• 150 students are interested in Mathematics.
• 200 students are interested in Physics.
• 175 students are interested in Chemistry.
• 50 students are interested in Mathematics and Physics.
• 60 students are interested in Physics and Chemistry.
• 40 students are interested in Mathematics and Chemistry.
• 30 students are interested in Mathematics, Physics, and Chemistry.
• Remaining students are interested in Humanities.

Options :-

Based on the above information, the number of students interested in Humanities is

1. 10
2. 30
3. 40
4. 45

Given that, 

• n(U)=450
• n(M)=150
• n(P)=200
• n(C)=175
• n(M∩P)=50
• n(P∩C)=60
• n(M∩C)=40
• n(M∩P∩C)=30

Now, n(M∪P∪C)=n(U)+n(M)+n(P)–n(C)–n(M∩P)–n(P∩C)−n(M∩C)+n(M∩P∩C)

⇒n(M∪P∪C)=150+200+175−50−60−40+30=555−150=405

Now, n(U)=n(M∪P∪C)+n(H)

⇒n(H)=450−405

⇒n(H)=45

∴ The number of students interested in Humanities is 45.

Correct Answer D

Last 15 Years GATE Previous Year Question Paper