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?

  1. 32760
  2. 15625
  3. 30
  4. 36
  5. 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?

  1. 360
  2. 120
  3. 540
  4. 720
  5. 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?

  1. 237144
  2. 251820
  3. 502340
  4. 72000
  5. 2073600

Correct Answer : E

Question 4

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

  1. 5040
  2. 40320
  3. 2520
  4. 4914
  5. 378

Correct Answer : A

Question 5

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

  1. 2400
  2. 1200
  3. 600
  4. 250
  5. 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?

  1. 250
  2. 90
  3. 100
  4. 870
  5. 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?

  1. 2534
  2. 1500
  3. 56321
  4. 42430
  5. 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?

  1. 1450
  2. 2920
  3. 3105
  4. 2002
  5. 1400

Correct Answer : D

Question 9

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

  1. 230
  2. 2952
  3. 5904
  4. 7695
  5. 5130

Correct Answer : B

Question 10

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

  1. 10,15
  2. 6,7
  3. 4,25
  4. 9,10
  5. 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?

  1. 8
  2. 4
  3. 2
  4. 6
  5. 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?

  1. 3006
  2. 3003
  3. 2997
  4. 3005
  5. 3009

Correct Answer : C

Question 13

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

  1. 6
  2. 7
  3. 8
  4. 9
  5. 4

Correct Answer : D

Question 14

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

  1. 6547
  2. 10000
  3. 3600
  4. 4536
  5. 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?

  1. 564480
  2. 282240
  3. 141120
  4. 70560
  5. 23416

Correct Answer : B