If ω is a complex cube root of unity, (x + 1) (x + &om

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 Multiple Choice QuestionsMultiple Choice Questions

241.

Let α  1 be a real root of the equation x3 - ax2 + ax - 1 = 0, where a  - 1 is a real number. Then, a root of this equation, among the following, is

  • α2

  • - 1α

  • 1α

  • - 1α2


242.

If f(x) = 2cosx10x - π22cosx1012cosx, then f'π = ?

  • 0

  • 2

  • π2

  • π - 6


243.

If z = 1 + i3, then Arg z + Arg z = ?

  • 0

  • π3

  • π2

  • 2π3


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244.

If ω is a complex cube root of unity, (x + 1) (x + ω)(x - ω - 1) is equal to

  • x3 - 1

  • x3 + 1

  • x3 + 2

  • x3 - 2


A.

x3 - 1

ω  cube root of unityie, ω3 = 1 and 1 + ω + ω2 = 0Then, x + 1x + ωx - ω - 1= x + 1x2 + ωx - ωx - ω2 - x - ω= x + 1x2 - x - ω +w2= x + 1x2 - x -  - 1        ω + ω2 = - 1= x + 1x2 - x + 1= x + 1x2 + 1  - x= x3 - 1


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245.

3 + i7 + 3 - i7 = ?

  • 1283

  • 2563

  • - 1283

  • - 2563


246.

If a > 0 and b- 4ac = 0, then the curve y = ax2 + bx + c

  • cuts the x-axis

  • touches the x-axis and lies below it

  • lies entirely above the x-axis

  • touches the x-axis and lies above it


247.

If tan(A) and tan(B) are the roots of the quadratic equation x- px + q = 0, then sin2(A + B) is equal to

  • p2p2 + q2

  • p2p2 +q2

  • 1 -  p1 - q2

  • p2p2 + 1 - q2


248.

The value of a for which the equations x+ ax + 1 = 0 and x4 + ax2 + 1 = 0 have acommon root is

  • - 2

  • - 1

  • 1

  • 2


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249.

Let z = a - i2; a  R. Then i + z2 - i - z2 = ?

  • 2

  • - 2

  • 4

  • - 4


250.

The locus of the complex number z such that argz - 2z +2 = π3 is 

  • a circle 

  • a straight line 

  • a parabola 

  • an ellipse


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