1.

if x , 2y and 3z are in AP where the distinct numbers x, yand z are in gp. Then the common ratio of the GP isA. 3B. `(1)/(3)`C. 2D. `(1)/(2)`

Answer» Correct Answer - B
Given x, 2y and 3z are in AP ,
then ,`2y=(x+3z)/(2)`
`implies y=(x+3z)/(4)`
`implies 4y=x+3z`
and x,y,z are in GP
then `(y)/(x)=(z)/(y) =lamda`
`implies y=x lamda and z=lamday - lamda^(2)x`
On subsitiuting these values in Eq (i) we get
`4(x, lamda )=x+3(lamda^(2)x)`
`implies 4lamdax=x+3lamda^(2)x`
`implies 4lamda=1+3lamda^(2)`
`implies 3lamda ^(2) -4lamda+1=0`
`=(3lamda-10(lamda-1)=0`
`therefore lamda =(1)/(3).lamda =1 `


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