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 Multiple Choice QuestionsMultiple Choice Questions

111.

If one root of the equation x2 + (1 - 3i)x - 2(1 + i) = 0 is - 1 + i, then the other root is

  • - 1 - i

  • - 1 - i2

  • i

  • 2i


112.

The equation x2 - 3x + 2 = 0 has

  • no real root

  • one real root

  • two real root

  • four real root


113.

For two complex numbers z1, z2 the relation z1 + z2 = z1 + z2 holds, if

  • arg(z1) = arg(z2)

  • arg(z1) + arg(z2) = π2

  • z1z2 = 1

  • z1 = z2


114.

If z + 4  3, then the greatest and the least value of z + 1 are

  • 6, - 6

  • 6, 0

  • 7, 2

  • 0, - 1


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115.

The region of the complex plane for which z - az + a = 1, [Re (a)  0] is

  • x - axis

  • y - axis

  • the straight line x = a

  • None of the above


116.

The number of non-zero integral solutions of the equation 1 - ix = 2x

  • infinite

  • 1

  • 2

  • None of these


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117.

Let α, α2 be the roots of x2 + x + 1 = 0, then the equation whose roots are α31, α62 is

  • x2 - x + 1 = 0

  • x2 + x - 1 = 0

  • x2 + x + 1 = 0

  • x60 + x30 + 1 = 0


C.

x2 + x + 1 = 0

Given equation is x2 + x + 1 = 0. Since, α, α2  are the roots of the equation.

 α + α2 = - 1           ...(i)        α3 = 1               ...(ii)Now, for the equation of roots are α31 and α62α31 + α62 = α311 + α31  α31 + α62 = α30α1 + α30 . α α31 + α62 = α310 . α1 + α310 . α α31 + α62 = α1 + α            using Eq. (ii) α31 + α62 = - 1                    using Eq. (i)Again α31 . α62 = α93                        = α331 = 1  Required equation is,x2 -  α31 + α62 x + α31 . α62 = 0 x2 + x +1 = 0


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118.

The values of p for which the difference between the roots of the equation x2 + px + 8 = 0 is 2, are

  • ± 2

  • ± 4

  • ± 6

  • ± 8


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119.

For any two complex numbers z1 and z2 and any real numbers a and b, az1 - az22 + bz1 + az22 is equal to

  • a2 + b2z1 + z2

  • a2 + b2z12 + z22

  • a2 + b2z12 - z22

  • None of these


120.

If w ( 1 )is a cube root of unity and (1 + w2)n = (1 + w4)n, then the least positive value of n is

  • 2

  • 3

  • 5

  • 6


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