MEDIUM
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A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics & Chemistry. It was found that all students passed in at least one of the subjects, 20 students passed in Mathematics, 25 students passed in Physics, 16 students passed in Chemistry, at most 11 students passed in both Mathematics and Physics, at most 15 students passed in both Physics and Chemistry, at most 15 students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is _____.

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Important Questions on Set Theory and Relations

MEDIUM
Consider the two sets:
A={mR: both the roots of x2-(m+1)x+m+4=0 are real } and B=[-3,5)
Which of the following is not true?
MEDIUM
A survey shows that 63% of the people in a city read newspaper A whereas 76% read news paper B. If  x% of the people read both the newspapers, then a possible value of x can be:
HARD

Let i=150Xi=i=1nYi=T, where each Xi contains 10 elements and each Yi contains 5 elements. If each element of the set T is an element of exactly 20 of sets Xi's and exactly 6 of sets Yi's then n is equal to :

HARD
Let A=θR:13sinθ+23cosθ2=13sin2θ+23cos2θ. Then
MEDIUM
In a class of 140 students numbered 1 to140 , all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is:
HARD
In a certain town, 25% families own a phone,15% families own a car, 65% families own neither a phone nor a car and 2000 families own both a car and a phone. Consider the following Statements (S):
S1: 35% families own at least one of a car or a phone.
S2: 40,000 families live in the town.
Then:
EASY
A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be:
EASY

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

Question Image

MEDIUM
In a certain town, 25% of the families own a phone and 15% own a car; 65% families own neither a phone nor a car and 2000 families own both a car and a phone. Consider the following three statements:

i 5% families own both a car and a phone.

ii 35% families own either a car or a phone.

iii 40000 families live in the town.

Then,
EASY
If U is the universal set with 100 elements; A and B are two sets such that nA=50, nB=60 nAB=20 then nA'B'=
HARD
For any three sets A, B and C the set (ABC)AB'C''C' is equal to
EASY
If A={x|xN,x is a prime number less than 12} and B={x|xNx is factor of 10}, then AB=
EASY
If X and Y are two sets, then X(YX)' equals
EASY
If nA=3, nB=6 and AB, then the number of elements in AB is equal to
EASY
In a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100, Physics 70, Chemistry 40, Mathematics and Physics 30, Mathematics and Chemistry 28, Physics and Chemistry 23, Mathematics, physics and Chemistry 18. The number of students who have opted Mathematics alone is
EASY
If n(P)=8, n(Q)=10 and n(R)=5 ('n' denotes cardinality) for three disjoint sets P, Q, R, then n(PUQUR)=
MEDIUM
If A and B are two non-empty sets, then B-AAB' is equal to
EASY
If AB, then AΔB is equal to
MEDIUM
If A=xR:x<2 and B=xR:x-23; then
MEDIUM
Two newspapers A and B are published in a city. It is known that 25% of the city population reads A and 20% reads B while 8% reads both A and B. Further, 30% of those who read A but not B look into advertisements and 40% of those who read B but not A also look into advertisements, while 50% of those who read both A and B look into advertisements. Then the percentage of the population who look into advertisements is: