If `k>0`, `|z|=\w\=k`, and `alpha=(z-bar w)/(k^2+zbar(w))`, then `Re(alpha)` (A) 0 (B) `k/2` (C) `k` (D) None of these

If (log)_k xdot(log)_5k=(log)_x5,k!=1,k >0, then x is equal to (a) k (b) 1/5 (c) 5 (d) none of these

If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition that ((w- barw z)/(1-z)) is a purely real, then the set of values of z is |z|=1,z!=2 (b) |z|=1a n dz!=1 z= z (d) None of these

If |z|=1 and w=(z-1)/(z+1) (where z!=-1), then R e(w) is 0 (b) 1/(|z+1|^2) |1/(z+1)|,1/(|z+1|^2) (d) (sqrt(2))/(|z|1""|^2)

If there is an error of k % in measuring the edge of a cube, then the percent error in estimating its volume is (a) k (b) 3k (c) k/3 (d) none of these

If the focus of the parabola x^2-k y+3=0 is (0,2), then a values of k is (are) 4 (b) 6 (c) 3 (d) 2

The value of k such that (x-4)/1=(y-2)/1=(z-k)/2 lies in the plane 2x-4y+z=7 is (A) 7 (B) -7 (C) no real value (D) 4

If z is a complex number lying in the fourth quadrant of Argand plane and |[(kz)/(k+1)]+2i|>sqrt(2) for all real value of k(k!=-1), then range of "a r g"(z) is a. (pi/8,0) b. (pi/6,0) c. (pi/4,0) d. none of these

The set of points on the axis of the parabola y^2=4x+8 from which the three normals to the parabola are all real and different is (a) {(k ,0)"|"klt=-2} (b) {(k ,0)"|"kgt=-2} (c) {(0, k)"|"k gt=-2} (d) none of these

If alpha is a complex constant such that alpha z^2+z+ baralpha=0 has a real root, then (a) alpha+ bar alpha=1 (b) alpha+ bar alpha=0 (c) alpha+ bar alpha=-1 (d)the absolute value of the real root is 1

If alpha=tan^(-1)((4x-4x^3)/(1-6x^2+x^2)),beta=2sin^(-1)((2x)/(1+x^2)) and tanpi/8=k , then (a) alpha+beta=pi for x in [(1,1)/k] (b) alpha+beta for x in (-k , k) (c) alpha+beta=pi for x in [(1,1)/k] (d) alpha+beta=0 for x in [-k , k]