Binomial Theorem And Its Simple Applications Question 159
Question: If the sum of the coefficients in the expansion of $ {{(a+b)}^{n}} $ is 4096, then the greatest coefficient in the expansion is
Options:
A) 924
B) 792
C) 1594
D) none of these
Show Answer
Answer:
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 $ .
BETA
