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

The value of a for which one root of the quadratic

 is twice as large as the other is

a)

b)

c)

d)

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)

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