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?
- 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 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?
- 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