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
$1-M^{2}$
$1-2 M$
$2 M ^{2}-1$
$2 M ^{2}+1$
The mean weight of $150$ students in a class is $60 \,kg.$ The mean weight of boys is $70\, kg$ and that of girls is $55 \,kg$. What is the number of boys in the class?
A class has $20$ boys and $30$ girls. The average age of boys is $11\, years $ and that of girls is $12\,years.$ What is the average age of the whole class in $year$
The average age of a group of $18$ persons is $32$ $years$ and $6 \,months.$ If two persons of age $65\, years$ each and one person of age $50\, years$ leave the group, the average age of the remaining persons in the group will be (in $years$)
$A , B , C$ and $D$ are four consecutive even numbers respectively and their average is $65 .$ What is the product of $A$ and $D ?$
The average age of $8$ members of a group is $40 \,years.$ The age of $1$ member is $55\, years.$ After his retirement a new member comes in his place of age $39 .$ What is the effect of his retirement on the average age of group ?