Important Questions of Complex Numbers and Quadratic Equations Mathematics | Zigya

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 Multiple Choice QuestionsMultiple Choice Questions

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51.

In an examination, 70% students passed in Physics80% students passed in Chemistry, 75% studentpassed in Mathematics and 85% students passed iBiology, and x% students failed in all the four subjectsWhat is the minimum value of x ?

  • 10

  • 12

  • 15

  • None of the above


52.

2x2 + 3x - α = 0 has roots 2 and β while the equatiox2 - 3mx + 2m2 = 0 has both roots positive, where > 0 anβ > 0. What is the value of α ?

  • 12

  • 1

  • 2

  • 4


53.

2x2 + 3x - α = 0 has roots 2 and β while the equatiox2 - 3mx + 2m2 = 0 has both roots positive, where > 0 anβ > 0. If β, 2, 2m are in GP, then what is the value of βm ?

  • 1

  • 2

  • 4

  • 6


54.

What is ω100 + ω200 + ω300 equal to, where ω is the cube root of unity ?

  • 1

  • 3ω

  • 3ω2

  • 0


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55.

If c > 0 and 4a + c < 2b, then ax2 - b+ c = 0 haa root in which one of the following intervals ?

  • (0, 2)

  • (2, 3)

  • (3, 4)

  • ( - 2, 0)


56.

If Rez  - 1z +1 = 0,,where z = x + iy is a complenumber, then which one of the following is corrcet ?

  • z = 1 + i

  • z = 2

  • z = 1 - i

  • z = 1


57.

If z = 32 + i2107 + 32 - i2107, then what is the imaginary part of z equal to ?

  • 0

  • 12

  • 32

  • 1


58.

If both the roots of the equation x2 - 2kx + k2 - 4 = 0 lie between 3 and 5, then whicone of the following is correct ?

  •  - 2 < k < 2

  •  - 5 < k < 3

  •  - 3 < k < 5

  •  - 1 < k < 3


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59.

What is the number of distinct solutions of thequation  z2 + z = 0 (where z is a complex number?

  • One

  • Two

  • Three

  • Five


60.

Which of the following are correct in respect of thsystem of equations x + y + z = 8+ 2z = 6 an3y + 5= ?

1. They have no solution, if k = 15.

2. They have infinitely many solutions, if k = 20

3. They have unique solution, if k = 25.

Select the correct answer using the code given below :

  • 1 and 2 only

  • 2 and 3 only

  • 1 and 3 only

  • 1, 2 and 3


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