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 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

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

If the lines ax+y+1=0 , x+by+1=0 and x+y+c=0 , ( a , b , c being distinct and different from 1 ) are concurrent, then 1/(1-a)+1/(1-b)+1/(1-c)= (A)    0    (B)    1    (C)    1/(a+b+c)    (D)   None of these

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 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

The measure of the angle between the internal and external bisectors of an angle is: (A)   60°     (B)   70°      (C)   80°      (D)   90°

Let vec a and vec b be unit vectors that are perpendicular to each other then [vec a+(vec a×vecb),vec b+(vec a×vec b), vec a × vec b] is equal to- (1)    1    (2)    0    (3)    -1    (4)    2

x=(sqrt(p^2+q^2)+sqrt(p^2-q^2))/(sqrt(p^2+q^2)-sqrt(p^2-q^2)) then q^2x^2-2p^2x+q^2=? (A)    3    (B)    -1    (C)    -2    (D)    0    

The co-ordinates of two fixed points A and B of a triangle ABC are (a,0) and (-a,0) respectively. If variable point C moves such that cot A+ cot B=lamda , (where lamda is a constant) then the locus of point C is:- (1)    y lamda =2a     (2)    y =lamda a     (3)    y a=2lamda     (4)     None of these.