Let `f(x)=a_0+a_1x+a_2x^2++a_n x^n+` and `(f(x))/(1-x)=b_0+b_1x+b_2x^2++b_n x^n+` , then `b_n+b_(n-1)=a_n` b. `b_n-b_(n-1)=a_n` c. `b_n//b_(n-1)=a_n` d. none of these

Suppose p(x)=a_0+a_1x+a_2x^2++a_n x^ndot If |p(x)|lt=e^(x-1)-1| for all xgeq0, prove that |a_1+2a_2++n a_n|lt=1.

If (3+x^(2008)+x^(2009))^(2010)=a_0+a_1x+a_2x^2++a_n x^n , then the value of a_0-1/2a_1-1/2a_2+a_3-1/2a_4-1/2a_5+a_6- is 3^(2010) b. 1 c. 2^(2010) d. none of these

If (1+x)^n=C_0+C_1x+C_2x^2++C_n x^n ,t h e nC_0C_2+C_1C_3+C_2C_4++C_(n-2)C_n= ((2n)!)/((n !)^2) b. ((2n)!)/((n-1)!(n+1)!) c. ((2n)!)/((n-2)!(n+2)!) d. none of these

If (1+x+x^2)^n=a_0+a_1x+a_2x^2++a_(2n)x_(2n), find the value of a_0+a_6++ ,n in Ndot

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (n !)/((n-1)!(n+1)!) b. ((2n)!)/((n-1)!(n+1)!) c. ((2n)!)/((2n-1)!(2n+1)!) d. none of these

f_n(x)=e^(f_(n-1)(x)) for all n in Na n df_0(x)=x ,t h e n d/(dx){f_n(x)} is (a) (f_n(x)d)/(dx){f_(n-1)(x)} (b) f_n(x)f_(n-1)(x) (c) f_n(x)f_(n-1)(x).......f_2(x)dotf_1(x) (d)none of these

xy=( x+y )^n and dy/dx = y/x then n= 1 b. 2 c. 3 d. 4

If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

If |x^n x^(n+2)x^(2n)1x^a a x^(n+5)x^(a+6)x^(2n+5)|=0,AAx in R ,w h e r en in N , then value of a is n b. n-1 c. n+1 d. none of these