A complex number z is said to be unimodular, if |z|= 1. suppose z_{1} and z_{2} are complex numbers such that is unimodular and z_{2} is not unimodular. Then, the point z_{1} lies on a
straight line parallel to X -axis
straight line parallel to Y -axis
circle of radius 2
circle of radius 2
6
-6
3
3
The normal to the curve x^{2} + 2xy-3y^{2} =0 at (1,1)
does not meet the curve again
meets the curve again in the second quadrant
meets the curve again in the third quadrant
meets the curve again in the third quadrant
If z is a complex number such that |z|≥2, then the minimum value of
is equal to 5/2
lies in the interval (1,2)
is strictly greater than 5/2
is strictly greater than 5/2
Let α and β be the roots of equation px^{2} +qx r =0 p ≠0. If p,q and r are in AP and = 4, then the value of |α- β| is
If the coefficients of x^{3} and x^{4} in the expansion of (1+ax+bx^{2})(1-2x)^{18} in powers of x are both zero, then (a,b) is equal to
The real number k for which the equation, 2x^{3} +3x +k = 0 has two distinct real roots in [0,1]
lies between 1 and 2
lies between 2 and 3
lies between -1 and 0
lies between -1 and 0
If the equations x^{2} + 2x + 3 = 0 and ax^{2} + bx + c = 0, a, b, c ∈ R, have a common root, then a : b : c is
1:2:3
3:2:1
1:3:2
1:3:2