The correct option is C 512
(1+x+x2+x3)5=a0+a1x+a2x2+a3x3+⋯+a15x15
Putting x=1 and x=−1 alternatively, we have
a0+a1+a2+a3+⋯+a15=45a0−a1+a2−a3+⋯−a15=0
Adding (1) and (2), we have 2(a0+a2+a4+⋯+a14)=45
⇒a0+a2+a4+⋯+a14=29=512
Alternate Solution:
(1+x+x2+x3)5=(1+x)5(1+x2)5
Now (1+x2)5 have only even powers of x
so, the sum will be 25
and sum of even power coefficient in (1+x)5 will be 25−1=24
Hence required sum is
24×25=29=512