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Question

If (x1,y1) and (x2,y2) are two ordered pair which satisfies the condition in comprehension (where x1,x2,y1,y2/ϵN),  then (x1x2)/(y1y2) is 


  1. 20

  2. 500

  3. 10

  4. 1000


Solution

The correct option is D

1000


If a, b, c, d are four terms in G.P. then loga, logb, logc and logd are in A.P.
log10x,log210x,log210y,log210(xy), in A.P.
log210(xy),log210ylog210x,    (i)
Also log210ylog210x,=log210xlog210x,    (2)
form(1)
(log10x+log10y)(log10xlog10y)=log210ylog210x(log10x+2log10y)(log10x)=log210ylog210xlog210y2log10y.log10x2log210x=0   (3)from(2)
log210y2log210x+log10x=0     (4)(3)(4)2log10y.log10xlog10x=0 x=1 or y=110
Now, if x=1y=1
Also, if x=1y=1
Also, if y=1102log210x=log10x14=0
logx10x=1±1+24=1±34x=x1±34=1±34
x=x1±34(1,1),(101+34,110)(10134,110) are three ordered pair

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