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  • Solve it, - Binomial theorem and its simple applications - JEE Main-4

The coefficient of the middle term in the binomial expansion in powers of x of  (1+\alpha x)^{4} and of (1-\alpha x)^{6} is the same if \alpha equals

  • Option 1)

    –3/10

  • Option 2)

    10/3

  • Option 3)

    –5/3

  • Option 4)

    3/5

 

Answers (1)

best_answer

As we havew learned

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

 

 T_M_1= ^4C_2 (\alpha x)^2 \\ T_M_2= ^6C_3 (-\alpha x)^3}

 

\Rightarrow ^4C_2\alpha ^2 = - ^6C_3\alpha ^3 \\ \Rightarrow \alpha = - \frac{^4C_2}{^6C_3}

 = \frac{-6 }{20} = -3 /10

 

 


Option 1)

–3/10

Option 2)

10/3

Option 3)

–5/3

Option 4)

3/5

Posted by

prateek

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