Loading [MathJax]/jax/output/CommonHTML/jax.js
MCQExams
0:0:2
CBSE
JEE
NTSE
NEET
Practice
Homework
×
CBSE Questions for Class 11 Engineering Maths Complex Numbers And Quadratic Equations Quiz 12 - MCQExams.com
CBSE
Class 11 Engineering Maths
Complex Numbers And Quadratic Equations
Quiz 12
If
z
=
√
3
+
i
√
3
−
i
, then the fundamental amplitude of z is
Report Question
0%
−
π
3
0%
π
3
0%
π
6
0%
None of these
What will be quadratic equation in x when the roots have arithmetic mean A and the geometric mean G?
Report Question
0%
x
2
+
2
A
x
+
G
2
=
0
0%
x
2
+
G
2
x
+
A
=
0
0%
x
2
+
2
A
x
+
G
2
=
0
0%
x
2
+
G
x
+
A
=
0
Arg
{
s
i
n
8
π
5
+
i
(
1
+
c
o
s
8
π
5
)
}
is equal to
Report Question
0%
−
3
π
10
0%
3
π
10
0%
4
π
5
0%
3
π
5
Argument of the complex number
(
−
1
−
3
i
2
+
i
)
Report Question
0%
45
0
0%
135
0
0%
225
0
0%
240
0
In which quadrant of the complex , the point
1
+
2
i
1
−
i
kies?
Report Question
0%
Fourth
0%
First
0%
Second
0%
Third
The amplitude of
sin
π
5
+
i
(
1
−
c
o
s
π
5
)
is
Report Question
0%
2
π
5
0%
π
15
0%
π
10
0%
π
5
Principal value of amplitude of (1+i) is
Report Question
0%
π
4
0%
π
12
0%
3
π
4
0%
π
Out of the following the solution of the____________quadratic equation is position and rational.
Report Question
0%
6
x
2
+
5
x
+
6
=
0
0%
6
x
2
−
13
x
+
6
=
0
0%
12
x
2
+
7
x
−
12
=
0
0%
2
x
2
+
x
−
3
=
0
If
a
+
b
+
c
=
0
then the equation
3
a
x
2
+
2
b
x
+
c
=
0
has
Report Question
0%
imaginary roots
0%
real and equal root
0%
real and different roots
0%
rational roots
The principal amplitude of (
s
i
n
40
o
+
i
c
o
s
40
o
)
5
is
Report Question
0%
70
o
0%
−
110
o
0%
110
o
0%
−
70
o
The modulus of the complex number z such that
|
z
+
3
−
i
|
=
1
and arg
z
=
π
is equal to
Report Question
0%
1
0%
2
0%
9
0%
4
0%
3
If z is a complex number of unit modules and argument
θ
, then the real part of
z
(
1
−
ˉ
z
)
z
(
1
+
z
)
is :
Report Question
0%
−
2
s
i
n
2
θ
2
0%
2
s
i
n
2
θ
2
0%
1
+
c
o
s
θ
2
0%
1
−
c
o
s
θ
2
The amplitude of
(
1
+
i
√
3
)
√
3
+
i
is
Report Question
0%
π
3
0%
π
6
0%
π
4
0%
2
π
3
The nature of the roots of the quadratic equation $$2x^2
4x + 3 = 0$$ are
Report Question
0%
real and distinct
0%
real and equal
0%
no real roots
0%
imaginary
Explanation
Given quadratic equation is,
2
x
2
+
4
x
+
3
=
0
∴
a
=
2
,
b
=
4
,
c
=
3
Thus, discriminant of this equation is given by,
D
=
b
2
−
4
a
c
∴
D
=
(
4
)
2
−
4
(
2
)
(
3
)
∴
D
=
16
−
24
∴
D
=
−
8
<
0
Thus, roots of the equation are imaginary
If
z
1
,
z
2
,
z
3
,
z
4
be the vertices of a square in Argand plane , then
Report Question
0%
`
2
z
2
=
(
1
−
i
)
z
1
+
(
1
+
i
)
z
3
0%
2
z
4
=
(
2
−
i
)
z
1
+
(
2
+
i
)
z
3
0%
2
z
2
=
(
3
−
i
)
z
1
+
(
3
+
i
)
z
3
0%
2
z
4
=
(
4
−
i
)
z
1
+
(
4
+
i
)
z
3
The complex numbers
z
1
,
z
2
,
z
2
satisfying
z
1
+
z
3
z
2
−
z
3
=
1
−
i
√
3
2
Report Question
0%
If area zero
0%
right angled isosceles
0%
equilateral
0%
obtuse angled
If
z
(
2
−
2
i
√
3
)
2
=
i
(
√
3
+
i
)
4
, then the amplitude of
z
is
Report Question
0%
π
6
0%
5
π
6
0%
−
π
6
0%
7
π
6
If
z
1
=
1
+
2
i
,
z
2
=
1
−
3
i
and
z
3
=
2
+
4
i
then, the points of the Argand diagram representing
z
1
z
2
z
3
,
2
z
1
z
2
z
3
,
−
7
z
1
z
2
z
3
are :
Report Question
0%
Vertices of an isosceles triangle
0%
Collinear
0%
Vertices of a right angled triangle
0%
Vertices of a equilateral triangle
Explanation
∴
z
′
1
=
z
1
z
2
z
3
=
(
1
+
2
i
)
(
1
−
3
i
)
(
2
+
4
i
)
⇒
2
(
1
−
3
i
+
2
i
−
6
i
2
)
(
1
+
2
i
)
⇒
2
(
1
−
i
+
6
)
(
1
+
2
i
)
(
∴
i
2
=
−
1
)
⇒
2
(
7
−
i
)
(
1
+
2
i
)
⇒
2
(
7
+
14
i
−
i
−
2
i
2
)
=
2
(
7
+
13
i
+
2
)
=
2
(
9
+
13
i
)
Therefore,
z
′
1
=
(
18
+
26
i
)
,
z
′
2
=
(
36
+
52
i
)
,
z
′
3
=
(
−
126
−
182
i
)
z
′
1
=
z
1
z
2
z
3
=
18
+
26
i
z
′
2
=
2
z
1
z
2
z
3
=
2
z
′
1
z
′
3
=
−
7
z
′
1
z
′
2
z
′
3
=
−
7
z
′
1
∴
z
1
z
2
z
3
,
2
z
1
z
2
z
3
,
−
7
z
′
1
z
′
2
z
′
3
are collinear
The roots of
(
x
−
41
)
49
+
(
x
−
49
)
41
+
(
x
−
2009
)
2009
=
0
are
Report Question
0%
all necessarily real
0%
non - real except one positive root
0%
nor - real except positive roots
0%
nonr real except for 3 roots of which exactly one is positive
The complex number
z
satisfies
z
+
|
z
|
=
2
+
8
i
. The value of
|
z
|
is
Report Question
0%
10
0%
13
0%
17
0%
23
0:0:2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0
Answered
1
Not Answered
19
Not Visited
Correct : 0
Incorrect : 0
Report Question
×
What's an issue?
Question is wrong
Answer is wrong
Other Reason
Want to elaborate a bit more? (optional)
Practice Class 11 Engineering Maths Quiz Questions and Answers
<
>
Support mcqexams.com by disabling your adblocker.
×
Please disable the adBlock and continue.
Thank you.
Reload page