A) 0
B) 1
C) \[\frac{1}{ab}\]
D) ab
Correct Answer: B
Solution :
[b] Given Exp. \[=\frac{1}{1+a+{{b}^{-1}}}+\frac{1}{1+b+{{c}^{-1}}}+\frac{1}{1+c+{{a}^{-1}}}\] \[=\frac{1}{1+a+{{b}^{-1}}}+\frac{{{b}^{-1}}}{1+{{b}^{-1}}{{c}^{-1}}+{{b}^{-1}}}+\frac{1}{a+ac+1}\] \[=\frac{1}{1+a+{{b}^{-1}}}+\frac{{{b}^{-1}}}{1+{{b}^{-1}}+a}+\frac{1}{a+{{b}^{-1}}+1}\] \[=\frac{1+a+{{b}^{-1}}}{1+a+{{b}^{-1}}}=1\] \[\because \] \[abc=1\] \[\Rightarrow \] \[{{(bc)}^{-1}}=a\] \[\Rightarrow \] \[{{b}^{-1}}{{c}^{-1}}=a\,\,and\,\,ac={{b}^{-1}}\]
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