If z=x+iy and `x^(2)+y^(2)=16`, then the range of `abs(abs(x)-abs(y))` is

If a^(2) +b^(2) = x, ab = y then the value of (a^(4) +b^(4))/(a^(2) -ab sqrt(2) +b^(2)) is

Let x=2i+j-2k" and "y=i+j . If z is a vector such that x.z=abs(z), abs(z-x)=2sqrt(2) and the angle between x times y and z is 30^(@) , then the magnitude of the vector (x timesy) timesz is:

If (x+1)/(x-1)=(a)/(b) and (1-y)/(1+y)=(b)/(a), then the value of (x-y)/(1+xy) is (2ab)/(a^(2)-b^(2)) (b) (a^(2)-b^(2))/(2ab) (c) (a^(2)+b^(2))/(2ab) (d) (a^(2)-b^(2)backslash)/(ab)

The number of values of y in [-2pi,2pi] satisfying the equation abs(sin2x)+abs(cos2x)=abs(siny) is

a ^(2) x + b^(2) y = c ^(2) , x + y = 2ab

f(x)=abs(x-1)+abs(x-2)+abs(x-3) . Find the range of f(x).