The sum of all real values of x satisfying the equation
 is:

• 3

• -4

• 6

• 6

A complex number z is said to be unimodular, if |z|= 1. suppose z₁ and z₂ are complex numbers such that  is unimodular and z₂ is not unimodular. Then, the point z₁ 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 x² + 2xy-3y² =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 px² +qx r =0 p ≠0. If p,q and r are in AP and  = 4, then the value of |α- β| is

7.

If the coefficients of x³ and x⁴ in the expansion of (1+ax+bx²)(1-2x)¹⁸ in powers of x are both zero, then (a,b) is equal to

• 
• 
• 
• 

If [a x b b x c c x a] = λ[a b c]², then λ is equal to 

• 0

• 1

• 2

• 2

The real number k for which the equation, 2x³ +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 x² + 2x + 3 = 0 and ax² + 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