If `f(x)=1-x+x^2-x^3++^(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^(5)in(1+2x+3x^(2)+...)^(-3/2)is(|x|<1)21 b.25c.26d .none of these

In the expansion of (x-1) (x-2) …(x-18) , the coefficient of x^(17) is

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

If f(x)=det[[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 ]]

If D(x)=det[[(x-1),(x-1)^(2),x^(3)(x-1),x^(2),(x+1)^(3)x,(x+1)^(2),(x+1)^(3) then the coefficient of x in D(x), is ]]

If f(x)=(x-1)(x-2)......(x-10), then coefficient of x^9 is (A) -55 Â Â (B)35 (C)15 (D) -55

Let f(x)=tan^(-1)((x^(3)-1)/(x^(2)+x)) , then the value of 17f'(2) is equal to

The range of the function f(x)=(x^2-x)/(x^2+2x) is R (b) R-[1] (c) R={-1/2,1} (d) none of these

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 (x-1)/(x)=3, then the value of 1+(1)/(x^(2)) is (a) 9(b) 10(c)11 (d) None of these