GATE CS 2019 Set 1 — Question 9
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumInclusion-Exclusion PrincipleSets & CombinatoricsEngineering Mathematics
Engineering Mathematics → Sets & Combinatorics → Inclusion-Exclusion Principle
Last updated
Question
In a college, there are three student clubs. Sixty students are only in the Drama club, 80 students are only in the Dance club, 30 students are only in the Maths club, 40 students are in both Drama and Dance clubs, 12 students are in both Dance and Maths clubs, 7 students are in both Drama and Maths clubs, and 2 students are in all the clubs. If 75% of the students in the college are not in any of these clubs, then the total number of students in the college is __________.
Correct answer
(C) 900
Solution
Let be the Drama club, be the Dance club, and be the Maths club.Given:
Calculate students in exactly two clubs:
It is given that of students are not in any club. This means of the total students () are in at least one club.
The total number of students in the college is 900.
Calculate students in exactly two clubs:
It is given that of students are not in any club. This means of the total students () are in at least one club.
The total number of students in the college is 900.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Sets & Combinatorics
2026 Set 2 Q3A day can only be cloudy or sunny. The probability of a day being cloudy is , independent of…2026 Set 2 Q5‘When it is raining, peacocks dance.’ Based only on this sentence, which one of the following…2026 Set 2 Q8Figures (i) and (ii) represent intercity highway systems. The black dots represent cities and the…2026 Set 1 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…2026 Set 2 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…