If z satisfies the equation z - z = 1 + 2i, then z is equal to f

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 Multiple Choice QuestionsMultiple Choice Questions

141.

If one AM 'A' and two GM p and q are inserted between two given numbers, then. find the value of p2q + q2p.

  • A

  • 2A

  • 3A

  • 4A


142.

If the roots of the equation x2 + ax + b = 0 are c and d, then one of the roots of the equation x2 + (2c + a)x + c2 + ac + b = 0

  • c

  • d - c

  • 2d

  • 2c


143.

If the axes are shifted to the point (1, - 2) without solution, then the equation 2x2 + y2 - 4x + 4y = 0 becomes

  • 2X2 + 3Y2 = 6

  • 2X2 + Y2

  • X2 + 2Y2

  • None of the above


144.

In a group ( G, *), then equation x * a = b has a

  • unique solution b * a-1

  • unique solution a-1 * b

  • unique solution a-1 * b-1

  • many solutions


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145.

The number of solutions of the equation sin(ex) = 5x + 5-x,  is

  • 0

  • 1

  • 2

  • infinitely many


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146.

If z satisfies the equation z - z = 1 + 2i, then z is equal to

  • 32 + 2i

  • 32 - 2i

  • 2 - 32i

  • 2 + 32i


B.

32 - 2i

We have, z - z = 1 + 2iIf z = x +iy, then this equation reduces to               x + iy - x + iy = 1 + 2i x2 + y2 - x + - iy = 1 + 2i

On comparing real and imaginary parts of both sides of this equation, we get

x2 + y2 - x = 1  x2 + y2 = 1 +x      x2 + y2 = 1 + x2      x2 + y2 = 1 + x2 + 2x               y2 = 1 + 2xand           - y = 2                 y = - 2

Putting this value in Eq. (i), we get

           (- 2)2 = 1 + 2x

              2x = 3                x = 32Hence,         z = x + iy                      = 32 - 2i


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147.

If z = 1 - i31 + i3, then arg (z) is

  • 60°

  • 120°

  • 240°

  • 300°


148.

For what values of m can the expression 2x2 + mxy + 3y2 - 5y - 2 be expressed as the product of two linear factors?

  • 0

  • ± 1

  • ± 7

  • 49


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149.

If n is an integer which leaves remainder one when divided by three, then 1 + 3in + 1 - 3in equals

  • - 2n + 1

  • 2n + 1

  • - (- 2)n

  • - 2n


150.

If z - 25z - 1 = 5,  find the value of z

  • 3

  • 4

  • 5

  • 6


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