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