If the average of $x$ and $\frac{1}{x} (x \neq 0)$ is $M$,then the average of $x^{2}$ and $\frac{1}{x^{2}}$ is

In an examination,out of $20$ students in a class,in Mathematics $2$ students scored $100$ marks,$3$ students scored $0$,and the average marks for the rest of the students was $40$. What is the average mark of the whole class? (in marks)

The average of a collection of $20$ measurements was calculated to be $56 \, cm$. But later,it was found that a mistake had occurred in one of the measurements which was recorded as $64 \, cm$,but should have been $61 \, cm$. The correct average must be? (in $cm$)

The average of three numbers is $135$. The largest number is $195$ and the difference between the other two is $20$. The smallest number is:

The sum of the ages of father and son at present is $33 \, \text{years}$. Two years ago, the product of their ages was $28 \, \text{years}$. What is the age of the father and the son (in $\text{years}$)?

The mean of the marks obtained by $100$ students is $60$. If the marks obtained by one of the students was incorrectly calculated as $75$ whereas the actual marks obtained by him were $65$,what is the correct mean of the marks obtained by the students?