# Problem Solving Practice Test 1

#### Q.1

If you join all the vertices of a heptagon, how many quadrilaterals will you get?

- A. 72
- B. 36
- C. 25
- D. 35
- E. 120
- Answer: D

#### Q.2

Four students have to be chosen 2 girls as the captain and vice-captain and 2 boys as captain and vice-captain of the school. There are 15 eligible girls and 12 eligible boys. In how many ways can they be chosen if Sunita is sure to be the captain?

- A. 114
- B. 1020
- C. 360
- D. 1848
- E. 1500
- Answer: D

#### Q.3

A teacher prepares a test. She gives 5 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices.

- A. 255
- B. 816
- C. 192
- D. 100
- E. 144
- Answer: B

#### Q.4

How many 5 digit numbers are there with distinct digits?

- A. 144
- B. 27216
- C. 4386
- D. 6432
- E. 720
- Answer: B

#### Q.5

In how many ways can 15 students be seated in a row such that the 2 most talkative children never sit together?

- A. 14!.14!
- B. 15.14!
- C. 14!
- D. 14! 13
- E. 15!
- Answer: D

#### Q.6

In a school 5 colours are allotted to each house. If the flag of Tagore House has to be a sequence of three blocks of different colours, then how many flags can they choose from?

- A. 9
- B. 27
- C. 60
- D. 20
- E. 15
- Answer: C

#### Q.7

Find the number of words which can be formed by using the letters of the word EQUATION if each word has to start with a vowel.

- A. 40320
- B. 1260
- C. 1080
- D. 400
- E. 25200
- 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 or 5 or both?

- A. 100
- B. 150
- C. 3125
- D. 1500
- E. 125
- Answer: D

#### Q.9

A straight road runs from north to south. It has two turnings towards east and three turnings towards west. In how many ways can a person coming from east get on the road and go west?

- A. 2
- B. 3
- C. 9
- D. 6
- E. 5
- Answer: D

#### Q.10

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

- A. 562
- B. 120
- C. 105
- D. 400
- E. 282
- Answer: B

#### Q.11

Four persons enter the lift of a seven storey building at the ground floor. In how many ways can they get out of the lift on any floor other than the ground floor?

- A. 720
- B. 1296
- C. 1663
- D. 360
- E. 2500
- Answer: B

#### Q.12

Ten different letters of an alphabet are given. 2 of these letters followed by 2 digits are used to number the products of a company. In haw many ways can the products be numbered?

- A. 52040
- B. 8100
- C. 5040
- D. 1000
- E. 4000
- 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