Q. A survey shows that 70% of people like dogs, 50% like cats, and 20% like both. What percentage of people like either dogs or cats?
A.
100%
B.
90%
C.
80%
D.
70%
Show solution
Solution
Using inclusion-exclusion, the percentage of people who like either dogs or cats is: 70% + 50% - 20% = 100%.
Correct Answer:
C
— 80%
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Q. If 15 students like both History and Geography, 25 like History, and 20 like Geography, how many students like only Geography?
Show solution
Solution
The number of students who like only Geography is: 20 - 15 = 5.
Correct Answer:
A
— 5
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Q. If 25% of a group like tea, 15% like coffee, and 5% like both, what percentage like either tea or coffee?
A.
35%
B.
30%
C.
25%
D.
20%
Show solution
Solution
Using inclusion-exclusion, the percentage who like either is 25% + 15% - 5% = 35%.
Correct Answer:
A
— 35%
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Q. If 25% of a group like tea, 35% like coffee, and 10% like both, what percentage like only tea?
A.
15%
B.
25%
C.
10%
D.
20%
Show solution
Solution
The percentage who like only tea is 25% - 10% = 15%.
Correct Answer:
A
— 15%
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Q. If 25% of a group of 200 people like sports, 15% like music, and 5% like both, what percentage of people like only sports?
A.
20%
B.
15%
C.
10%
D.
5%
Show solution
Solution
The percentage of people who like only sports is 25% - 5% = 20%.
Correct Answer:
A
— 20%
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Q. If 25% of a group of 200 people like tea, 15% like coffee, and 5% like both, what percentage like only tea?
A.
20%
B.
15%
C.
10%
D.
5%
Show solution
Solution
The number of people who like only tea is 25% of 200 - 5% of 200 = 20%.
Correct Answer:
A
— 20%
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Q. If 25% of a population likes apples, 15% likes oranges, and 5% likes both, what percentage likes either fruit?
A.
35%
B.
30%
C.
25%
D.
20%
Show solution
Solution
Using inclusion-exclusion, the percentage that likes either fruit is 25% + 15% - 5% = 35%.
Correct Answer:
A
— 35%
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Q. If 25% of a population likes apples, 35% likes oranges, and 10% likes both, what percentage likes only apples?
A.
15%
B.
25%
C.
10%
D.
5%
Show solution
Solution
The percentage of people who like only apples is 25% - 10% = 15%.
Correct Answer:
A
— 15%
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Q. If 25% of a population likes reading, 15% likes writing, and 5% likes both, what percentage likes either reading or writing?
A.
35%
B.
30%
C.
25%
D.
20%
Show solution
Solution
Using inclusion-exclusion, the percentage of people who like either activity is: 25% + 15% - 5% = 35%.
Correct Answer:
A
— 35%
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Q. If 40 students like Mathematics, 30 like Science, and 10 like both subjects, how many students like only Mathematics?
Show solution
Solution
The number of students who like only Mathematics is 40 - 10 = 30.
Correct Answer:
B
— 20
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Q. If 60% of students like reading fiction, 40% like reading non-fiction, and 10% like both, what percentage of students like at least one genre?
A.
90%
B.
100%
C.
80%
D.
70%
Show solution
Solution
Using inclusion-exclusion, the percentage is 60% + 40% - 10% = 90%.
Correct Answer:
A
— 90%
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Q. If 60% of students like reading, 40% like writing, and 10% like both, what percentage of students like only reading?
A.
50%
B.
40%
C.
30%
D.
20%
Show solution
Solution
The percentage of students who like only reading is 60% - 10% = 50%.
Correct Answer:
A
— 50%
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Q. If 60% of students like reading, 40% like writing, and 10% like both, what percentage of students like only writing?
A.
30%
B.
40%
C.
10%
D.
50%
Show solution
Solution
The percentage of students who like only writing is 40% - 10% = 30%.
Correct Answer:
A
— 30%
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Q. If 60% of students play cricket, 40% play football, and 10% play both, what percentage of students play either cricket or football?
A.
90%
B.
80%
C.
70%
D.
60%
Show solution
Solution
Using inclusion-exclusion, the percentage of students who play either cricket or football is: 60% + 40% - 10% = 90%.
Correct Answer:
B
— 80%
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Q. If 60% of students play cricket, 40% play football, and 10% play both, what percentage of students play only one sport?
A.
90%
B.
80%
C.
70%
D.
60%
Show solution
Solution
The percentage playing only cricket is 60% - 10% = 50%, and only football is 40% - 10% = 30%. Thus, total playing only one sport is 50% + 30% = 80%.
Correct Answer:
B
— 80%
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Q. If 60% of students play cricket, 40% play football, and 10% play both, what percentage of students play only cricket?
A.
50%
B.
40%
C.
30%
D.
20%
Show solution
Solution
The percentage of students who play only cricket is 60% - 10% = 50%.
Correct Answer:
A
— 50%
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Q. If 60% of students play cricket, 50% play football, and 30% play both, what percentage of students play either cricket or football?
A.
50%
B.
60%
C.
80%
D.
100%
Show solution
Solution
Using inclusion-exclusion, the percentage playing either is 60% + 50% - 30% = 80%.
Correct Answer:
C
— 80%
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Q. If 60% of students play football, 40% play basketball, and 10% play both, what percentage of students play either sport?
A.
90%
B.
80%
C.
70%
D.
60%
Show solution
Solution
Using inclusion-exclusion, the percentage playing either sport is 60% + 40% - 10% = 90%.
Correct Answer:
A
— 90%
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Q. If 60% of students play football, 40% play basketball, and 10% play both, what percentage of students play either football or basketball?
A.
90%
B.
80%
C.
70%
D.
60%
Show solution
Solution
Using inclusion-exclusion, the percentage of students who play either sport is: 60% + 40% - 10% = 90%.
Correct Answer:
A
— 90%
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Q. If 80% of a population likes tea, 60% likes coffee, and 30% likes both, what percentage likes at least one of the two?
A.
50%
B.
60%
C.
80%
D.
100%
Show solution
Solution
Using inclusion-exclusion, the percentage liking at least one is 80% + 60% - 30% = 110%, which is capped at 100%.
Correct Answer:
C
— 80%
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Q. In a class of 50 students, 20 study English, 25 study Hindi, and 10 study both. How many students study only one language?
Show solution
Solution
The number of students studying only one language is: (20 - 10) + (25 - 10) = 35.
Correct Answer:
A
— 35
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Q. In a class of 50 students, 20 study English, 25 study Mathematics, and 10 study both. How many students study only one subject?
Show solution
Solution
The number of students studying only English is 20 - 10 = 10, and only Mathematics is 25 - 10 = 15. Thus, total studying only one subject is 10 + 15 = 25.
Correct Answer:
A
— 35
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Q. In a class of 50 students, 20 study History, 25 study Geography, and 10 study both. How many students study only Geography?
Show solution
Solution
The number of students who study only Geography is 25 - 10 = 15.
Correct Answer:
A
— 15
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Q. In a class of 50 students, 20 study Mathematics, 25 study Science, and 10 study both. How many students study only Science?
Show solution
Solution
The number of students who study only Science is 25 - 10 = 15.
Correct Answer:
A
— 15
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Q. In a class of 50 students, 25 study English, 20 study Hindi, and 5 study both. How many students study only one language?
Show solution
Solution
The number of students studying only English is 25 - 5 = 20, and only Hindi is 20 - 5 = 15. Thus, total studying only one language is 20 + 15 = 35.
Correct Answer:
D
— 35
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Q. In a class of 60 students, 25 study History, 30 study Geography, and 10 study both. How many students study only Geography?
Show solution
Solution
The number of students studying only Geography is 30 - 10 = 20.
Correct Answer:
A
— 20
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Q. In a class of 80 students, 50 like English, 30 like Hindi, and 10 like both. How many students like only Hindi?
Show solution
Solution
The number of students who like only Hindi is 30 - 10 = 20.
Correct Answer:
A
— 20
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Q. In a class of 80 students, 50 like history, 30 like geography, and 10 like both. How many students like only geography?
Show solution
Solution
The number of students who like only geography is 30 - 10 = 20.
Correct Answer:
A
— 20
Learn More →
Q. In a class of 80 students, 50 study English, 40 study Hindi, and 20 study both. How many students study only Hindi?
Show solution
Solution
The number of students studying only Hindi is 40 - 20 = 20.
Correct Answer:
A
— 20
Learn More →
Q. In a group of 150 people, 90 like basketball, 60 like soccer, and 30 like both. How many people like neither sport?
Show solution
Solution
The number of people who like at least one sport is 90 + 60 - 30 = 120, so those who like neither is 150 - 120 = 30.
Correct Answer:
A
— 30
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Showing 1 to 30 of 55 (2 Pages)
Venn Diagrams MCQ & Objective Questions
Venn Diagrams are essential tools in mathematics and logic that help students visualize relationships between different sets. Understanding Venn Diagrams is crucial for scoring well in exams, as they frequently appear in objective questions and MCQs. By practicing Venn Diagrams MCQ questions, students can enhance their problem-solving skills and improve their exam preparation, ensuring they are well-equipped to tackle important questions.
What You Will Practise Here
Understanding the basic structure of Venn Diagrams
Identifying union, intersection, and difference of sets
Solving problems involving two or three sets
Interpreting complex Venn Diagrams with multiple categories
Applying Venn Diagrams to real-life scenarios
Learning key definitions and formulas related to set theory
Practicing objective questions with detailed explanations
Exam Relevance
Venn Diagrams are a significant part of the curriculum for CBSE, State Boards, NEET, and JEE. Students can expect questions that require them to analyze relationships between sets, often presented in the form of diagrams. Common question patterns include identifying the number of elements in specific regions of the diagram or solving problems that involve logical reasoning based on set operations.
Common Mistakes Students Make
Confusing the concepts of union and intersection
Misinterpreting the areas represented in the Venn Diagram
Overlooking the importance of labels and set notation
Failing to account for elements that belong to multiple sets
Rushing through problems without visualizing the diagram first
FAQs
Question: What are Venn Diagrams used for in mathematics?Answer: Venn Diagrams are used to illustrate the relationships between different sets, helping to visualize concepts like union, intersection, and differences.
Question: How can I improve my skills in solving Venn Diagrams MCQs?Answer: Regular practice with Venn Diagrams objective questions and understanding the underlying concepts will significantly enhance your skills.
Now is the time to boost your confidence! Dive into our collection of Venn Diagrams practice MCQs and test your understanding. Mastering these concepts will not only prepare you for exams but also sharpen your analytical skills for future challenges.
