If `f(x)=1-x+x^2-x^3+...+x^(15)+x^(16)-x^(17)` , then the coefficient of `x^2inf(x-1)` is `826` b. `816` c. `822` d. none of these

The coefficient of x^5in(1+2x+3x^2+....)^(-3//2)i s(|x|<1) 21 b. 25 c. 26 d. none of these

If f(x)=|[x-2, (x-1)^2, x^3] , [(x-1), x^2, (x+1)^3] , [x,(x+1)^2, (x+2)^3]| then coefficient of x in f(x) is

The coefficient of x^(49) in the product (x-1)(x-3)(x-99)i s -99^2 b. 1 c. -2500 d. none of these

The coefficient of x^4 in (x//2-3//x^2)^10 is (405)/(256) b. (504)/(259) c. (450)/(263) d. none of these

Coefficient of x^(18)in(1+x+2x^2+3x^3++18 x^(18))^2 equal to 995 b. 1005 c. 1235 d. none of these

The number of distinct terms in the expansion of (x+1/x+x^2+1/(x^2))^(15) is/are (with respect to different power of x ) 255 b. 61 c. 127 d. none of these

If (x^2+x−2)/(x+3) 1) f(x) then find the value of lim_(x->1) f(x)

The coefficient of x^n in (1+x)^(101)(1-x+x^2)^(100) is nonzero, then n cannot be of the form 3r+1 b. 3r c. 3r+2 d. none of these

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 f(x)= |1x x+1 2x x(x-1)(x+1) x3 x(x-1) x(x-1)(x-2) (x+1)x(x-1)| then f(500) is equal to 0 b. 1 c. 500 d. -500