In a survey of $600$ students in a school,$150$ students were found to be taking tea and $225$ taking coffee,$100$ were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

In a city,$25\%$ of families have a telephone and $15\%$ have a car,while $65\%$ of families have neither a telephone nor a car. If $2000$ families have both a car and a telephone,then consider the following statements:
$1.$ $10\%$ of families have both a car and a telephone.
$2.$ $35\%$ of families have either a car or a telephone.
$3.$ $40,000$ families live in the city.
Which of these statements are true?

In a class of $60$ students,$40$ opted for $NCC$,$30$ opted for $NSS$ and $20$ opted for both $NCC$ and $NSS$. If one of these students is selected at random,then the probability that the student selected has opted neither for $NCC$ nor for $NSS$ is

Out of $100$ students in a class,$55$ passed in Mathematics and $67$ passed in Physics. The number of students who passed only in Physics is:

If $A = \{x \in \mathbb{R} : |x - 2| > 1\}$,$B = \{x \in \mathbb{R} : \sqrt{x^2 - 3} > 1\}$,$C = \{x \in \mathbb{R} : |x - 4| \geq 2\}$,and $\mathbb{Z}$ is the set of all integers,then the number of subsets of the set $(A \cap B \cap C)^c \cap \mathbb{Z}$ is .... .

In a hostel,$60 \%$ of the students read Hindi newspaper,$40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. $A$ student is selected at random. Find the probability that she reads neither Hindi nor English newspapers.