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 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. 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

Score: 0/10