130

**Correct Answer : B **

**Question 10**

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

- 10,15
- 6,7
- 4,25
- 9,10
- 8,19

**Correct Answer : E **

**Question 11**

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

- 8
- 4
- 2
- 6
- 3

**Correct Answer : D **

**Question 12**

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

- 3006
- 3003
- 2997
- 3005
- 3009

**Correct Answer : C **

**Question 13**

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

- 6
- 7
- 8
- 9
- 4

**Correct Answer : D**

**Question 14**

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

- 6547
- 10000
- 3600
- 4536
- 5040

**Correct Answer : D**

**Question 15**

**In how many ways can 9 students be seated in a row such that the tallest child and the shortest child never sit together?**

- 564480
- 282240
- 141120
- 70560
- 23416

**Correct Answer : B**

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