The expression 1 + in1 - in - 

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 Multiple Choice QuestionsMultiple Choice Questions

41.

If x = ω – ω2 – 2. Then the value of (x4 + 3x3 + 2x2 – 11x – 6) is

  • 0

  • -1

  • 1

  • 1

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42.

If α, β ∈ C are the distinct roots, of the equation x2 -x + 1 = 0, then α101 + β107 is equal to

  • 2

  • -1

  • 0

  • 1


43.

The sum of the coefficients of all odd degree terms in the expansion of x + x3 -15 + x - x3-15, (x>1) is

  • 2

  • -1

  • 0

  • 1


44.

The common chord of the circles x2 + y2 - 4x - 4y = 0 and 2x2+ 2y2 = 32 subtends at the origin an angle equal to

  • π3

  • π4

  • π6

  • π2


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45.

The locus of the mid-points of the chords of the circle x2 + y2 + 2x - 2y - 2= 0, which make an angle of 90° at the centre is

  • x2 + y- 2x - 2y = 0

  • x2 + y- 2x + 2y = 0

  • x2 + y+ 2x - 2y = 0

  • x2 + y+ 2x - 2y - 1 = 0


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46.

The expression 1 + in1 - in - 2

  • - in + 1

  •  in + 1

  • - 2in + 1

  • 1


C.

- 2in + 1

1 + in1 - in - 2

1 + in1 - in 1 - i- 2

1 +i1 - in1 - i2

1 +i1 - i × 1 + i1+ in1 + i2 - 2i

1 +2i - 11 - i2n1 + i2 - 2i

1 +2i - 11 - (- 1)n1 - 1 - 2i

2i2n- 2i

in(- 2i)n = - 2in + 1


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47.

Let z = .x + iy, where x and y are real. The  points (x, y) in the X-Y plane for which z + iz - i is purely imaginary, lie on

  • a straight line

  • An ellipse

  • a hyperbola

  • a circle


48.

If p, q are odd integers, then the roots of the equation 2px2 + (2p + q) x + q= 0 are

  • rational

  • irrational

  • non-real

  • equal


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49.

If a, b {1, 2, 3} and the equation ax2 + bx + 1 = 0 has real roots, then

  • a > b

  • a  b

  • number of possible ordered pairs (a, b) is 3

  • a<b


50.

The complex number z satisfying the equation z - i = z + 1 = 1 is

  • 0

  • 1 + i

  • - 1 + i

  • 1 - i


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