Question

papers
(iii) The G.M. of 3 and 24 with weight 2 and 1 respectively is
(A) 8
(B) 4
(C) 6
(D) 9​

Answer 1

Answer:

square root of 3x2 and 24 and 1 = 12÷2×1= 6

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

$\sf{The \: geometric \: mean \: of \: n \: terms \: \: x_1,x_2,....x_n}$

$\sf{with \: weights \: \: w_1, w_2,.....,w_n \: respectively \: is \: }$

$= \displaystyle \sf{ \bigg({\prod\limits_{i = 1}^{n} {x_i}^{w_i} \bigg) }^{ \frac{1}{\sum\limits_{i = 1}^{n}w_i} }}$

TO DETERMINE

The G.M. of 3 and 24 with weight 2 and 1 respectively

CALCULATION

$\sf{Here \: \: \: x_1 = 3 \: \: and \: \: x_2 = 24}$

$\sf{Also \: \: w_1 = 2 \: \: \: and \: \: \: w_2 = 1}$

So

$= \displaystyle \sf{ \bigg({\prod\limits_{i = 1}^{2} {x_i}^{w_i} \bigg) }}$

$= \displaystyle \sf{ {x_1}^{w_1} \times {x_2}^{w_2} \: }$

$= \sf{ {3}^{2} \times {24}^{1} }$

$= \sf{ {3}^{2} \times 3 \times 8 }$

$= \sf{ {3}^{3} \times {2}^{3} }$

$= \sf{ {6}^{3} }$

Also

$= \displaystyle \sf{ \sum\limits_{i = 1}^{2}w_i}$

$= \displaystyle \sf{ w_1 +w_2 }$

$= \sf{ 2 + 1\: }$

$= \sf{3}$

Hence the Geometric mean

$= \displaystyle \sf{ \bigg({\prod\limits_{i = 1}^{2} {x_i}^{w_i} \bigg) }^{ \frac{1}{\sum\limits_{i = 1}^{2}w_i} }}$

$= \displaystyle \sf{ \bigg({ {6}^{3} \bigg) }^{ \frac{1}{3} }}$

$= \sf{6}$

RESULT

Hence The G.M. of 3 and 24 with weight 2 and 1 respectively is 6