11th Class Mathematics Other Series Question Bank Critical Thinking

  • question_answer If \[x>1,\ y>1,z>1\] are in G.P., then \[\frac{1}{1+\text{In}\,x},\ \frac{1}{1+\text{In}\,y},\] \[\ \frac{1}{1+\text{In}\,z}\]  are in       [IIT 1998; UPSEAT 2001]

    A) A.P.

    B) H.P.

    C) G.P.

    D) None of these

    Correct Answer: B

    Solution :

    \[x,\ y,\ z\] are in G.P.  Hence \[{{y}^{2}}=xz\] \[\therefore \]\[2\log y=\log x+\log z\] \[\Rightarrow \]\[2(\log y+1)=(1+\log x)+(1+\log z)\] \[\Rightarrow \]\[1+\log x,\ 1+\log y,\ 1+\log z\] are in A.P. \[\Rightarrow \]\[\frac{1}{1+\log x},\ \frac{1}{1+\log y},\ \frac{1}{1+\log z}\] are is H.P.

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