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Question

Coefficient of the middle term in the expansion of the binomial (1+x)40 is equal to?

A
220(135......39)(20)!
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B
The sum of the coefficients of the two middle terms in (1+x)39
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C
202122....40(20)!
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D
(20C0)2+(20C1)2+(20C2)2+....+(20C20)2
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Solution

The correct options are
B The sum of the coefficients of the two middle terms in (1+x)39
D (20C0)2+(20C1)2+(20C2)2+....+(20C20)2
In (1+x)40 middle term is 21st i.e. (T20+1)th
(T20+1)=40C20x20
Co-efficient is 40C20=40!×20!20!=40!
and middle term of (1+x)39 are 39C20 and 39C19
=39C20 +39C19=40C20=40!

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