UPSEE 2018 Solved Paper

Since, middle term has greatest coefficient.
∴ Greatest coefficient = Coefficient of middle term... (i)
Since, 2n is an even.
∴ Middle term =(

2n

2

+1) th term =(n+l) th term
=Tn+1=‌2nCnxn−n(

1

x

)n
=‌nCn xn

1

xn

=‌2nCn
Now, coefficient of middle term
=‌2nCn=

2n!

n!n!

∴ Greatest coefficient of
(x+

1

x

)2n=‌nCn[ from Eq. (i) ]
=

2n!

n!n!

=

[1.3.5........(2n−1)]2n.n!

n!n!

=

[1.3.5.......(2n−1)2n]

n!