Problem Solving Practice Test 01.docx

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