If mean of a, b, c is M and a b+b c+c a=0, then mean of a^{2}, b^{2}, c^{2} is

English

Gujarati

Hindi

4.Average

hard

If the mean of $a, b, c$ is $M$ and $a b+b c+c a=0,$ then the mean of $a^{2}, b^{2}, c^{2}$ is

A

$M ^{2}$

B

$3 M ^{2}$

C

$6 M ^{2}$

D

$9 M ^{2}$

Solution

Given $\frac{a+b+c}{3}=M$

or $(a+b+c)=3 M$

$(a+b+c)^{2}=9 M^{2}$

i.e. $a^{2}+b^{2}+c^{2}+2(a b+b c+c a)=9 M^{2}$

$a b+b c+c a =0$

$a^{2}+b^{2}+c^{2} =9 M^{2}$

Standard 13

Quantitative Aptitude

Share

Similar Questions

The average of runs of a cricket player of $10$ innings was $32 .$ How many runs must he score in his next innings so as to increase his average of runs by $4 ?$

medium

What is the age of a class teacher?

$I.$ There are $11$ students in the class.

$II.$ The average age of the students and the teacher is $14$ years.

$III.$ The average age of the teacher and the students is $3$ years more than that of the students.

hard

The average age of a graph of $9$ students is $20\, years.$ When $6$ more students joined the group, the average age falls by $2\, years.$ Then the average age of new students is

medium

In a family, the average age of a father and a mother is $35\, years.$ The average age of the father, mother and their only son is $27\, years.$ What is the age of the son ? (in $years$)

easy

The average age of board of directors of a company, having $10$ directors was $48$ years. Coincidentally when a director aged $53$ resigned from the board of directors, another director died on the same day. So a new director joined the board of directors aged $34.$ Next year in the same month the average age of all the $9$ directors was found to be $46 \,years.$ The age of the late (i.e., dead) director at the time of his death was (in $years$)

hard