# Problem Solving Practice Test 2

#### Q.1

Six points lie on a circle. How many quadrilaterals can be drawn joining these points?

- A. 72
- B. 36
- C. 25
- D. 15
- E. 120
- Answer: D

#### Q.2

There are 3 children of a lady. In how many ways is it possible to dress them for a party if the first child likes 3 dresses, second likes 4 and the third likes 5 but the third child has out grown one of them? Each child has a different set of clothes.

- A. 11
- B. 10
- C. 60
- D. 48
- E. 15
- Answer: D

#### Q.3

How many three-digit odd numbers can be formed from the digits 1, 3, 5, 0 and 8?

- A. 25
- B. 60
- C. 75
- D. 100
- E. 15
- Answer: B

#### Q.4

Find the number of words formed by permuting all the letters of the word INDEPENDENCE.

- A. 144
- B. 1663200
- C. 136050
- D. 6432
- E. 720
- Answer: B

#### Q.5

There are 12 children in a party. For a game they have to be paired up. How many different pairs can be made for the game?

- A. 46
- B. 24
- C. 120
- D. 66
- E. 132
- Answer: D

#### Q.6

How many different differences can be obtained by taking only 2 numbers at a time from 3, 5,2,10 and 15?

- A. 49
- B. 1898
- C. 1440
- D. 4320
- E. 720
- Answer: C

#### Q.7

In a class test there are 5 questions. One question has been taken from each of the 4 chapters. The first two chapters have 3 questions each and the last two chapters have 6 questions each. The fourth question can be picked from any of the chapters. How many different question papers could have been prepared?

- A. 540
- B. 1260
- C. 1080
- D. 400
- E. 4860
- Answer: E

#### Q.8

How many five digit numbers can be formed using the digits 0, 2, 3,4and 5, when repetition is allowed such that the number formed is divisible by 2 and 5?

- A. 100
- B. 150
- C. 3125
- D. 500
- E. 125
- Answer: D

#### Q.9

In how many ways can five rings be worn in 3 fingers?

- A. 81
- B. 625
- C. 15
- D. 243
- E. 125
- Answer: D

#### Q.10

How many pentagons can be drawn by joining the vertices of a polygon with 10 sides?

- A. 562
- B. 252
- C. 105
- D. 400
- E. 282
- Answer: B

#### Q.11

Find the number of words formed by permuting all the letters of the word INDEPENDENCE such that the E???s do not come together.

- A. 24300
- B. 1632960
- C. 1663200
- D. 30240
- E. 12530
- Answer: B

#### Q.12

Ten different letters of an alphabet are given. Words with 6 letters are formed with these alphabets. How many such words can be formed when repetition is not allowed in any word?

- A. 52040
- B. 21624
- C. 182340
- D. 151200
- E. 600000
- Answer: D

#### Q.13

If P(2n+1,n-1):P(2n-1,n) = 3:5, find n.

- A. 2
- B. 4
- C. 6
- D. 8
- E. 10
- Answer: B

#### Q.14

A polygon has 20 diagonals. How many sides does it have?

- A. 12
- B. 11
- C. 10
- D. 9
- E. 8
- Answer: E

#### Q.15

A box contains 5 red and 4 blue balls. In how many ways can 4 balls be chosen such that there are at most 3 balls of each colour?

- A. 132
- B. 242
- C. 60
- D. 120
- E. 240
- Answer: D