Venn Diagram

Q.

In how many ways, a party of 5 men and 5 women be seated at a circular table, so that no two women are adjacent?

1. 720

2. 14400

3. 1440

4. 2880

Q.

A group of 120 students, 90 take mathematics and 72 take economics. If 10 students take neither of the two, how many students take both:

1. 20

2. 52

3. 30

4. 62

Q. Draw appropriate Venn diagram for each of the following: (i) (ii) (iii) (iv)

Q.

In a class of 40 students 14 take physics and 29 take chemistry. If 5 students take both, how many students take neither of the subjects?

1. 2

2. 38

3. 14

4. 5

Q.

There was a survey in a city about number of people reading newspaper A, B and C. There are 42% of people read newspaper A; 51% of people read newspaper B and 68% of people read paper C. 30% of people read both newspaper A and B. 28% reads B and C and 36% read C and A. 8% do not read any newspaper. Find the percentage of people who read all the three newspapers.

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Q. 37. In a survey of 700 people it was found that 250 persons read newspaper A, 200 read newspaper B, 100 read newspaper C, 50 read both A&B, 30 read both A&C & 15 read both B and C.if 3 persons read all three newspapers then find the number of persons who read . (I) atleast 1 newspaper. (II) exactly 1 newspaper. (III) atmost 1 newspaper.

Q.

In a town of 10, 000 families it was found that 40% family buy newspaper A, 20% buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then number of families which buy A only is __.

Q.

In a class of 100 students, 12 students drink only milk and 5 students drink only coffee and 8 students drink only Tea. Other report says 30 students take both coffee and tea, 25 students take milk and tea and 20 students take only milk and coffee. 10 students drink all the three. Find the number of students who do not drink anything.

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Q. 32. In a group of 500 students 170 play cricket 130 play football and 150 play hockey 90 play cricket and football 40 play football and hockey 50 play hockey and cricket 200 play none of these 3 games Find how many play all the 3 games , and exactly two of the three games

Q.

Out of 900 modules tested, 400 modules are from mathematics and 200 are from physics, how many modules are tested from both the subjects:

1. 200

2. 500

3. 600

4. 30

Q.

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I and 3 read all three newspapers, find

(i) the number of people who read atleast one of the newspapers.

(ii) the numbers of people who read exactly one newspaper.

Q. Q.15 10 different things are arranged in a circle, then number of ways to select three objects, such that atleast two of the objects are consecutive

Q. Write the set $\left\{\frac{1}{2},\frac{2}{5},\frac{3}{10},\frac{4}{17},\frac{5}{26},\frac{6}{37},\frac{7}{50}\right\}$ in the set-builder form.

Q. Given three sets $A,B\&C$such that $A\subset B$ and $B\&C$ are disjoint sets, then the correct representation of the three sets is:

1. 
2. 
3. 
4. 

Q. The area of the region bounded by the curves y = sinx, y = sin2x and ordinates x = π to x = 2π in square units, is equal to

Q. Calculate the A.M. and S.D. for the following distribution:

Class:	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency:	18	16	15	12	10	5	2	1

Q. In a group of $65$ people, $40$ like cricket, $10$ like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

Q. In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people likes products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only?

Q. If $A\times B=\left\{\right(a,x),(a,y),(b,x),(b,y\left)\right\}$ Find $A$ and $B$.

Q. Given, $P\left(A\right)=\frac{3}{5}$ and $P\left(B\right)=\frac{1}{5}$. Find $P\left(A\text{or}B\right)$, if $A$ and $B$ are mutually exclusive events.

Q.

Out of 200 students who are trying to improve their vocabulary, 120 students read newspaper H, 50 read newspaper T and 30 read both newspaper H and T. find the number of students

i) who read H but not T _____

ii) who read T but not H _____

iii) who don't read any newspaper _____

1. 30, 20, 60

2. 90, 20, 60

3. 90, 20, 30

4. 20, 30, 60

Q.

Shaded region in the following figure illustrates

1. 

2. 

3. 

4. 

Q. In a group of 1000 people, there are 750 who can speak Hindi and 400 who can speak Bengali. How many can speak Hindi only? How many can speak Bengali? How many can speak both Hindi and Bengali?

Q. In a group of 50 persons, 14 drink tea but not coffee and 30 drink tea. Find:
(i) how may drink tea and coffee both;
(ii) how many drink coffee but not tea.

Q. A survey shows that 76% of the Indians like oranges, whereas 62% like bananas. What percentage of the Indians like both oranges and bananas?

Q.

Let U be the universal set and $A\cup B\cup C=U$. Then {$(A-B)\cup (B-C)\cup (C-A)$}. Then U is equal to

1. A∪B∪C

2. A∩(B∪C)

3. A∩B∩C

4. A∪(B∩C)

Q. In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find: (i) the number of people who read at least one of the newspapers. (ii) the number of people who read exactly one newspaper.

Q. Given two sets $X$ and $Y$ such that $n\left(X\right)=20,n\left(Y\right)=25\text{and}n\left(XUY\right)=40,$ then $n(X-Y)=$

1. $20$
2. $5$
3. $10$
4. $15$

Q. Express the given complex number in the form $a+ib:$$(\frac{1}{5}+i\frac{2}{5})-(4+i\frac{5}{2})$

Q.

If A, B and C are three sets such that $A\cap B=A\cap CandA\cup B=A\cup C$, then

1. $A\cap B=\varphi$

2. A = C

3. B = C

4. A = B