`(e^x x^(16) (1-x)^(1001) (2-x)^(1003))/((x-1/x)^(2017) (x+1/x)^(2006)(x^2-x+1)) <0`

The expression (1)/(1+(x)/(1-(x)/(x+2)))div ((1)/(1-x)+(1)/(1+x))/((1)/(1-x)-(1)/(1+x)) (a) (2x)/(x^(2)+2x+2) (b) (2x)/(x^(2)-1) (c) 1 (d) x^(2)-1

The coefficient of x^1007 in the expansion (1+x)^(2006)+x(1+x)^(2005)+x^2(1+x)^(2004)x^3(1+x)^(2003)+..... +x^(2006) is

The coefficient of x^(1007) in the expansion (1+x)^(2006)+x(1+x)^(2005)+x^(2)(1+x)^(2004)x^(3)(1+x)^(2003)+....+x^(2000)

(2^(x-1)*4^(x+1))/(8^(x-1))=16

Coefficient of x^(1001) in (1-x)^(901)(1+x+x^(2))^(900) is

Coefficient of x^(2009) in (1+x+x^(2)+x^(3)+x^(4))^(1001) (1-x)^(1002) is (a) 0 (b) 4."^(1001)C_(501) (c) -2009 (d) none of these

16. "4^(x)-3^(x-(1)/(2))=3^(x+(1)/(2))-2^(2x-1).

int e^(x)((x-2)/((x-1)^(2)))dx is equal to (i) (e^(x))/(x-1)+C (ii) (e^(x))/((x-1)^(2))+C( iii) (2e^(x))/((x-1)^(2))+C( iv )(e^(x)-1)/(x-1)+C