List of top Mathematics Questions on Venn Diagrams

In a class XII of a school, \(40\%\) of the students study Mathematics, \(30\%\) study Physics and \(20\%\) study Chemistry. \(20\%\) of the class study both Mathematics and Physics, \(10\%\) study both Mathematics and Chemistry and \(10\%\) study both Physics and Chemistry. \(5\%\) of the class study all the three subjects. If a student is selected at random from the class, find the probability that he studies neither Mathematics nor Physics nor Chemistry.
In a class there are 40 students. 16 passed in Chemistry, 20 passed in Physics, 25 passed in Math. 15 students passed in both Math and Physics.15 students passed in both Math and Chemistry and 10 students passed in both Physics and Chemistry. Find the maximum number of students that passed in all the subjects.

Let f: ℝ → ℝ be defined as
\(f(x) = \left\{   \begin{array}{ll}     [e^x] &  x < 0 \\     [a e^x + [x-1]] & 0 \leq x < 1 \\     [b + [\sin(\pi x)]] &  1 \leq x < 2 \\     [[e^{-x}] - c] &  x \geq 2 \\   \end{array} \right.\)
Where a, b, c ∈ ℝ and [t] denotes greatest integer less than or equal to t. 
Then, which of the following statements is true?

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 18. How many students have offered Mathematics alone?
Draw appropriate Venn diagram for each of the following: 
(i) (A ∪ B)' 
(ii) A' ∩ B'
(iii) (A ∩ B)'
(iv) A' ∪ B'