| The geometric mean of (x

_{1}, x_{2}, x_{3},…. X_{n}) is X and the geometric mean of (y_{1}, y_{2}, y_{3},….Y_{n}) is Y. Which of the following is/are correct?1. The geometric mean of

(x_{1}y_{1}, x_{2}y_{2}, x_{3}y_{3}, …. X_{n}y_{n}) is XY.

2. The geometric mean of

is

Select the correct answer using the code given below :

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

### Right Answer is: C

#### SOLUTION

Let us consider an example(x1,x2,x3,…..xn)

=(1, 2, 4, 2)

G.M = =2=X

and (y1,y2,y3,…..yn)

=(2,3,4,6) = =2(3^{2})^{1/4}

Y=2√3

Now GM of (x1y1,x2y2,x3y3…..xnyn)

G.M of (2,6,16,12) = =4√3 XY

Hence statement 1 is correct

Now,

G.M of (x1/y1,x2/y2,x3/y3…..xn/yn)

G.M of (12,23,44,26)

=1/√3 =X/Y

Hence 2nd statement is also true

Both 1 and 3 are correct.