MCQ Questions for Class 11 Engineering Maths Complex Numbers And Quadratic Equations Quiz 12

$z=\dfrac { \sqrt { 3 } +i }{ \sqrt { 3 } -i }$ , then the fundamental amplitude of z is

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$-\dfrac { \pi }{ 3 }$
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$\dfrac { \pi }{ 3 }$
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$\dfrac { \pi }{ 6 }$
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None of these

What will be quadratic equation in x when the roots have arithmetic mean A and the geometric mean G?

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${ x }^{ 2 }+2Ax+{ G }^{ 2 }=0$
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${ x }^{ 2 }+{ G }^{ 2 }x+A=0$
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${ x }^{ 2 }+2Ax+{ G }^{ 2 }=0$
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${ x }^{ 2 }+Gx+A=0$

Arg

$\left\{ sin\dfrac { 8\pi }{ 5 } +i\left( 1+cos\dfrac { 8\pi }{ 5 } \right) \right\}$ is equal to

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$\quad -\frac { 3\pi }{ 10 }$
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$\quad \frac { 3\pi }{ 10 }$
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$\quad \frac { 4\pi }{ 5 }$
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$\quad \frac { 3\pi }{ 5 }$

Argument of the complex number

$\left( \dfrac { -1-3i }{ 2+i } \right)$

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${ 45 }^{ 0 }$
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$135^{ 0 }$
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$225^{ 0 }$
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$240^{ 0 }$

In which quadrant of the complex , the point

$\dfrac { 1+2i }{ 1-i }$ kies?

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Fourth
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First
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Second
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Third

The amplitude of

$\sin \dfrac { \pi }{ 5 } +i\left( 1-cos\dfrac { \pi }{ 5 } \right)$ is

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$\dfrac { 2\pi }{ 5 }$
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$\dfrac { \pi }{ 15 }$
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$\dfrac { \pi }{ 10 }$
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$\dfrac { \pi }{ 5 }$

Principal value of amplitude of (1+i) is

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$\dfrac { \pi }{ 4 }$
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$\dfrac { \pi }{ 12 }$
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$\dfrac { 3\pi }{ 4 }$
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$\pi$

Out of the following the solution of the____________quadratic equation is position and rational.

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$6{x^2} + 5x + 6 = 0$
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$6{x^2} - 13x + 6 = 0$
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$12{x^2} + 7x - 12 = 0$
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$2{x^2} + x - 3 = 0$

$a+b+c=0$ then the equation

$3{ ax }^{ 2 }+2bx+c=0$ has

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imaginary roots
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real and equal root
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real and different roots
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rational roots

The principal amplitude of (

$sin40^o + i cos40^o)^5$ is

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$70^o$
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$-110^o$
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$110^o$
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$-70^o$

The modulus of the complex number z such that

$\left | z+3-i \right |=1$ and arg

$z=\pi$ is equal to

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1
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2
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9
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4
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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 :

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${ -2sin }^{ 2 }\dfrac { \theta }{ 2 }$
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${ 2sin }^{ 2 }\dfrac { \theta }{ 2 }$
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$1+cos\dfrac { \theta }{ 2 }$
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$1-cos\dfrac { \theta }{ 2 }$

The amplitude of

$\dfrac {(1 + i\sqrt {3})}{\sqrt {3} + i}$ is

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$\dfrac {\pi}{3}$
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$\dfrac {\pi}{6}$
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$\dfrac {\pi}{4}$
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$\dfrac {2\pi}{3}$

The nature of the roots of the quadratic equation $$2x^2 4x + 3 = 0$$ are

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real and distinct
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real and equal
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no real roots
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imaginary

Explanation

Given quadratic equation is,

$2{ x }^{ 2 }+4x+3=0$

$\therefore a=2,b=4,c=3$

Thus, discriminant of this equation is given by,

$D={ b }^{ 2 }-4ac$

$\therefore D={ \left( 4 \right) }^{ 2 }-4\left( 2 \right) \left( 3 \right)$

$\therefore D=16-24$

$\therefore D=-8<0$

Thus, roots of the equation are imaginary

${ z }_{ 1 },{ z }_{ 2 },{ z }_{ 3 },{ z }_{ 4 }$ be the vertices of a square in Argand plane , then

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` ${ 2z }_{ 2 }=\left( 1-i \right) { z }_{ 1 }+\left( 1+i \right) { z }_{ 3 }$
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${ 2z }_{ 4 }=\left( 2-i \right) { z }_{ 1 }+\left( 2+i \right) { z }_{ 3 }$
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${ 2z }_{ 2 }=\left( 3-i \right) { z }_{ 1 }+\left( 3+i \right) { z }_{ 3 }$
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${ 2z }_{ 4 }=\left( 4-i \right) { z }_{ 1 }+\left( 4+i \right) { z }_{ 3 }$

The complex numbers

${ z }_{ 1 },{ z }_{ 2 },{ z }_{ 2 }$ satisfying

$\dfrac { { z }_{ 1 }+{ z }_{ 3 } }{ { z }_{ 2 }-{ z }_{ 3 } } =\dfrac { 1-i\sqrt { 3 } }{ 2 }$

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If area zero
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right angled isosceles
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equilateral
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obtuse angled

$z(2 - 2i\sqrt {3})^{2} = i(\sqrt {3} + i)^{4}$ , then the amplitude of

$z$ is

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$\dfrac {\pi}{6}$
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$\dfrac {5\pi}{6}$
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$-\dfrac {\pi}{6}$
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$\dfrac {7\pi}{6}$

$z_{1}=1+2i,z_{2}=1-3i$ 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 :

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Vertices of an isosceles triangle
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Collinear
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Vertices of a right angled triangle
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Vertices of a equilateral triangle

Explanation

$\therefore z'_1=z_1z_2z_3=(1+2i)(1-3i)(2+4i)$

$\Rightarrow 2(1-3i+2i-6i^2)(1+2i)$

$\Rightarrow 2(1-i+6)(1+2i)$

$(\therefore i^2=-1)$

$\Rightarrow 2(7-i)(1+2i)\Rightarrow 2(7+14i-i-2i^2)=2(7+13i+2)=2(9+13i)$

Therefore,

$z'_1=(18+26i),\,z'_2=(36+52i),\,z'_3=(-126-182i)$

$z'_1=z_1z_2z_3=18+26i$

$z'_2=2z_1z_2z_3=2z'_1$

$z'_3=-7z'_1z'_2z'_3=-7z'_1$

$\therefore \,z_1z_2z_3,\,2z_1z_2z_3,\,-7z'_1z'_2z'_3$ are collinear

The roots of

$(x-41)^{49}+(x-49)^{41}+(x-2009)^{2009}=0$ are

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all necessarily real
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non - real except one positive root
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nor - real except positive roots
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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

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10
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13
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17
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23

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

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Practice Class 11 Engineering Maths Quiz Questions and Answers

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

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Practice Class 11 Engineering Maths Quiz Questions and Answers

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