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

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

Option: 1

1594
 


Option: 2

792
 


Option: 3

924
 


Option: 4

928


Answers (1)

best_answer

Put x=y=1 in (x+y)^n to obtain the sum of the coefficients.

\begin{array}{ll} \therefore & 2^n=4096 \equiv\left(2^4\right)^3 \\ \Rightarrow & n=12 \end{array}

As the number of terms in the expansion of (x+y)^n is odd (n=12),{ }^n C_r \equiv{ }^{12} C_r is the greatest when r \equiv \frac{n}{2}=\frac{12}{2}=6. Hence, the greatest coefficient ={ }^{12} C_6=924.

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Nehul

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