If α and β are the roots

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 Multiple Choice QuestionsMultiple Choice Questions

281.

The imaginary part of

3 +2 - 5412 - 3 - 2 - 5412 can be

  •  - 6

  • 6

  •  - 26

  • 6


282.

Let α, β are roots of x2 + px + 2 = 0 and 1α, 1β are the roots of 2x2 - 2qx + 1 = 0.Then find the value of α + 1ββ + 1αα - 1αβ - 1β

  • 949 - p2

  • 949 + p2

  • 499 - q2

  • 949 - q2


283.

If z1, zare complex numbers such that Re(z1) = |z= 1| and Re(z2) = |z2 = 1| and arg (z1 – z2) = π6, then Im (z1 + z2) is equal to :

  • 23

  • 32

  • 13

  • 23


284.

If a and b are real numbers suchthat (2 + α)4 = a + bα, where α =  - 1 + i32 then a + b is equal to :

  • 33

  • 24

  • 9

  • 57


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285.

Let λ  0 be in R. If α and β are the roots of the equation, x2  x + 2λ = 0 and α and γ are the roots of the equation, 3x2  10x + 27λ = 0, then βγλ is equal to 

  • 27

  • 36

  • 9

  • 18


286.

If α is the positive root of the equation, p(x) = x2  x  2 = 0, thenlimxα1 - cospxx +α - 4 = ?

  • 32

  • 32

  • 12

  • 12


287.

The product of the roots of the equation 9x2 – 18|x| + 5 = 0 is

  • 2581

  • 527

  • 259

  • 59


288.

If the four complex numbers z, z, z - 2Rez and z - 2Rez represent the vertices of a square of side 4 units in the Argand plane, then |z| is equal to :

  • 4

  • 2

  • 42

  • 22


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289.

If α and β are the roots of the equation, 7x2  3x  2 = 0, then the value of α1 - α2 + β1 - β2 is equal to 

  • 124

  • 2736

  • 2716

  • 38


C.

2716

α + β = 37, αβ = - 27α1 - α2 + β1 - β2 = α + β - αβα + β1 - α21 - β2 = α + β - αβα + β1 + αβ2 - α2 + β2 α + β - αβα + β1 + αβ2 - α2 + β2 + 2αβ = 37 + 27371 + 272 - 372 - 227 = 2716


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290.

The value of  - 1 + i31 - i30 is : 

  • 65

  • 215i

  • - 215

  •  - 215i


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