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7.Binomial Theorem
normal
In the expansion of ${\left( {\frac{{x\,\, + \,\,1}}{{{x^{\frac{2}{3}}}\,\, - \,\,{x^{\frac{1}{3}}}\,\, + \,\,1}}\,\, - \,\,\frac{{x\,\, - \,\,1}}{{x\,\, - \,\,{x^{\frac{1}{2}}}}}} \right)^{10}}$, the term which does not contain $x$ is :
A
$^{10}C_0$
B
$^{10}C_7$
C
$^{10}C_4$
D
none
Solution
$\frac{{{{\left( {{x^{\frac{1}{3}}}} \right)}^3}\,\, + \,\,1}}{{{x^{\frac{2}{3}}}\,\, – \,\,{x^{\frac{1}{3}}}\,\, + \,\,1}} = x^{1/3} + 1 $
$\Rightarrow (x^{1/3} – x^{1/2})^{10}$
Standard 11
Mathematics
