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 |z|=k and omega=(z-k)/(z+k) , then Re (omega) =

If plane 2x+3y+6z+k=0 is tangent to the sphere x^(2)+y^(2)+z^(2)+2x-2y+2z-6=0 , then a value of k is (a) 26 (b) 16 (c) -26 (d) none of these

If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition that ((w- bar w 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 (c) z=bar z (d) None of these

Four distinct points (k, 2k), (2, 0), (0, 2) and (0,0) lie on a circle for : (A) k = 0 (B) k = 6/5 (C) k = 1 (D) k = -1

In the relation y = r sin ( omega t - kx) , the dimensions of omega//k are

The centre of circle which passes through A (h, 0), B (0, k) and C (0, 0) is : (A) (h/2, 0) (B) (0, k/2) (C) (h/2, k/2) (D) (h, k)

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 "arg"(z) is (pi/8,0) b. (pi/6,0) c. (pi/4,0) d. none of these

Assume X, Y, Z, W and P are matrices of order 2 xxn , 3 xxk , 2 xxp , n xx3 and p xxk , respectively. Choose the correct answer The restriction on n, k and p so that P Y + W Y will be defined are:(A) k = 3, p = n (B) k is arbitrary, p=2 (C) p is arbitrary, k=3 (D) k=2 , p=3

For the solution of the gases W, X, Y and z in water at 298 K , the Henrys law constants ( K _ H ) are 0.5, 2, 35 and 40 kbar, respectively. The correct plot for the given data is :

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]