A) \[{{T}_{12}}={{T}_{13}}\]
B) \[{{x}^{2}}{{T}_{13}}={{T}_{12}}\]
C) \[{{T}_{12}}=x{{T}_{12}}\]
D) \[{{T}_{12}}+{{T}_{13}}=25\]
E) \[{{x}^{2}}{{T}_{12}}={{T}_{13}}\]
Correct Answer: E
Solution :
\[\therefore \] \[{{T}_{12}}{{=}^{23}}{{C}_{11}}{{x}^{11}}{{\left( \frac{1}{x} \right)}^{12}}{{=}^{23}}{{C}_{11}}\frac{1}{x}\] and \[{{T}_{13}}{{=}^{23}}{{C}_{12}}{{x}^{12}}{{\left( \frac{1}{x} \right)}^{11}}\] \[\Rightarrow \] \[{{T}_{13}}{{=}^{23}}{{C}_{11}}x\] \[\Rightarrow \] \[{{T}_{13}}={{x}^{2}}\,{{\,}^{23}}{{C}_{11}}\frac{1}{x}\] \[={{x}^{2}}{{T}_{12}}\]
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