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Sum of coefficients of all terms

If 2nC6 is ...

Question

If $^{2 n} C_{6}$ is the greatest coefficient in the expansion of ${(1 + x)}^{2 n}, n ϵ N,$ then $n$ bino is

A

6

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B

7

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C

5

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D

8

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Solution

The correct option is A 6
The term with the greatest coefficient of x will be the middle term.
$=^{2 n} C_{n}$
Now it has been given that the term $^{2 n} C_{6}$ is the greatest term.
Therefore
$^{2 n} C_{6} =^{2 n} C_{n}$
$n = 6$

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