Question

The range of the values of the term independent of $x$ in the expansion of ${\left( {x{{\sin }^{ - 1}}{\rm{\alpha }} + \frac{{{{\cos }^{ - 1}}{\rm{\alpha }}}}{x}} \right)^{10}},{\rm{\alpha }} \in \left[ { - 1,1} \right]$ is

Accepted Answer

$\left[ { - \frac{{{{\rm{\;}}^{10}}{{\rm{C}}_5}{\rm{.}}{{\rm{\pi }}^{10}}}}{{{2^5}}},{\rm{\;}}\frac{{{{\rm{\;}}^{10}}{{\rm{C}}_5}{\rm{.}}{{\rm{\pi }}^{10}}}}{{{2^{20}}}}} \right]$

Answer

$\left[ {\frac{{{{\rm{\;}}^{10}}{{\rm{C}}_5}{\rm{.}}{{\rm{\pi }}^{10}}}}{{{2^5}}},{\rm{\;}} - \frac{{{{\rm{\;}}^{10}}{{\rm{C}}_5}{{\rm{\pi }}^{10}}}}{{{2^{20}}}}} \right]$

Answer

$\left[ {\frac{{{{\rm{\;}}^{10}}{{\rm{C}}_5}{\rm{.}}{{\rm{\pi }}^5}}}{{{2^5}}},{\rm{\;}}\frac{{{{\rm{\;}}^{10}}{{\rm{C}}_5}{\rm{.}}{{\rm{\pi }}^5}}}{{{2^{20}}}}} \right]$

Answer

$\left[ { - \frac{{{{\rm{\;}}^{10}}{{\rm{C}}_5}{\rm{.}}{{\rm{\pi }}^5}}}{{{2^5}}},{\rm{\;}}\frac{{{{\rm{\;}}^{10}}{{\rm{C}}_5}{\rm{.}}{{\rm{\pi }}^5}}}{{{2^{20}}}}} \right]$

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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