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  • If the sum of the coefficients in the expansion of  is 4096, then the greatest coefficient in

If the sum of the coefficients in the expansion of (a+b)^n is 4096, then the greatest coefficient in the expansion is 
 

Option: 1

924


Option: 2

792


Option: 3

1594


Option: 4

None of these 
 


Answers (1)

We know that the sum of the coefficients in a binomial expansion is obtained by replacing each variable by unit in the given expression. Therefore, 
Sum of the coefficients in (\mathrm{a}+\mathrm{b})^{\mathrm{n}}=(1+1)^{\mathrm{n}}

\Rightarrow 4096=2^n \Rightarrow 2^n=2^{12} \Rightarrow n=12

Hence, n is even. So, the greatest coefficient is { }^n C_{e / 2} \text { i.e. }{ }^{12} C_6=924

Posted by

Ramraj Saini

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