# Problem Solving Practice Test 3

#### Q.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?

- A. 32760
- B. 15625
- C. 30
- D. 36
- E. 46656
- Answer: B

#### Q.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?

- A. 360
- B. 120
- C. 540
- D. 720
- E. 180
- Answer: B

#### Q.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?

- A. 237144
- B. 251820
- C. 502340
- D. 72000
- E. 2073600
- Answer: E

#### Q.4

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

- A. 5040
- B. 40320
- C. 2520
- D. 4914
- E. 378
- Answer: A

#### Q.5

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

- A. 2400
- B. 1200
- C. 600
- D. 250
- E. 390
- Answer: B

#### Q.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?

- A. 250
- B. 90
- C. 100
- D. 870
- E. 900
- Answer: D

#### Q.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?

- A. 2534
- B. 1500
- C. 56321
- D. 42430
- E. 20160
- Answer: E

#### Q.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?

- A. 1450
- B. 2920
- C. 3105
- D. 2002
- E. 1400
- Answer: D

#### Q.9

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

- A. 230
- B. 2952
- C. 5904
- D. 7695
- E. 5130
- Answer: B

#### Q.10

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

- A. 10,15
- B. 6,7
- C. 4,25
- D. 9,10
- E. 8,19
- Answer: E

#### Q.11

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

- A. 8
- B. 4
- C. 2
- D. 6
- E. 3
- Answer: D

#### Q.12

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

- A. 3006
- B. 3003
- C. 2997
- D. 3003
- E. 3009
- Answer: C

#### Q.13

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

- A. 6
- B. 7
- C. 8
- D. 9
- E. 4
- Answer: D

#### Q.14

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

- A. 6547
- B. 10000
- C. 3600
- D. 4536
- E. 5040
- Answer: D

#### Q.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?

- A. 564480
- B. 282240
- C. 141120
- D. 70560
- E. 23416
- Answer: B