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)

    1594

  • Option 2)

    792

  • Option 3)

    924

  • Option 4)

    2924.

 

Answers (1)

As we learnt in

Gretest Binomial Coefficient -

In Binomial expansion of \left ( x+a \right )^{n} greatest coefficient is ^{n}c_{\frac{n}{2}} when n is even

and ^{n}c_{\frac{n+1}{2}} & ^{n}c_{\frac{n-1}{2}} When n is odd.

 

- wherein

\dpi{120} \dpi{120} \because \, ^{n}c_{\frac{n+1}{2}}= ^{n}c_{\frac{n-1}{2}}

 

 Sum of coefficients of (a+b)^{n}=2^{n}

(2)^{n}=4096

i.e. n = 12

So the greatest coefficient = ^{12}C_{6}=924

Correct option is 3. 

 


Option 1)

1594

This is an incorrect option.

Option 2)

792

This is an incorrect option.

Option 3)

924

This is the correct option.

Option 4)

2924.

This is an incorrect option.

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