Question Bank  Modern Math  Hemant Malhotra

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

Q21) All the possible 5digit numbers are formed using the digits 1,2,3,4,5  repetition is allowed. If one of those numbers is selected at random what is the probability that it will have exactly one digit repeated and that too occurring twice

Q22)

Q23) N students are seated at desks in an m x n array, where m, n >= 3. Each student shakes hands with the students who are adjacent horizontally, vertically or diagonally. If there are 81 handshakes, what is N?

students those are in middle will shake hands with 8 students
those who are in corner will shake hands with 3 students
and those who are in sides will shake hands with 5 students
now number of handshakes students who are in corner then will be 4 corners so number of handshakes will be 4 * 3/2
now students who are in middle (m2) * (n2) * 8/2
becuase let m =5 and n =4 then students who are in middle will be=6 then handshakes wll be(52) * (42) * 8/2 = 48/2 = 24 same here if m and n then number of handhshakes will be (m2) * (n2) * 8/2now who are in sides of grid if 5 * 4 then number of studets who are in side will be 10 which is nothing but 2m4+2n4
so number of handshakes wiill be (2m+2n8) * 5/2
so total handshakes =81Solving, you will get
16 * m * n  12m  12n = 316
m=4 and n=7
so N = m * n = 28

Q24) There are ten 50 paise coins placed on a table. Six of these show tails and four show heads. A coin is chosen at random and flipped over (not tossed). This operation is performed seven times. One of these coins is then covered. Of the remaining nine coins, five show tails and four show heads. The covered coin shows:
a) A head
b) A tail
c) More likely a head
d) More likely a tail