MATHEMATICAL TOOLS FOR PHYSICS

If in a class there are 200 students in which 120 take Mathematics, 90 take Physics, 60 take Chemistry, 50 take Mathematics & Physics, 50 take Mathematics & Chemistry, 43 take Physics & Chemistry and 38 take Mathematics Physics & Chemistry, then the number of students who hace taken exactly one subject is

In a class, 18 students took Physics, 23 students took Chemistry and 24 students took Mathematics of these 13 took both Chemistry and Mathematics, 12 took both Physics and Chemistry and 11 took both Physics and Mathematics. If 6 students offered all the three subjects, find: (ii) How many took Maths but not Chemistry.

There are 11 teachers who teach Mathematics or Physics in a school, Of these, 7 teach Mathematics and 3 teach both Mathematics and Physics. How many teach Physics?

In a school there are 30 teachers who teach Mathematics or Physics. Of these teachers, 20 teach. Mathematics and 15 teach Physics, 5 teach both Mathematics and Physics. The number of teaches teaching only Mathematics is:

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

A class has 172 students. The following data shows the number of students opting one or more subjects: Mathematics 125, Physics 95, Chemistry 65 Mathematics and Physics 55 Mathematics and Chemistry 53 Physics and Chemistry 48 Mathematics, Physics and Chemistry 43 The number of students who opted only Physics is