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If the sum of the coefficients in the ex...

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

A

924

B

792

C

1594

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We know that the sum of the coefficient in a binomial expansion is obtained by replacing each variable by '1' in the given expression. Therefore, sum of the coefficient in `(a+b)^(n)` is given by `(1+1)^(n)`,
`:. 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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CENGAGE-BINOMIAL THEOREM-Exercise (Single)
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  13. If sum(r=0)^n{ar(x-alpha+2)^r-br(alpha-x-1)^r}=0, then prove that bn-(...

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  17. If the three consecutive in the expansion of (1+x)^n are 28, 56, and 7...

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