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 average age of $6$ members of a family is $20\, years.$ If the age of a servant is included, the average age increased by $25 \%$. What is the age (in $years$) of the servant ?
The average score of Sachin after $25$ innings is $46$ runs per innings. If after the $26^{th}$ innings, his average runs increased by $2$ runs, then what is his score in the $26^{\text {th }}$ innings?
In a school with $600$ students, the average age of the boys is $12$ $years$ and that of the girls is $11\, years.$ If the average age of the school is $11 \,years$ and $9 \,months,$ then the number of girls in the school is
The average of five numbers is $6.9 .$ If one of the numbers is deleted, the average of the remaining numbers is $4.4 .$ What is the value of the number deleted?
Average age of $5$ boys is $16$ $year$ of which that of $4$ boys is $16\, year\, 3\, months.$ The age of the $5^{th}$ boy is