The largest coefficient in the expansion of (1 + x)10 is: - Vidyadip

MCQ

The largest coefficient in the expansion of $(1 + x)10$ is:

✓
$\frac{10!}{(5!)^2}$
B
$\frac{10!}{5!}$
C
$\frac{10!}{(5!\times4!)^2}$
D
$\frac{10!}{(5!\times4!)}$

✓

Answer

Correct option: A.

$\frac{10!}{(5!)^2}$

Given: $(1 + x)10$
The greatest coefficient will always occur in the middle term.
Hence, the total number of terms in an expansion is $11. ($ i.e. $10 + 1 = 11)$
Therefore, middle term $ =\Big[\big(\frac{10}{2}\big)+1\Big]=5+1=6\text{th }\text{term}.$
So, $T6 ={^{10}C_5} \times x^5$
Therefore, the coefficient of the greatest term $={^{10}C_5}$$=\frac{10!}{(5!)^2}.$

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