The modulus of 1 - i3 + i + 4i

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 Multiple Choice QuestionsMultiple Choice Questions

101.

If

  • π

  • - π

  • π/2

  • - π/2


102.

For any complex number z, the minimum value of z + z - 1 is

  • 0

  • 1

  • 2

  • - 1


103.

If a, b, c are real, then both the roots of the equation (x - b)(x - c) + (x - c)(x - a) + (x - a)(x - b) = 0

  • positive

  • negative

  • real

  • imaginary


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104.

The modulus of 1 - i3 + i + 4i5 is

  • 5 unit

  • 115 unit

  • 55 unit

  • 125


C.

55 unit

Let z = 1 - i3 + i + 4i5        = 5 - 5i + 12i - 453 +i = 1 + 7i53 + i        = 1 + 7i3 - i59 + 1 = 1 + 2i5        = 10 + 20i50 = 1 + 2i5 z = 152 + 252 = 151 + 4 = 55


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105.

If α, β be the roots of x2 - a(x - 1) + b = 0, then the value of 1α2 -  + 1β2 -  + 2a +b is

  • 4a + b

  • 1a + b

  • 0

  • - 1


106.

The sum of all real roots of the equation x - 22 + x - 2 - 2 = 0 is

  • 7

  • 4

  • 1

  • 5


107.

The quadratic equation whose roots are three times the roots of 3ax2 + 3bx + c = 0 is

  • ax2 + 3bx + 3c = 0

  • ax2 + 3bx + c

  • 9ax2 + 9bx + c

  • ax2 + bx + 3c


 Multiple Choice QuestionsShort Answer Type

108.

Find the values of 'a' for which the expression x2 - (3a - 1)x + 2a2 + 2a - 11 is always positive


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 Multiple Choice QuestionsMultiple Choice Questions

109.

The value of (1 - w + w2)5 + (1 + w - w2)5, where w and w2 are the complex cube roots of unity, is

  • 0

  • 32w

  • - 32

  • 32


110.

Let α, β be the roots of x2 - 2xcosϕ + 1 = 0, then the equation whose roots are αn, βn is

  • x2 - 2xcos - 1 = 0

  • x2 - 2xcos + 1 = 0

  • x2 - 2xsin + 1 = 0

  • x2 + 2xsin - 1 = 0


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