The middle term in the expansion of (\frac{a}{x}+bx)^{12}will be

  • Option 1)

    12C_6 a^{6}b^{6}

  • Option 2)

    12C_6\frac{a^{6}b^{6}}{x}

  • Option 3)

    12C_6\frac{a^{6}b^{6}}{x^{2}}

  • Option 4)

    12C_6 a^{6}b^{6}x^{2}

 

Answers (1)

As learnt in concept

Middle term in Binomial Expression if n is even -

In the expression of 

\left ( x+a \right )^{n}:^{n}c_{\frac{n}{2}}\cdot x^{\frac{n}{2}}\cdot y^{\frac{n}{2}} is

middle term if n is even

 

- wherein

where \left ( \frac{n}{2}+1 \right ) th term is middle term

 

 middle term is _{C_{6}}^{12}(\frac{a}{x})^{6} (bx)^{6}

=_{C_{6}}^{12}a^{6}b^{6}


Option 1)

12C_6 a^{6}b^{6}

This is correct option

Option 2)

12C_6\frac{a^{6}b^{6}}{x}

This is incorrect option

Option 3)

12C_6\frac{a^{6}b^{6}}{x^{2}}

This is incorrect option

Option 4)

12C_6 a^{6}b^{6}x^{2}

This is incorrect option

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