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99 Percentile Qs Bank for JEE MainMathematicsSets and Relations

A class has 175 students. The following data shows the number of students opting for one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone?

Options

  1. A35
  2. B48
  3. C60
  4. D22

Correct answer

C. 60

Step-by-step solution

Given, n M = 100 ,   n P = 70 ,   n C = 40                 n M ∩ P = 30 ,   n M ∩ C = 28 ,                   n P ∩ C = 23 and n M ∩ P ∩ C = 18 ∴    n M ∩ P ′ ∩ C ′ = n [ M ∩ ( P ∪ C ) ' ] = n M - [ n M ∩ P + n M ∩ C - n ( M ∩ P ∩ C ) ] = 100 - [ 30 + 28 - 18 ] = 60

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