Q.

The greatest coefficient in the expansion of (1+x)40 is

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a

1.3.5....3920!220

b

1.3.5....3920!

c

40!20!

d

40!

answer is A.

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Detailed Solution

The greatest coefficient of (1+x)n is Cn2   n , if n is even=C402   40=C20   40=40!20!20!=(40.39.38….4.3.2.1)20!20!=(40.38.36….4.2)(39.37….3.1)20!20!=220(20.19.18….2.1)(1.3….39)20!20!=1.3….3920!220
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