# 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

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

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

Q. 4
How many 5 digit numbers are there with distinct digits?
• a. 144
• b. 27216
• c. 4386
• d. 6432
• e. 720

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!

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

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

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

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

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

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

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

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

Q. 14
A polygon has 20 diagonals. How many sides does it have?
• a. 12
• b. 11
• c. 10
• d. 9
• e. 8