Set Theory Test...

All the students of a batch opted Psychology, Business, or both. 73% of the students opted Psychology and 62% opted Business. If there are  220 students, how many of them opted for both Psychology and business?

In an examination $$80\%$$  passed in English, $$85\%$$ in Maths, $$75\%$$ in both and $$40$$ students failed in both subjects. Then the number of  students appeared are

$$p\cap (q\cup r)=?$$

There are 19 hockey players in a club. On a  particular day 14 were wearing the prescribed hockey shirts, while 11 were wearing the  prescribed hockey pants. None of then was without hockey pant  or hockey shirt. How many of  them were in complete  hockey uniform?

In an examination, $$34\%$$ of  the candidates fail in Arithmetic and $$42\%$$ in  English. If $$20\%$$ fail in Arithmetic and English, the  percentage of those passing in both subjects is :

If $$A$$ and $$B$$ have some elements in common, then $$n(A \cup B)$$ is:

The smallest set $$A$$ such that $$A\cup \left\{ 1,2 \right\} =\left\{ 1,2,3,5,9 \right\} $$ is 

If $$A \cap B = \phi$$, then $$A \Delta B$$ =

The equation x + cosx $$=$$ a has exactly one positive root. Complete set of values of 'a' is

In a science talent examination, 50% of the candidates fail in Mathematics and 50% fail in Physics. If 20% fail in both these subjects, then the  percentage who pass in both Mathematics and Physics is: