The value of   - 1 + i32n

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 Multiple Choice QuestionsMultiple Choice Questions

21.

If the difference between the roots of the equation x2 + kx + 1 = 0 is strictly less than 5, where  k  2, then k can be any element of the interval

  • ( - 3, - 2]  [2, 3)

  • ( - 3, 3)

  •  - 3,  - 2  2, 3

  • None of the above


22.

If the roots of the equation x2 + px + q = 0 are in the same ratio as those of the equation x2 + lx + m = 0, then which one of the following is correct ?

  • p2m = l2q

  • m2p = l2q

  • m2p = q2l

  • m2p2 = l2q


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23.

The value of   - 1 + i32n +  - 1 - i32n where n is not a multiple of 3 and i =  - 1, is

  • 1

  •  - 1

  • i

  •  - i


B.

 - 1

 - 1 + i32n +  - 1 - i32n= ωn + ω2nPut n = 1, 2, 4 not multiple of 3ω1 + ω21 = ω +ω2 = - 1   1 + ω + ω2 = 0ω2 + ω22 = ω2 +ω4 = ω2 + ω4 = ω2 +ω3 . ω = ω2 + ω= - 1                         ω3 = 1

Another method:

 - 1 + i32n +  - 1 - i32n= ωn + ω2nPut n = 1, 2, 4 not multiple of 3ω1 + ω21 = ω +ω2 = - 1   ω2 = 0ω2 + ω22 = ω2 +ω4                     = ω2 +ω3 . ω = ω2 + ω            ω3 = 1                     = - 1 


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24.

If 1, ω, ω2 are the cube roots of unity, then (1 + ω)(1 + ω2)(1 + ω3)(1 + ω + ω2) is equal to

  •  - 2

  •  - 1

  • 0

  • 2


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25.

If the graph of a quadratic polynomial lies entirely above x-axis, then which one of the following is correct ?

  • Both the roots are real

  • One root is real and the other is complex

  • Both the roots are complex

  • Cannot say


26.

The modulus and principal argument of the complex number 1 + 2i1 - 1 - i2 are respectively

  • 1, 0

  • 1, 1

  • 2, 0

  • 2, 1


27.

If z + 4  3, then maximum value of z +1 is

  • 0

  • 4

  • 6

  • 10


28.

The number of roots of the equation z2 = 2z is

  • 2

  • 3

  • 4

  • zero


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29.

If cotα and cotβ are the roots of the equation x2 + bx + c = 0 with b  0, then the value of cot(α + β) is

  • c - 1b

  • 1 - cb

  • bc - 1

  • b1 - c


30.

The roots of the equation :

q - rx2 + r - px + p - q = 0 are

  • r - pq - r, 12

  • p - qq - r, 1

  • q - rp - q, 1

  • r - pp - q, 12


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