The ratio of the coefficient of x10in⁡1−x210and the term independent of x  in x−2x10,is

Given, 1−x210 and x−2x10To find Ratio of coefficient of x10 in 1−x210 and the term of independent of xin⁡x−2x10Now, let (r+1) th term in 1−x210contains x10Thus, coefficient of x10 is −10C5Again, let term be independent of x in x−2x10∴ Tr+1=10Cr(x)10−r−2xr=(−1)r10Cr(2)r(x)10−2rTo get term independent of x, put 10 - 2r =0 =r r = bThus, the term independent of X in x−2x10 is −10C5(2)5.'. Required ratio =−10C5−10C5(2)5=1(2)5=132=1:32