CBSE Questions for Class 11 Commerce Applied Mathematics Number Theory Quiz 12 - MCQExams.com

The modulus of the complex number $$z$$ such that $$\left| z + 3 - i\right | = 1$$ and $$\arg{z} = \pi$$ is equal to
  • $$1$$
  • $$2$$
  • $$4$$
  • $$3$$
The roots of the equation $$(3b+c-4a)x^2+(3c+a-4b)x+(3a+b-4c)= 0$$ are 
  • Irrational
  • Rational
  • Non-real
  • Imaginary
$$\frac { { z }_{ 2 }-{ 2z }_{ 2 } }{ { z }_{ 2 }-{ z }_{ 1 }{ z }_{ 2 } } $$ is unimodular then
  • $$|{ z }_{ 2 }|=2$$
  • $$|{ z }_{ 1 }|=1$$
  • Both A and B
  • None of these
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 :
  • $${ -2sin }^{ 2 }\dfrac { \theta }{ 2 } $$
  • $${ 2sin }^{ 2 }\dfrac { \theta }{ 2 } $$
  • $$1+cos\dfrac { \theta }{ 2 } $$
  • $$1-cos\dfrac { \theta }{ 2 } $$
This equation $$(x-5)^{11}+(x-5^{2})^{11}+....+(x-5^{11})^{11}=0$$ has 
  • all the roots real
  • one real and 10 imaginary roots
  • real roots namely $$x=5,5^{2}....,5^{9},5^{10},5^{11}$$
  • none
If z= $$\dfrac { 1 }{ { \left( 2+3i \right)  }^{ 2 } } ,\quad then\left| z \right| $$=
  • $$\dfrac { 1 }{ 13 } $$
  • $$\dfrac { 1 }{ 5 } $$
  • $$\dfrac { 1 }{ 12 } $$
  • none of these
The complex number z satisfies the equation z + |z| = 2 + 8i. Then the value of |z| is
  • 15
  • 16
  • 17
  • 18
The complex number $$z$$ satisfies $$z+|z|=2+8i$$. The value of $$|z|$$ is 
  • 10
  • 13
  • 17
  • 23
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
For two unimodular complex numbers $$ z_1 $$ and $$ z_2 $$,
$$ \left[ \begin{matrix} \bar { z_{ 1 } }  & -z_{ 2 } \\ \bar { z_{ 1 } }  & z_{ 1 } \end{matrix} \right] ^{ -1 } \left[ \begin{matrix} z_1  & z_2 \\- \bar { z_{ 2 } }  & \bar{ z_1}  \end{matrix} \right] ^{ -1 } $$ is equal to 
  • $$ \begin{bmatrix} z_1 & z_2 \\ \bar {z_1} & \bar {z_2} \end{bmatrix} $$
  • $$ \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} $$
  • $$ \begin{bmatrix} \dfrac{1}{2} & 0 \\ 0 & \dfrac{1}{2} \end{bmatrix} $$
  • None of these
0:0:1


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