The mean proportion between $$\left( {3 + \sqrt 2 } \right)$$ and $$\left( {12 - \sqrt {32} } \right)$$ is = ?
A. $$\sqrt 7 $$
B. $$2\sqrt 7 $$
C. 6
D. $$\frac{{15 - 3\sqrt 2 }}{2}$$
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & \left( {3 + \sqrt 2 } \right):x:\left( {12 - \sqrt {32} } \right) \cr & a:b:c \cr & {\text{mean proportion}} \cr & \Rightarrow {b^2} = a \times c \cr & \Rightarrow {x^2} = \left( {3 + \sqrt 2 } \right) \times \left( {12 - \sqrt {32} } \right) \cr & \Rightarrow {x^2} = \left( {3 + \sqrt 2 } \right) \times \left( {12 - 4\sqrt 2 } \right) \cr & \Rightarrow {x^2} = \left( {3 + \sqrt 2 } \right) \times 4\left( {3 - \sqrt 2 } \right) \cr & \Rightarrow {x^2} = 4 \times \left\{ {{{\left( 3 \right)}^2} - {{\left( {\sqrt 2 } \right)}^2}} \right\} \cr & \Rightarrow {x^2} = 28 \cr & \Rightarrow x = 2\sqrt 7 \cr} $$Related Questions on Ratio
If a : b : c = 3 : 4 : 7, then the ratio (a + b + c) : c is equal to
A. 2 : 1
B. 14 : 3
C. 7 : 2
D. 1 : 2
If $$\frac{2}{3}$$ of A=75% of B = 0.6 of C, then A : B : C is
A. 2 : 3 : 3
B. 3 : 4 : 5
C. 4 : 5 : 6
D. 9 : 8 : 10
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