A) \[{{10}^{3}}\]
B) 100
C) \[{{10}^{4}}\]
D) 10
Correct Answer: D
Solution :
\[200={}^{6}{{C}_{3}}{{\left( \frac{1}{{{X}^{x+{{\log }_{10}}x}}} \right)}^{\frac{3}{2}}}\times {{x}^{\frac{1}{4}}}\] \[\Rightarrow \]\[10={{x}^{\frac{3}{2(1+lo{{g}_{10}}x)}+\frac{1}{4}}}\] \[\Rightarrow \]\[1=\left( \frac{3}{2(1+t)}+\frac{1}{4} \right)t\] where \[t={{\log }_{10}}\text{x}\] \[\Rightarrow \]\[{{t}^{2}}+3t-4=0\] \[\Rightarrow \]\[t=1,-4\] \[\Rightarrow \]\[x=10,{{10}^{-4}}\] \[\Rightarrow \]\[x=10\,\,\,(As\,x>1)\]
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