# Problem Solving Practice Test 1

**Question 1**

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

- 72
- 36
- 25
- 35
- 120

**Correct Answer : D **

**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?**

- 114
- 1020
- 360
- 1848
- 1500

**Correct Answer :D **

**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.**

- 255
- 816
- 192
- 100
- 144

**Correct Answer : B **

**Question 4**

**How many 5 digit numbers are there with distinct digits?**

- 144
- 27216
- 4386
- 6432
- 720

**Correct Answer : B **

**Question 5**

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

- 14!.14!
- 15.14!
- 14!
- 14! 13
- 15!

**Correct Answer : D **

**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?**

- 9
- 27
- 60
- 20
- 15

**Correct Answer : C **

**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.**

- 40320
- 1260
- 1080
- 400
- 25200

**Correct Answer : E **

**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?**

- 100
- 150
- 3125
- 1500
- 125

**Correct Answer : D **

**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?**

- 2
- 3
- 9
- 6
- 5

**Correct Answer : D **

**Question 10**

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

- 562
- 120
- 105
- 400
- 282

**Correct Answer : B **

**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?**

- 720
- 1296
- 1663
- 360
- 2500

**Correct Answer : B **

**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? **

- 52040
- 8100
- 5040
- 1000
- 4000

**Correct Answer : D **

**Question 13**

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

- 2
- 4
- 6
- 8
- 10

**Correct Answer : B**

**Question 14**

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

- 12
- 11
- 10
- 9
- 8

**Correct Answer : E **

**Question 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? **

- 132
- 242
- 60
- 120
- 240

**Correct Answer : D**