If P(x)=13x+11+3x+15n−1−3x+15n is a 5th degree polynomial, then value of n is

P(x)=15na(1+a)n−(1−a)nwhere     a=3x+1Now,   P(x)=25na nC1a+nC3a3+… Note that n must be odd, so that 3x+1 does not appear in P(x).∴           P(x)=25n nC1+nC3a2+…+nCnan−1                       =25n nC1+nC3(3x+1)+nC5(3x+1)2 +…+nCn(3x+1)(n−1)/2                        For this to be a polynomial of degree 5, n-12=5⇒n=11.