Question Bank  Modern Math  Hemant Malhotra

Q4) If the letters of the word REGULATIONS are arranged at random, the chances that there will be exactly four letters between R and E is

Q5) How many three digit odd nos. can be formed from the digits : 2, 0, 3, 5? (repetition not allowed).

Q6) How many different arrangement can be made out of the letters in the expression a^3 b^2 c^4 when written at full length?

Q7) In a class of 33 students, 20 play cricket, 25 footballs and 18 table tennis.15 play both cricket and football, 12 play football and table tennis, 10 table tennis and cricket. Each student plays at least one game. Find the number of students:
Q.1 Who play only cricket?
Q.2 Who play all the three games?
Q.3 Who play only two games?
Q.4 Who play only one game?

Q8) A bouquet of 25 flowers is to be made out of 4 different types of flowers, namely Rose, Sunflower, Jasmine and Carnation. Sufficient numbers of flowers are available of each type. Minimum five roses and five sunflowers mu st be used. At least one flower of each other type must be used while making the bouquet. Calculate the total number of ways in which the flowers for the bouquet can be selected.
a) 100
b) 150
c) 560
d) None of these

Q9) Out of 8 students in Section A, 10 students in Section B and 12 students in Section C, a teacher wants to create a team of three to represent the school in interschool quiz competition. In how many ways the team can be formed such that all the members of the team are not from the same section?

Q10) In a colony, 100 persons visited U.S., 80 visited U.K. and 60 visited Canada. 100 visited at least two of the above three countries. 30 visited all the three countries. 50 visited none of the three countries. What is the number of persons in the colony?
a) 180
b) 210
c) 160
d) Cannot be determined.

Q11) An institution, conducted a survey among its 300 students who appeared in the CAT examination. Among them 20% got a call from IIMA, 40% from IIMB, 35% from IIMC and 20% did not get a call from any of these institutes. 50% of those who got a call from IIMA did not get any other call. 25% of those who got a call from IIMB, also got a call from IIMA. How many of them got a call from only IIMC?
a) 10
b) 15
c) 90
d) 110

Q12) World’s top 200 tennis players took part in French open tournament and Wimbledon tournament. Among the players, who took part in singles or doubles events, 60% took part in doubles event and 50% took part in the French open tournament. Among those who participated in French Open tournament 60% took part in singles. 20% of the players took part in both singles and doubles events. Every player who participated in singles and double events of a tournament, has participated in both the events of the other tournament as well.
How many players took part in only Doubles?
a) 60
b) 40
c) 80
d) 100

Q13) There are a total 100 persons in a class. 40 failed in exam A , 50 failed in exam B , 45 failed in exam C. There are a total 32 students who failed in exactly 2 exams.Only 1 student passed in all exams. Find the number of students who failed in all 3 exams

@hemant_malhotra ans in 96

Q14) Four boxes are labeled as A, B, C and D. Each box contains three balls  one red, one blue and one green. In how many ways can a person pick 2 red and 3 blue balls?
(a) 48
(b) 24
(c) 8
(d) 16

Q15) Fourteen fruits and twenty two flowers are to be distributed among 10 people in such a way that each person gets something. Anyone who gets more than two flowers cannot get more than one fruit and anyone who gets more than one fruit cannot get more than three flowers. What is the maximum number of flowers that one can get?
(a) 3
(b) 5
(c) 19
(d) 22

Q16) Twelve students are made to stand in a row. The class teacher has to select three students from these 12 students such that there are at least 3 students standing between any two of the three students selected. In how many ways can this be done?

Q17) Ten persons sit in two rows such that five persons can sit in each row. If each girl sits beside or in front of or behind a boy and each boy sits beside or in front of or behind a girl, then what is the maximum possible number of girls that can be seated in the arrangement?
a) 7
b) 5
c) 6
d) 8

Q18) In a colony, 100 persons visited U.S., 80 visited U.K. and 60 visited Canada. 100 visited at least two of the above three countries. 30 visited all the three countries. 50 visited none of the three countries. What is the number of persons in the colony?
a) 180
b) 210
c) 160
d) Cannot be determined.


Q19) If 100 items are distributed among X men and Y women (Y > X). Find the probability that the number of items received by men is odd

Q20) Some children were standing around a circle. It was observed that the number of distinct pairs in which children were standing was one fifth of the distinct pairs in which children were not standing side by side. Find the number of children

Imagine a n sided polygon inside circle
and all children on vertices of that polygon so number of children =
now number of diagonals in a polygon of side n
=nc2  n
nc2 (means choose any two vertices and remove n sides )
it's give n=(nc2n)/5
so 5n=nc2n
so 6n=nc2
so n=13