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

Score: 0/10