Problem Solving Practice Test 1

Question 1

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

1. 72
2. 36
3. 25
4. 35
5. 120

Question 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?

1. 114
2. 1020
3. 360
4. 1848
5. 1500

Question 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.

1. 255
2. 816
3. 192
4. 100
5. 144

Question 4

How many 5 digit numbers are there with distinct digits?

1. 144
2. 27216
3. 4386
4. 6432
5. 720

Question 5

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

1. 14!.14!
2. 15.14!
3. 14!
4. 14! 13
5. 15!

Question 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?

1. 9
2. 27
3. 60
4. 20
5. 15

Question 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.

1. 40320
2. 1260
3. 1080
4. 400
5. 25200

Question 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?

1. 100
2. 150
3. 3125
4. 1500
5. 125

Question 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?

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

Question 10

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

1. 562
2. 120
3. 105
4. 400
5. 282

Question 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?

1. 720
2. 1296
3. 1663
4. 360
5. 2500

Question 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?

1. 52040
2. 8100
3. 5040
4. 1000
5. 4000

Question 13

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

1. 2
2. 4
3. 6
4. 8
5. 10

Question 14

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

1. 12
2. 11
3. 10
4. 9
5. 8