# 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

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

Q. 3
In the editorial group’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. 2073600
• c. 251820
• d. 502340
• e. 72000

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

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

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. 870
• c. 90
• d. 100
• e. 900

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. 20160
• c. 1500
• d. 56321
• e. 42430

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. 2002
• c. 2920
• d. 3105
• e. 1400

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

Q. 10
Find the possible values of n if 30 P(n,6) = P(n+2,7).
• a. 10,15
• b. 8,19
• c. 6,7
• d. 4,25
• e. 9,10

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. 6
• c. 4
• d. 2
• e. 3

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. 2997
• c. 3003
• d. 3003
• e. 3009

Q. 13
If P(n-1,3):P(n,3) = 1:9, find n.
• a. 6
• b. 9
• c. 7
• d. 8
• e. 4

Q. 14
How many four-digit numbers are there with distinct digits?
• a. 6547
• b. 4536
• c. 10000
• d. 3600
• e. 5040