If the mean of $a, b, c$ is $M$ and $ab + bc + ca = 0$,then the mean of $a^2, b^2, c^2$ is

The average weight of $8$ sailors in a boat is increased by $1 \, kg$ if one of them weighing $56 \, kg$ is replaced by a new sailor. The weight of the new sailor is (in $kg$):

The average of $30$ numbers is $12$. The average of the first $20$ of them is $11$ and that of the next $9$ is $10$. The last number is:

The total marks obtained by a student in Physics,Chemistry and Mathematics together is $120$ more than the marks obtained by him in Chemistry. What is the average marks obtained by him in Physics and Mathematics together?

The cost of $5 \,kg$ of apples is $Rs. \, 450$. The cost of $12$ dozen mangoes is $Rs. \, 4320$,and the cost of $4 \,kg$ of oranges is $Rs. \, 240$. What is the total cost of $8 \,kg$ of apples,$8$ dozen mangoes,and $8 \,kg$ of oranges? (in $Rs.$)

If the average of $m$ numbers is $n^{2}$ and that of $n$ numbers is $m^{2}$,then the average of $(m + n)$ numbers is