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