If `z=i log(2-sqrt3),` then `cosz = a.-1` b. `(-1)/2` c. `1` d. `2`

If z^3+(3+2i)z+(-1+i a)=0 has one real root, then the value of a lies in the interval (a in R) a. (-2,1) b. (-1,0) c. (0,1) d. (-2,3)

If |z^2-3|=3|z| , then the maximum value of |z| is a. 1 b. (3+sqrt(21))/2 c. (sqrt(21)-3)/2 d. none of these

If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, then the value of x y z is a. 1 b. 2 c. -1 d. 2

Let L be the line of intersection of the planes 2x+3y+z=1a n dx+3y+2z=2. If L makes an angle alpha with the positive x-axis, then cosalpha equals a. 1/2 b. 1 c. 1/(sqrt(2)) d. 1/(sqrt(3))

If z_1, z_2 in C ,z_1^ 2 in R ,z_1(z_1^ 2-3z_2 ^2)=2 a n d z_2(3z_1 ^2-z_2^ 2)=11 , then the value of z_1^ 2+z_2^ 2 is a. 10 b. 12 c. 5 d. 8

If z=x+i y , then he equation |(2z-i)/(z+1)|=m represents a circle, then m can be (a) 1/2 b. 1 c. 2 d. 3

If (log)_3{5+4(log)_3(x-1)}=2, then x is equal to 4 (b) 3 (c) 8 (d) (log)_2 16

Given z=(1+isqrt(3))^(100), then [Re(z)//Im(z)] equals (a) 2^(100) b. 2^(50) c. 1/(sqrt(3)) d. sqrt(3)

If the volume of tetrahedron A B C D is 1 cubic units, where A(0,1,2),B(-1,2,1)a n dC(1,2,1), then the locus of point D is a. x+y-z=3 b. y+z=6 c. y+z=0 d. y+z=-3

The line (x-2)/3=(y+1)/2=(z-1)/-1 intersects the curve x y=c^(2),z=0 if c is equal to a. +-1 b. +-1//3 c. +-sqrt(5) d. none of these