The locus of z satisfying the inequality z + 2i2z&

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 Multiple Choice QuestionsMultiple Choice Questions

1.

A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of 2 cm/s2 and pursues the insect which is crawling uniformly along a straight line at a speed of 20 cm/s. Then the lizard will catch the insect after

  • 20 s

  • 1 s

  • 21 s

  • 21 s

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2.

The value of λ such that the system of equations 2x - y - 2z = 2; x - 2y + z = - 4; x + y + λz = 4, has no solution, is

  • 3

  • 1

  • 0

  • - 3


3.

Performing 3 iterations of bisection method the smallest positive approximate root of the equation x3 - 5x + 1 = 0, is

  • 0.25

  • 0.125

  • 0.52

  • 0.1875


4.

The feasible region represented x1 + x2  1, - 3x1 + x2  3, (x1, x2  0) is

  • a polygon

  • a singleton set

  • empty set

  • None of these


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5.

The set of all solutions of the inequation x2 - 2x + 5  0 in R is

  • R - - , - 5

  • R - 5, 

  • ϕ

  • R - - , - 4


6.

The set of values of x for which the inequalities x2 - 3x - 10 < 0, 10x - x2 - 16 > 0 hold simultaneously, is

  • (- 2, 5)

  • (2, 8)

  • (- 2, 8)

  • (2, 5)


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7.

The locus of z satisfying the inequality z + 2i2z + i < 1, where z = x + iy, is

  • x2 + y2 < 1

  • x2 - y2 < 1

  • x2 + y2 > 1

  • 2x2 + 3y2 < 1 


C.

x2 + y2 > 1

Let z = x + iyGiven, z + 2i2z + i < 1 x2 + y + 222x2 + 2y + 12 < 1 x2 + y2 + 4 + 4y < 4x2 + 4y2 + 1 + 4y 3x2 + 3y2 > 3    x2 + y2 > 1


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8.

The set of all real values for which the function

fx = 1 - cos2x . λ + sinx, x   - π2, π2,

has exactly one maxima and exactly one minima, is

  • - 12, 12 - 0

  • - 32, 32

  • - 12, 12

  • - 32, 32 - 0


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