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 the expansion of (x/2-3/x^(2))^(10) is

The coefficient of x^2y^3 in the expansion of (1-x+y)^(20) is (20 !)/(213 !) b. -(20 !)/(213 !) c. (20 !)/(15!2!3!) d. none of these

If x^m occurs in the expansion (x+1//x^2)^ 2n then the coefficient of x^m is ((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^5in(1+2x+3x^2+....)^(-3//2)i s(|x|<1) 21 b. 25 c. 26 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

If in the expansion of (1+x)^n ,a ,b ,c are three consecutive coefficients, then n= (a c+a b+b c)/(b^2+a c) b. (2a c+a b+b c)/(b^2-a c) c. (a b+a c)/(b^2-a c) d. none of these

The coefficient of x^5 in the expansion of (x^2-x-2)^5 is -83 b. -82 c. -86 d. -81

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

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

Which of the following is not the solution of (log)_3(x^2-2)<(log)_3(3/2|x|-1) is (a) (sqrt(2),2) (b) (-2,-sqrt(2)) (c) (-sqrt(2),2 (d) none of these