A) 924
B) 792
C) 1594
D) none of these
Correct Answer: A
Solution :
[a] 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 \[{{(a+b)}^{n}}\]is given by \[{{(1+1)}^{n}}\] \[\therefore 4096={{2}^{n}}\]or \[{{2}^{n}}={{2}^{12}}\]or \[n=12\] Hence, n is even. So, the greatest coefficient is \[^{n}{{C}_{n/2,}}\]i.e., \[^{12}{{C}_{6}}=924\].
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