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

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

The coefficient of x^6 in series e^(2x) is 4/(25) b. 3/(45) c. 2/(45) d. None of these

The coefficient of x^(19) in the polynomial (x-1)(x-2)(x-2^2)(x-2^(19)) is 2^(20)-2^(19) b. 1-2^(20) c. 2^(20) d. none of these

The coefficient of x^8y^(10) in the expansion of (x+y)^(18) is a. \ ^(18)C_8 b. \ ^(18)P_(10) c. 2^(18) d. none of these

Observe the following statements : Statement -I : In the expansion of (1+x)^50, the sum of the coefficients of odd powers of x is 2^50 . Statement -II : The coefficient of x^4 in the expansion of (x/2 - (3)/(x^2))^10 is equal to 504/259 . Then the true statements are :

The coefficient of x^3 in the expansion of (1-x+x^2)^5 is (a). -83 (b). 0 (c) .^(30)C_(10) (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 x^m occurs in the expansion (x+1//x^2)^(2n) , then the coefficient of x^m is a. ((2n)!)/((m)!(2n-m)!) b. ((2n)!3!3!)/((2n-m)!) c. ((2n)!)/(((2n-m)/3)!((4n+m)/3)!) d. none of these

The coefficient of x^(10) in the expansion of (1+x^2-x^3)^8 is 476 b. 496 c. 506 d. 528

The factors of x^4-x^2-10x-25 are (a) (x^2+3x+5)(x^2-3x+5) (b) (x^2+3x+5)(x^2+3x-5) (c) (x^2+x+5)(x^2-x+5) (d) none of these