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 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

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.

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

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

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 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