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

The coefficient of x^70 in the product (x-1)(x^2-2)(x^3-3)....(x^12-12) is (a) 4 . (b) 6 (c) 8 (d) 12

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^(20) in (1 + 3x + 3x^(2) + x^(3))^(20) ,I s

Find the coefficient of x^99 and x^98 in the polynomial (x-1)(x-2)(x-3)………..(x-100).

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^49 in the expansion of (x-1)(x-1/2)(x-1/2^2)........(x-1/2^49) is equal to

The coefficient of x^15 in the product (1-x)(1-2x) (1-2^2 x) (1-2^3 x) …. (1-2^15 x) is : (a) 2^105 - 2^121 (b) 2^121 - 2^105 (c) 2^104 - 2^120 (d) 2^108 -2^110

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

Show that the coefficient of x^49 in ( x + 1) (x + 3) ( x+ 5) ……(x + 99) is 2500

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