In a survey of $400$ students in a school,$100$ were listed as taking apple juice,$150$ as taking orange juice and $75$ were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.

In a survey of $220$ students of a higher secondary school,it was found that at least $125$ and at most $130$ students studied Mathematics; at least $85$ and at most $95$ studied Physics; at least $75$ and at most $90$ studied Chemistry; $30$ studied both Physics and Chemistry; $50$ studied both Chemistry and Mathematics; $40$ studied both Mathematics and Physics and $10$ studied none of these subjects. Let $m$ and $n$ respectively be the least and the most number of students who studied all the three subjects. Then $m+n$ is equal to .............................

In a group of $70$ people,$37$ like coffee,$52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

Let $Z$ be the set of integers. If $A = \{ x \in Z : 2^{(x + 2)(x^2 - 5x + 6)} = 1 \}$ and $B = \{ x \in Z : -3 < 2x - 1 < 9 \}$,then the number of subsets of the set $A \times B$ is:

In a battle,$70\%$ of the combatants lost one eye,$80\%$ an ear,$75\%$ an arm,$85\%$ a leg,and $x\%$ lost all the four limbs. The minimum value of $x$ is:

In a certain town, $60 \%$ of the families own a car, $30 \%$ own a house and $20 \%$ own both a car and a house. If a family is randomly chosen, what is the probability that this family owns a car or a house but not both?