If two numbers have arithmetic mean 9 and geometric mean 4, then the numbers are roots of the quadratic equation

a)

b)

c)

d)

If  and  are roots of the equation , z being complex. Further assume that the origin, and  form an equilateral triangle, then

a)

b)

c)

d)

If z and w are two non-zero complex numbers such that  and  then  is equal to

a) 1

b) –1

c)

d)

If then

a) x = 4n

b) x = 2n

c) x = 4n + 1

d) x = 2n + 1

where n is any positive integer

The number of real roots of the equation  is

a) 2

b) 4

c) 1

d) 3

If  and  then the equation having the roots  and  as its roots is

a)

b)

c)

d)

If ω is an imaginary cube root of unity then  equals

a) 128ω

b) –128ω

c) 128ω²

d) –128ω²

If  then

a) x = 3, y = 1

b) x = 1, y = 3

c) x = 0, y = 3

d) x = 0, y = 0

The number of real roots of  is

a) 0

b) 2

c) 1

d) 4

The equation  represents a

a) circle

b) straight line

c) hyperbola

d) parabola

If  where r = 1, 2, .  .  . , n then  is equal to

a) cos α + sin α

b)

c)

d)

Statement 1: If   is purely imaginary then
Statement 2:  that is |a + ib| = |a – ib|
Then which one of the following is true

a) Statement 1 is false. Statement 2 is true.

b) Statement 1 is true. Statement 2 is true. Statement 2 is correct explanation for Satement1.

c) Statement 1 is true. Statement 2 is true. Statement 2 is not a correct explanation for Satement1.

d) Statement 1 is true. Statement 2 is false.

The number of real values of the parameter k for which  with real coefficients will have exactly one solution is

a) 2

b) 1

c) 4

d) None of these

If x² + px +1 is a factor of the expression ax³ + bx + c then

a)

b)

c)

d) None of these

The vector z = −4 + 5i is turned counter-clockwise through an angle of  and stretched times. The complex number corresponding to the newly obtained vector is

a)

b)

c)

d) None of these

 is equal to

a) 1

b) –1

c) 0

d) None of these

For all complex numbers satisfying  and, the minimum value of  is

a) 0

b) 2

c) 7

d) 17

If a and d are two complex numbers then the sum of (n + 1) terms of the following series   is

a)

b) na

c) 0

d) None of these

If z is a complex number such that |2z – 5| + |2z + 5| = 10 then the locus of z is

a) A straight line

b) A circle

c) A parabola

d) None of these

The area of the triangle whose vertices are expressed by the complex numbers 0, z,  (where 0 < α < π) equals

a)

b)

c)

d)

The set  is equal to

Find the maximum and minimum value of  

If z be a complex number satisfying |z – 3 – 2i| ≤ 2 then the minimum value of |2z – 6 + 5i| is