CBSE Questions for Class 11 Engineering Maths Complex Numbers And Quadratic Equations Quiz 12 - MCQExams.com

If $$z=\dfrac { \sqrt { 3 } +i }{ \sqrt { 3 } -i } $$, then the fundamental amplitude of z is
  • $$-\dfrac { \pi }{ 3 } $$
  • $$\dfrac { \pi }{ 3 } $$
  • $$\dfrac { \pi }{ 6 } $$
  • None of these
What will be quadratic equation in x when the roots have arithmetic mean A and the geometric mean G?
  • $${ x }^{ 2 }+2Ax+{ G }^{ 2 }=0$$
  • $${ x }^{ 2 }+{ G }^{ 2 }x+A=0$$
  • $${ x }^{ 2 }+2Ax+{ G }^{ 2 }=0$$
  • $${ x }^{ 2 }+Gx+A=0$$
Arg $$\left\{ sin\dfrac { 8\pi  }{ 5 } +i\left( 1+cos\dfrac { 8\pi  }{ 5 }  \right)  \right\}$$ is equal to
  • $$\quad -\frac { 3\pi }{ 10 } $$
  • $$\quad \frac { 3\pi }{ 10 } $$
  • $$\quad \frac { 4\pi }{ 5 } $$
  • $$\quad \frac { 3\pi }{ 5 } $$
Argument of the complex number $$\left( \dfrac { -1-3i }{ 2+i }  \right) $$
  • $${ 45 }^{ 0 }$$
  • $$135^{ 0 }$$
  • $$225^{ 0 }$$
  • $$240^{ 0 }$$
In which quadrant of the complex , the point $$\dfrac { 1+2i }{ 1-i } $$ kies?
  • Fourth
  • First
  • Second
  • Third
The amplitude of $$\sin \dfrac { \pi  }{ 5 } +i\left( 1-cos\dfrac { \pi  }{ 5 }  \right) $$ is 
  • $$\dfrac { 2\pi }{ 5 } $$
  • $$\dfrac { \pi }{ 15 } $$
  • $$\dfrac { \pi }{ 10 } $$
  • $$\dfrac { \pi }{ 5 } $$
Principal value of amplitude of (1+i) is 
  • $$\dfrac { \pi }{ 4 } $$
  • $$\dfrac { \pi }{ 12 } $$
  • $$\dfrac { 3\pi }{ 4 } $$
  • $$\pi $$
Out of the following the solution of the____________quadratic equation is position and rational.
  • $$6{x^2} + 5x + 6 = 0$$
  • $$6{x^2} - 13x + 6 = 0$$
  • $$12{x^2} + 7x - 12 = 0$$
  • $$2{x^2} + x - 3 = 0$$
If $$a+b+c=0$$ then the equation $$3{ ax }^{ 2 }+2bx+c=0$$ has
  • imaginary roots
  • real and equal root
  • real and different roots
  • rational roots
The principal amplitude of ($$sin40^o + i cos40^o)^5$$ is
  • $$70^o$$
  • $$-110^o$$
  • $$110^o$$
  • $$-70^o$$
The modulus of the complex number z such that $$\left | z+3-i \right |=1 $$ and arg $$z=\pi $$ is equal to 
  • 1
  • 2
  • 9
  • 4
  • 3
If z is a complex number of unit modules and argument $$\theta $$, then the real part of $$\dfrac { z(1-\bar { z } ) }{ z(1+z) } $$ is :
  • $${ -2sin }^{ 2 }\dfrac { \theta }{ 2 } $$
  • $${ 2sin }^{ 2 }\dfrac { \theta }{ 2 } $$
  • $$1+cos\dfrac { \theta }{ 2 } $$
  • $$1-cos\dfrac { \theta }{ 2 } $$
The amplitude of $$\dfrac {(1 + i\sqrt {3})}{\sqrt {3} + i}$$ is
  • $$\dfrac {\pi}{3}$$
  • $$\dfrac {\pi}{6}$$
  • $$\dfrac {\pi}{4}$$
  • $$\dfrac {2\pi}{3}$$
The nature of the roots of the quadratic equation $$2x^2  4x + 3 = 0$$ are
  • real and distinct
  • real and equal
  • no real roots
  • imaginary
If $${ z }_{ 1 },{ z }_{ 2 },{ z }_{ 3 },{ z }_{ 4 }$$ be the vertices of a square in Argand plane , then
  • `$${ 2z }_{ 2 }=\left( 1-i \right) { z }_{ 1 }+\left( 1+i \right) { z }_{ 3 }$$
  • $${ 2z }_{ 4 }=\left( 2-i \right) { z }_{ 1 }+\left( 2+i \right) { z }_{ 3 }$$
  • $${ 2z }_{ 2 }=\left( 3-i \right) { z }_{ 1 }+\left( 3+i \right) { z }_{ 3 }$$
  • $${ 2z }_{ 4 }=\left( 4-i \right) { z }_{ 1 }+\left( 4+i \right) { z }_{ 3 }$$
The complex numbers $${ z }_{ 1 },{ z }_{ 2 },{ z }_{ 2 }$$ satisfying $$\dfrac { { z }_{ 1 }+{ z }_{ 3 } }{ { z }_{ 2 }-{ z }_{ 3 } } =\dfrac { 1-i\sqrt { 3 }  }{ 2 } $$
  • If area zero
  • right angled isosceles
  • equilateral
  • obtuse angled
If $$z(2 - 2i\sqrt {3})^{2} = i(\sqrt {3} + i)^{4}$$, then the amplitude of $$z$$ is
  • $$\dfrac {\pi}{6}$$
  • $$\dfrac {5\pi}{6}$$
  • $$-\dfrac {\pi}{6}$$
  • $$\dfrac {7\pi}{6}$$
If $$z_{1}=1+2i,z_{2}=1-3i$$ and $$z_{3}=2+4i$$ then, the points of the Argand diagram representing $$z_{1}z_{2}z_{3},2z_{1}z_{2}z_{3},-7z_{1}z_{2}z_{3}$$ are :
  • Vertices of an isosceles triangle
  • Collinear
  • Vertices of a right angled triangle
  • Vertices of a equilateral triangle
The roots of $$(x-41)^{49}+(x-49)^{41}+(x-2009)^{2009}=0$$  are 
  • all necessarily real
  • non - real except one positive root
  • nor - real except positive roots
  • nonr real except for 3 roots of which exactly one is positive
The complex number $$z$$ satisfies $$z+|z|=2+8i$$. The value of $$|z|$$ is 
  • 10
  • 13
  • 17
  • 23
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