Venn Diagrams PYQs for UPSC (2011-2024) | Solved Questions & PDF Download

Master Venn Diagrams for UPSC with solved Previous Year Questions (PYQs) from 2011 to 2024. This page provides detailed solutions, practice questions, and a free downloadable PDF to help you ace your UPSC preparation.

Why Venn Diagrams Matter in UPSC?

Venn Diagrams are a crucial part of the UPSC CSAT (Civil Services Aptitude Test). They test your ability to:

➡️ Visualize relationships between different sets of data.
➡️ Solve logical reasoning and data interpretation problems.
➡️ Understand overlaps and differences between groups.

This page breaks down the concepts and provides year-wise solved questions to help you master this topic.

Key Concepts in Venn Diagrams

Before diving into the questions, let’s quickly revise the key concepts:

1. Basics of Venn Diagrams

➡️ Venn Diagrams use circles to represent sets and their relationships.
➡️ Overlapping circles show common elements between sets.
➡️ Non-overlapping circles show distinct sets.

2. Types of Venn Diagrams

➡️ Two-Set Venn Diagrams: Used to compare two groups.
➡️ Three-Set Venn Diagrams: Used to compare three groups.
➡️ Complex Venn Diagrams: Used for more than three groups.

3. Common Terms

➡️ Union (A ∪ B): All elements in A or B.
➡️ Intersection (A ∩ B): Elements common to A and B.
➡️ Complement (A'): Elements not in A.

Year-Wise Venn Diagrams PYQs (2011-2024)

Q1. There are 100 students in a particular class. 60% students play cricket, 30% student play football and 10% students play both the games. What is the number of students who play neither cricket nor football? [CSAT 2011]

(a) 25

(b) 20

(d) 15

Solution:

Given that,

There are 100 students in a particular class.

60% students play cricket = 60

30% student play football = 30

10% students play both the games = 10

Now,

Let number of students playing cricket and football be C and F

Let p be the % of student playing neither cricket nor football

n(C∩F) = 10

n (C) = 60, n (F) = 30

So,

60 + 30 + p - 10 = 100

p = 20

Hence option (b) is correct

Q2. In the below figure, circle P represents hardworking people, circle Q represents intelligent people, circle R represents truthful people, and circle S represents honest people. Which region represents the people who are intelligent, honest and truthful but not hardworking? [CSAT 2012]

(a) 6

(b) 7

(d) 11

Solution:

Given that,

Circle P represents hardworking people,

Circle Q represents intelligent people,

Circle R represents truthful people

Circle S represents honest people.

Now,

The region representing the people who are intelligent, honest and truthful but not hardworking will be intersection of R, S and Q

Thus number 6 represents the given condition

Hence option (a) is correct

Q3. Out of 120 applications for a post, 70 are male and 80 have a driver's license. What is the ratio between the minimum to maximum number of males having driver's license? [CSAT 2013]

(a) 1 to 2

(b) 2 to 3

(d) 5 to 7

Solution:

Given that,

Out of 120 applications for a post, 70 are male and 80 have a driver's license.

Now,

Number of females = 120 - 70 = 50

Maximum number of males posses driving licence = 70

Minimum number of driving licence male have = 80 - 50 = 30

Ratio = 30 : 70 = 3 : 7

Hence option (c) is correct

Q4. There are 50 students admitted to a nursery class. Some students can speak only English and some can speak only Hind. 10 student can speak both English and Hindi. If the number of students who can speak English is 21, then how many students can speak Hindi how many can speak only Hindi and how many can speak only English? [CSAT 2014]

(a) 21, 11 and 29 respectively.

(b) 28, 18 and 22 respectively.

(d) 39, 29 and 11 respectively.

Solution:

Given that,

There are 50 students admitted to a nursery class.

Some students can speak only English and some can speak only Hind.

10 student can speak both English and Hindi.

The number of students who can speak English 21

Now,

Number of students who can speak only English = 21 - 10 = 11

Number of students who can speak Hindi = 50 - 11 = 39

Number of students who can speak only Hindi = 39 - 10 = 29

Hence option (d) is correct

Q5. Out of 130 students appearing in an examination, 62 failed in English, 52 failed in Mathematics, whereas 24 failed in both English and Mathematics. The number of students who passed finally is [CSAT 2015]

(a) 40

(b) 50

(d) 60

Solution:

Given that,

Out of 130 students appearing in an examination, 62 failed in English, 52 failed in Mathematics, whereas 24 failed in both English and Mathematics.

Now,

Number of students failed in at least one subject = 62 + 52 - 24 = 90

Number of students passed = 130 - 90 = 40

Hence option (a) is correct

Q6. In a town, 45% population read magazine A, 55% read magazine B, 40% read magazine C, 30% read magazines A and B, 15% read magazines B and C, 25% read magazines A and C; and 10% read all the three magazines. What percentage do not read any magazine? [CSAT 2015]

(a) 10%

(b) 15%

(d) 25%

Solution:

Given that,

In a town, 45% population read magazine A, 55% read magazine B, 40% read magazine C, 30% read magazines A and B, 15% read magazines B and C, 25% read magazines A and C; and 10% read all the three magazines.

Now,

Percentage of persons reading at least one magazine = 55 + 45 + 40 - 30 - 25 - 15 + 10 = 80

Percentage of persons not reading magazines = 100 - 80 = 20%

Hence option (c) is correct

Q7. In a group of persons travelling in a bus, 6 persons can speak Tamil, 15 can speak Hindi and 6 can speak Gujarati. In that group none can speak any other language. If 2 persons in the group can speak two languages only and one person can speak all the three languages, then how many persons are there in the group? [CSAT 2015]

(a) 21

(b) 22

(d) 24

Solution:

Given that,

In a group of persons travelling in a bus 6 persons can speak Tamil, 15 can speak Hindi and 6 can speak Gujarati. In that group none can speak any other language.

2 persons in the group can speak two languages only and one person can speak all the three languages.

Now,

Assuming two people can speak Tamil and Hindi both.

Number of people speaking only Tamil = 6 - 1 - 2 = 3

Number of people speaking only Hindi = 15 - 2 - 1 = 12

Number of people speaking only Gujarati = 6 - 1 = 5

Total number of people speaking only 1 language = 3 + 5 + 12 = 20

2 persons in the group can speak two languages only and one person can speak all the three languages = 2 + 1 = 3

Total = 20 + 3 = 23

Hence option (c) is correct

Q8. 19 boys turn out for playing hockey. Of these, 11 are wearing hockey shirts and 14 are wearing hockey pants. There are no boys without shirts and/or pants. What is the number of boys wearing full uniform? [CSAT 2018]

(a) 3

(b) 5

(d) 8

Solution:

Given that,

19 boys turn out for playing hockey.

11 are wearing hockey shirts

14 are wearing hockey pants.

There are no boys without shirts and/or pants.

Now,

Number of boys not wearing hockey shirt = 19 - 11 = 8

Boys wearing full uniform = 14 - 8 = 6 (No. of boys wearing hockey pants – No of boys not wearing hockey shirts)

Hence option (c) is correct

Q9. In a group of 15 people; 7 can read French, 8 can read English while 3 of them can read neither of these two languages. The number of people who can read exactly one language is [CSAT 2019]

(a) 10

(b) 9

(d) 4

Solution:

Given that,

Total people = 15

7 can read French

8 can read English

3 of them can read neither of these two languages.

Now,

Number of people reading at least one language = 15 - 3 = 12

Number of people reading both languages = 7 + 8 - 12 = 3

Number of people reading only French = 7 - 3 = 4

Number of people reading only English = 8 - 3 = 5

Number of people reading only one language = 4 + 5 = 9

Hence option (b) is correct

Q10. In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct? [CSAT 2019]

1. At least 30 Indian participants are vegetarian.

2. At least 10 Indian participants are non- vegetarian.

Select the correct answer using the codes given below:

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Solution:

Given that,

In a conference, out of a total 100 participants, 70 are Indians.

60 of the total participants are vegetarian

Now,

Non vegetarians participants = 100 - 60 = 40

1. At least 30 Indian participants are vegetarian.

Considering 40 Indians to be non- vegetarians

Then vegetarians = 70 - 40 = 30

Hence statement 1 is correct

2. At least 10 Indian participants are non- vegetarian.

Considering 60 vegetarians to be Indians

Non vegetarians = 70 - 60 = 10

Hence statement 2 is correct

Q11. In a school, 60% students play cricket. A student who does not play cricket, plays football. Every football player has got a two- wheeler. Which of the following conclusions cannot be drawn from the above data? [CSAT 2019]

1. 60% of the students do not have two- wheelers.

2. No cricketer has a two-wheeler.

3. Cricket players do not play football.

Select the correct answer using the code given below:

(a) 1 and 2 only

(b) 2 and 3 only

(d) 1, 2 and 3

Solution:

Given that,

In a school, 60% students play cricket. A student who does not play cricket, plays football. Every football player has got a two- wheeler.

Now,

1. 60% of the students do not have two- wheelers.

As it is not mentioned that cricketers have two wheeler or not. Thus it cannot be concluded.

2. No cricketer has a two-wheeler.

As it is not mentioned that cricketers have two wheeler or not. Thus it cannot be concluded.

3. Cricket players do not play football.

As it is not mentioned that Cricket players do not play football, only student who does not play cricket, plays football. Thus it cannot be concluded

Hence option (d) is correct

Q12. In a group of 120 persons, 80 are Indians and rest are foreigners, Further, 70 persons in the group can speak English. The number of Indians who can speak English is [CSAT 2021]

(a) 20

(b) 30

(d) 30 or more

Solution:

Given that,

In a group of 120 persons, 80 are Indians and rest are foreigners, Further, 70 persons in the group can speak English.

Now,

Number of foreigners = 120 - 80 = 40

Minimum number of Indians speaking English = 70 - 40 = 30

So at least 30 or more Indians can speak English.

Hence option (d) is correct

Q13. In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee. No one taking milk takes tea. Each person takes at least one drink.[CSAT 2023]

Question: How many persons attended the party?

Statement-1: 50 persons took milk.

Statement-2: Number of persons who attended the party is five times the number of persons who took milk only.

Which one of the following is correct in respect of the above Question and the Statements?

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.

(b) The Question can be answered by using either Statement alone.

(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

(d) The Question cannot be answered even by using both the Statements together.

Solution:

Given that,

In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee.

No one taking milk takes tea.

Each person takes at least one drink.

Now,

Persons taking only tea = 75 - 15 = 60

Persons taking only coffee = 60 - 15 = 45

Statement-1: 50 persons took milk.

As total persons are not mentioned. Also, it cannot be determined that 50 persons include persons having both coffee and tea.

Statement 1 alone is not sufficient.

Statement-2: Number of persons who attended the party is five times the number of persons who took milk only.

Let M be to persons who took only milk

So,

M + 120 = 5M

M = 30

Total persons = 120 + 30 = 150

Statement 2 alone is sufficient

Q14. In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject? [CSAT 2024]

(a) 15%

(b) 20%

(d) 35%

Solution:

Given that,

English = 80% student passed

Hindi = 70% students passed

Failed = 15% in both the subjects

Now,

Failed in English = 100 - 80 = 20%

Failed in Hindi = 100 - 70 = 30%

Failed in both the subjects = 15%

So,

Students Failed only in English = 20 - 15 = 5%

Students failed only in Hindi = 30 - 15 = 15%

Total students failed only in one subject = 15% + 5% = 20%

Hence option (b) is correct

ANSWER KEY

1. B

2. A

3. C

4. D

5. A

6. C

7. C

8. C

9. B

10. C

11. D

12. D

13. A

14. B

Download Venn Diagrams PYQs PDF

➡️ Download the complete set of Venn Diagrams PYQs (2011-2024) with solutions in PDF format.
➡️ Click Here to Download PDF

FAQs on Venn Diagrams for UPSC

1. Are Venn Diagrams important for UPSC?

➡️ Yes, Venn Diagrams are a crucial topic for the UPSC CSAT paper. They test your logical reasoning and data interpretation skills.

2. How to prepare for Venn Diagrams in UPSC?

➡️ Understand basic concepts like unions, intersections, and complements.
➡️ Practice PYQs regularly.
➡️ Use reliable resources like NCERT books and online platforms like iassetu.com.

3. What are the most frequently asked Venn Diagrams questions in UPSC?

➡️ Two-set and three-set Venn Diagrams
➡️ Problems involving unions, intersections, and complements
➡️ Complex Venn Diagrams with more than three sets

Conclusion

Practicing Venn Diagrams PYQs is essential for cracking the UPSC CSAT paper. This page provides year-wise solved questions, practice problems, and a free PDF download to help you prepare effectively. Bookmark this page and revisit it regularly for updates.

For more UPSC preparation resources, explore iassetu.com. Happy learning!