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