Complex Numbers And Quadratic Equations CBSE Questions & Answers

Complex Numbers And Quadratic Equations

This is Mathematics Class 11 Complex Numbers and Quadratic Equations CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
\({i^2} + {i^4} + {i^6} + ...........\) up to 2k + 1 terms , for all k belongs to natural numbers N .
  • A
    1
  • B
    -1
    Correct
  • C
    0
  • D
    none of these
2
\(1 + i + {i^2} + {i^3} + .......\) up to 4n terms is equal to
  • A
    -1
  • B
    0
    Correct
  • C
    none of these
  • D
    1
3
\(1 + i + {i^2} + {i^4} + {i^4} + {i^6} + .......\) up to 1001 terms is equal to
  • A
    -1
  • B
    1
    Correct
  • C
    0
  • D
    none of these
4
If If \(\omega \) is a non real cube root of unity and \({\left( {1 + \omega } \right)^9} = a + b\omega ;a,b \in R,\) then a and b are respectively the numbers :
  • A
    1 , 0
  • B
    -1 , 0
    Correct
  • C
    0 , -1
  • D
    0 , 1
5
If \({\text{ | z | }} = {\text{ 1}}\) , then \({{z - 1} \over {z + 1}},z \ne - 1is\)
  • A
    none of these
  • B
    purely real
  • C
    purely imaginary or zero
    Correct
  • D
    non-real
6
The equation \({\text{| 4z }}--{\text{ 1 | }} = {\text{ 4 | z }}--{\text{ 5 |}}\) represents :
  • A
    a parabola
  • B
    a circle
  • C
    an ellipse
  • D
    a straight line
    Correct
7
If \({\left( { - 1 + \sqrt 3 i} \right)^n} + {\left( { - 1 - \sqrt 3 i} \right)^n} = {2^n}\alpha ,\) then \(\alpha \) is equal to :
  • A
    -1
  • B
    none of these
  • C
    2
  • D
    2 or -1
    Correct
8
If ( x + iy ) ( 3 – 4i ) = (5 + 12i ) , then \(\sqrt {{x^2} + {y^2}} = \)
  • A
    5/13
  • B
    65
  • C
    16
  • D
    13/5
    Correct
9
he locus of the equation \(\left| {{{3z - 1} \over {z - 1}}} \right| = 1\) is
  • A
    none of these
  • B
    a circle
    Correct
  • C
    a straight line
  • D
    an ellipse
10
\(\sqrt { - 8} \sqrt { - 18} \sqrt { - 4} \) is
  • A
    -24i
    Correct
  • B
    24i
  • C
    24
  • D
    -24
11
If \(\alpha = {z \over {\overline z }},\) then \({\text{|}}\alpha {\text{|}}\) is equal to :
  • A
    -1
  • B
    1
    Correct
  • C
    0
  • D
    none of these
12
If z = x + iy ; x, y \(\in \) R then :
  • A
    \(z\bar z = {\left| z \right|^2}\)
    Correct
  • B
    none of these
  • C
    \(z\bar z < {\left| z \right|^2}\)
  • D
    \(z\bar z > {\left| z \right|^2}\)
13
The smallest positive integer n for which \({\left( {{{1 + i} \over {1 - i}}} \right)^n} = 1\) is :
  • A
    none of these
  • B
    2
  • C
    4
    Correct
  • D
    8
14
If \(z = {\left( {{{\sqrt 3 } \over 2} + {i \over 2}} \right)^5} + {\left( {{{\sqrt 3 } \over 2} - {i \over 2}} \right)^5},\)then
  • A
    Re ( z ) \(> \)0
  • B
    Im ( z ) \(<\) 0
  • C
    Im ( z ) = 0
    Correct
  • D
    none of these
15
If the cube roots of unity are 1, \(\omega ,{\omega ^2},\)then roots of the equation \({\left( {x - 1} \right)^3} + 8 = 0\) are :
  • A
    \( - 1,1 - 2\omega ,1 - 2{\omega ^2}\)
    Correct
  • B
    -1 ,-1 , -1
  • C
    none of these
  • D
    \( - 1, - 1 + 2\omega ,1 + 2{\omega ^2}\)