Sum of the series `1+2^2x+3^2x^2+4^2x^3+.....to oo`, `|x|<1` is:
(A)   `(1+x)/(1-x)^3`   (B)   `(1-x)/(1+x)^3`   
(C)   `(2+x)/(1-x)^3`   (D)   `(1-x)/(1+x)^2`

The value of x/y, if x=0x_1x_2x_1x_2............, where x_1,x_2, are consecutive digits after the decimal point in the number x and if y=0y_1y_2y_1y_2............, where y_1,y_2, are consecutive digits after the decimal point in the number y is: (A).    (y_1y_2)/(x_1x_2)    (B).    (x_1x_2)/(y_1y_2)    (C).    (x_1)/(y_2)    (D).    (x_2)/(y_1)   

If a^(1/2)+b^(1/2)-c^(1/2)=0 , then the value of (a+b-c)^2 is: (A)    2ab    (B)    2bc    (C)    4ab    (D)    4ac

If int (1+xtanx)^(-2) dx=1/(x+f(x))+c; then value of f(x) is (1)   xtanx    (2)   cotx    (3)   tanx    (4)   tan^2x

If m and x are two real numbers where m in I, then e^(2micot^(-1)x)((x*i+1)/(x*i-1))^m (A)   cos x+i sin x   (B)   m/2   (C)   1    (D)   (m+1)/2

If m and x are two real numbers where m in I , then e^(2micot^(-1)x)((x*i+1)/(x*i-1))^m (A)    cos x+i sin x    (B)    m/2    (C)    1     (D)    (m+1)/2

If m and x are two real numbers where m in I , then e^(2micot^(-1)x)((x*i+1)/(x*i-1))^m (A)    cos x+i sin x    (B)    m/2    (C)    1     (D)    (m+1)/2

If m and x are two real numbers where m in I , then e^(2micot^(-1)x)((x*i+1)/(x*i-1))^m (A)    cos x+i sin x    (B)    m/2    (C)    1     (D)    (m+1)/2

int (px^(p+2q-1)-qx^(q-1))/(x^(2p+2q)+2x^(p+q)+1) dx is equal to (1)    -x^p/(x^(p+q)+1)+C     (2)    x^q/(x^(p+q)+1)+C     (3)    -x^q/(x^(p+q)+1)+C     (4)    x^p/(x^(p+q)+1)+C    

int (px^(p+2q-1)-qx^(q-1))/(x^(2p+2q)+2x^(p+q)+1) dx is equal to (1)    -x^p/(x^(p+q)+1)+C     (2)    x^q/(x^(p+q)+1)+C     (3)    -x^q/(x^(p+q)+1)+C     (4)    x^p/(x^(p+q)+1)+C    

If alpha , beta are the roots of 6x^2-2x+1=0 and s_x=alpha^n+beta^n , then Lt_(n->oo) sum_(r=1)^n s_r is (a)    5/17    (b)    0     (c)    3/37     (d)   none