The common chord of the circles x2 + y2 - 4x - 4y = 0 and 2x2+ 2y

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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


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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


D.

π2

Given, equation of circles are x2 + y2 - 4x - 4y = 0 and 2x2+ 2y2 = 32

or x2 + y2 - 4x - 4y = 0 and x2+ y2 = 16

 equation of common chord is

x2 + y2 - 4x - 4y - x2 + y2 - 16 = 0

 - 4x - 4y + 16 = 0

 x + y = 4

This common chord passes through (2, 2), i.e. centre of first circle.

Also, (0, 0) is at the circumference of the first circle.

Thus, Common chord will subtent π2 angle at (0, 0).

 


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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


46.

The expression 1 + in1 - in - 2

  • - in + 1

  •  in + 1

  • - 2in + 1

  • 1


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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