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Published on: 21/10/2025
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Questions + Answers key
Take MCQ Mathematics Test
1.
Number of solutions of the equation Z2 + |Z|2= 0 and Z \(\ne\) 0 _______.
1
2
3
infinite many
2.
A polynomial equation has _______.
atleast two roots
atleast one root
atmost three roots
atmost two roots
3.
If Z \(\ne\) 0 is a complex number, then _______.
Re(z) = 0 \(\Rightarrow\) Im (Z2) = 0
Re(z2) = 0 \(\Rightarrow\)Im (Z2) = 0
Re(z) = 0 \(\Rightarrow\) Re(z2) = 0
None of the above
4.
If x2 + 1= 0, then solution is _______.
i,-i
1,-i
-1, i
None of these
5.
If Z = i9 +i19, then Z is equal to _______.
0 + 0i
1+ 0i
0 + i
1+ 2i
6.
\(\text { If } z=5 i\left(-\frac{3}{5} i\right), \text { then } z \text { is equal to }\) _______.
0 + 3i
3 + 0i
0-3i
-3+0i
7.
If Z1 = 2 + 3 i and Z2 = = 3 - 2 i, then Z1 - Z2 is equal to _______.
-1 + 5 i
5 - i
i + 5
None of these
8.
If z + 0 = z, where Z = x + i y and 0 = 0 + i 0, then 0 is called _______.
additive identity
additive inverse
closure
None of these
9.
Which of the following is true?
1- i <1+ i
2i + 1>- 2i + 1 .
2i > 1
None of these
10.
\(\text { If } x=\sqrt{-16}, \text { then }\)_______.
x = 4i
x = 4
x = -4
All of these
11.
If difference in roots of the equation x2 - px +8 = 0 is 2, thenp is equal to _______.
±6
±2
±1
±5
12.
If \(\sqrt{5} x^{2}+x+\sqrt{5}=0\) then which of the following is/are correct?
I. Discriminant, D = -19.
\(\text { II. } x=\frac{-1 \pm \sqrt{19} i}{2 \sqrt{5}} \text { . }\)
Only I is correct
Only II is correct
Both are correct
Both are incorrect
13.
If x2 + x + 1= 0, then which of the following are correct?
\(x=\frac{-1+\sqrt{3} i}{2}\)
\(x=\frac{-i-\sqrt{3}}{2}\)
\(x=\frac{1+\sqrt{3} i}{2}\)
\(x=\frac{1-\sqrt{3} i}{2}\)
14.
Roots of x2 + 2 = 0 are _______.
\(\pm \sqrt{2} i\)
2
2i
None of these
15.
If P(x) is a n degree polynomial, then number of roots are _______.
1
2
3
n
16.
The value of arg (x), when x < 0 is _______.
0
\(\frac{\pi}{2}\)
\(\pi\)
None of these
17.
The geometrical representation of complex number \(z=\frac{-16}{1+i \sqrt{3}}, \text { is }\) _______.
18.
Polar form of the complex number z = 1+ i\(\sqrt{3}\), is _______.
\(2\left(\cos \frac{\pi}{3}-i \sin \frac{\pi}{3}\right)\)
\(2\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right)\)
\(2\left(\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}\right)\)
\(2\left(\cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}\right)\)
19.
Representation of z = x + iy in terms of rand e is called _______.
polar form of the complex number
cartesian form of the complex number
complex form of the complex number
real form of the complex number
20.
The value of (z + 3) (\(\bar{z}\) + 3) is equivalent to _______.
\(|z+3|^{2}\)
\(|z-3|\)
\(z^{2}+3\)
None of these
21.
\(\text { If }|1-i|^{n}=2^{n}, \text { then } n \text { is equal to }\)_______.
1
0
-1
None of these
22.
Which of the following are correct?
\(\text { I. }|3+i|=\sqrt{10} ;|2-5 i|=\sqrt{29}\)
\(\text { II. }(\overline{3+i})=3-i ;(\overline{2-5 i})=2+5 i \text { and }(-\overline{3 i-5})=3 i-5\)
\(\text { III. } z^{-1}=\frac{\bar{z}}{|z|^{2}} \text { or } Z \bar{z}=|z|^{2}, z \neq 0\)
I and III are correct
I and II are correct
All are correct
None of these
23.
The conjugate of a complex number z = a + ib, is _______.
\(\bar{z}=a+i b\)
\(\bar{z}=a-i b\)
\( \bar{z}=i a+b\)
\(\bar{z}=i a-b\)
24.
\(\text { If }(x-i y)^{1 / 3}=a+i b, \text { where } x, y, a, b \in R \text { then the }\)\(\text { value of } \frac{x}{a}+\frac{y}{b} \text { is equal to }\)_______.
\(4\left(a^{2}-b^{2}\right)\)
\(4\left(a^{2}+b^{2}\right)\)
\(2\left(a^{2}-b^{2}\right)\)
\(2\left(a^{2}+b^{2}\right)\)
25.
If z = i39, then simplest form of z is equal to _______.
1+ 0i
0+ i
0+ 0i
1+ i
26.
\(\text { If } z_{1}=6+3 i \text { and } z_{2}=2-i, \text { then } \frac{z_{1}}{z_{2}} \text { is equal to }\) _______.
\(\frac{1}{5}(9+12 i)\)
\(9+12 i\)
\(3+2 i\)
\(\frac{1}{5}(12+9 i)\)
27.
If z is non-zero complex number and z = a + ib, then inverse of z is _______.
\(\frac{a}{a^{2}+b^{2}}+\frac{-b i}{a^{2}+b^{2}}\)
\(\frac{a}{a^{2}-b^{2}}+\frac{-b i}{a^{2}-b^{2}}\)
\(\frac{a}{a^{2}-b^{2}}+\frac{i b}{a^{2}-b^{2}}\)
\(\frac{-a}{a^{2}+b^{2}}+\frac{-b i}{a^{2}+b^{2}}\)
28.
If Z is a complex number and z + (-z) = 0, then _______.
(-z) is called additive inverse of z
-z is additive identity of z
= z is closure of z
-z is commutative of z
29.
If x, y\(\in\) R, then x + iy is a non-real complex number, if _______.
x = 0
y = 0
x \(\ne\) 0
y \(\ne\) 0
30.
Which of the following represent correct form of set of complex numbers?
\(C=\{x+i y: x \in R, y \in R \text { and } i=\sqrt{-1}\}\)
\(C=\{x+i y: x \in R, y \in I\}\)
\(C=\{x+i y: x \in I, y \in I\}\)
All of these
31.
Two complex numbers are equal, if and only if _____.
their real and imaginary parts are separately equal
their real parts are only equal
their imaginary parts are only equal
None of the above
32.
Which of the following options define 'imaginary number'?
Square root of any number
Square root of positive number
Square root of negative number
Cube root of number
33.
The length of the latusrectum of the parabola 9x2 - 6x + 36y + 19= 0, is ______.
36
9
6
4
34.
Vertex of the parabola 9x2 - 6x + 36y + 9 = 0, is ______.
\(\left(\frac{1}{3},-\frac{2}{9}\right)\)
\(\left(-\frac{1}{3},-\frac{1}{2}\right) \)
\(\left(-\frac{1}{3}, \frac{1}{2}\right)\)
\(\left(\frac{1}{3}, \frac{1}{2}\right)\)
35.
The area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latusrectum is _______.
12 sq units
16 sq units
18 sq units
24 sq units
36.
When the axis of symmetry is along the X-axis the parabola opens to the _______.
right, if the coefficient of x is positive
left, if the coefficient of x is negative
Both (a) and (b)
Neither (a) nor (b)
37.
The eccentricity of parabola is always _______.
0
1
<1
>1
38.
The number of possible orientations of parabola is _______.
1
2
3
4
39.
The equation of a parabola is simplest, if the vertex is at the ...A...and the axis of symmetry is along the ...B.... Here, Aand Brespectively are _______.
origin, X-axis
origin, Y-axis
Both (a) and (b)
None of these
40.
In the parabola y2 = 4ax,the length of the chord passing through the vertex and inclined to the axis at π/4 is ________.
\(4\sqrt { 2 } a\)
\(3\sqrt { 2 } a\)
\(2\sqrt { 2 } a\)
\(\sqrt { 2 } a\)
1.
(d)
infinite many
2.
(b)
atleast one root
3.
(a)
Re(z) = 0 \(\Rightarrow\) Im (Z2) = 0
4.
(a)
i,-i
5.
(a)
0 + 0i
6.
(b)
3 + 0i
7.
(a)
-1 + 5 i
8.
(a)
additive identity
9.
(d)
None of these
10.
(a)
x = 4i
11.
(a)
±6
12.
(c)
Both are correct
13.
(a)
\(x=\frac{-1+\sqrt{3} i}{2}\)
14.
(a)
\(\pm \sqrt{2} i\)
15.
(d)
n
16.
(c)
\(\pi\)
17.
(b)
18.
(b)
\(2\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right)\)
19.
(a)
polar form of the complex number
20.
(a)
\(|z+3|^{2}\)
21.
(b)
0
22.
(c)
All are correct
23.
(b)
\(\bar{z}=a-i b\)
24.
(a)
\(4\left(a^{2}-b^{2}\right)\)
25.
(b)
0+ i
26.
(a)
\(\frac{1}{5}(9+12 i)\)
27.
(a)
\(\frac{a}{a^{2}+b^{2}}+\frac{-b i}{a^{2}+b^{2}}\)
28.
(a)
(-z) is called additive inverse of z
29.
(d)
y \(\ne\) 0
30.
(a)
\(C=\{x+i y: x \in R, y \in R \text { and } i=\sqrt{-1}\}\)
31.
(a)
their real and imaginary parts are separately equal
32.
(c)
Square root of negative number
33.
(d)
4
34.
(a)
\(\left(\frac{1}{3},-\frac{2}{9}\right)\)
35.
(c)
18 sq units
36.
(c)
Both (a) and (b)
37.
(b)
1
38.
(d)
4
39.
(c)
Both (a) and (b)
40.
(a)
\(4\sqrt { 2 } a\)
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