Questions

M.C.Q (1 Marks)

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19 questions · timed · auto-graded

MCQ 11 Mark
Statement $(a+i b)<(c+i d)$ is true for which of the followings :
  • A
    $a^2+b^2=0$
  • B
    $b^2+c^2=0$
  • C
    $a^2+c^2=0$
  • $b^2+d^2=0$
Answer
Correct option: D.
$b^2+d^2=0$
(D)
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MCQ 21 Mark
$\left(\frac{1+i}{\sqrt{2}}\right)^8+\left(\frac{1-i}{\sqrt{2}}\right)^8$ is equal to:
  • A
    $2 i$
  • B
    $-2 i$
  • $2$
  • D
    $-2$
Answer
Correct option: C.
$2$
(C )
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MCQ 31 Mark
A complex number is pure imaginary if:
  • A
    its imaginary part is zero
  • B
    its both real and imaginary parts are zero
  • its both parts are zero
  • D
    None of the above
Answer
Correct option: C.
its both parts are zero
(C )
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MCQ 41 Mark
If $(3,4),(2,5)$ and $(-9,16)$ are there complex numbers then:
  • A
    these are the vertices of right angled triangle
  • B
    these are the vertices of equilateral triangle
  • C
    these are the vertices of isosceles triangle
  • these are collinear
Answer
Correct option: D.
these are collinear
(D)
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MCQ 51 Mark
Let $z$ be a complex number, then $z+\bar{z}$ and $z \bar{z}$ are :
  • both real
  • B
    both imaginary
  • C
    only one real
  • D
    None of these
Answer
Correct option: A.
both real
(A)
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MCQ 61 Mark
Let $z$ be a complex number then $z+\bar{z}$ is :
  • pure real
  • B
    pure imaginary
  • C
    not decided
  • D
    None of these
Answer
Correct option: A.
pure real
(A)
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MCQ 71 Mark
If $z=\left(\frac{1}{2}, 1\right)$, then $z^{-1}$ is equal to :
  • A
    $\left(-\frac{2}{5}, \frac{4}{5}\right)$
  • B
    $\left(\frac{1}{5}, \frac{2}{5}\right)$
  • C
    $\left(\frac{1}{5},-\frac{2}{5}\right)$
  • $\left(\frac{2}{5},-\frac{4}{5}\right)$
Answer
Correct option: D.
$\left(\frac{2}{5},-\frac{4}{5}\right)$
(D)
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MCQ 81 Mark
If $(x-i y)(1-i)=1+5 i$ then:
  • A
    $x=-2, y=3$
  • B
    $x=2, y=-3$
  • $x=-2, y=-3$
  • D
    $x=2, y=3$
Answer
Correct option: C.
$x=-2, y=-3$
(C )
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MCQ 101 Mark
If $(x+i y)(2-3 i)=4+i$ then $x+i y$ is equal to :
  • A
    $\frac{14}{13}+i \frac{5}{13}$
  • $\frac{5}{13}+i \frac{14}{13}$
  • C
    $\frac{-14}{13}+i \frac{5}{13}$
  • D
    $\frac{5}{13}-i \frac{14}{13}$
Answer
Correct option: B.
$\frac{5}{13}+i \frac{14}{13}$
(B)
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MCQ 121 Mark
If $\left(\frac{1+i}{1-i}\right)^n=1$ then the minimum value of integer $n$ is:
  • A
    2
  • 4
  • C
    6
  • D
    8
Answer
Correct option: B.
4
(B)
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MCQ 131 Mark
The pure real complex number lies :
  • at $x$-axis
  • B
    at $y$-axis
  • C
    at any axis
  • D
    None of these
Answer
Correct option: A.
at $x$-axis
(A)
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MCQ 141 Mark
The conjugate of $\frac{3+2 i}{5-3 i}$ :
  • A
    $\frac{1}{34}(19 i-9)$
  • $\frac{1}{34}(9-19 i)$
  • C
    $\frac{-1}{34}(9+19 i)$
  • D
    $\frac{1}{34}(9+19 i)$
Answer
Correct option: B.
$\frac{1}{34}(9-19 i)$
(B)
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MCQ 151 Mark
If $2+(2 a+5 i b)=8+10 i$, then :
  • A
    $a=2, b=3$
  • $a=3, b=2$
  • C
    $a=2, b=2$
  • D
    $a=3, b=3$
Answer
Correct option: B.
$a=3, b=2$
(B)
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MCQ 161 Mark
The real and imaginary parts of $\frac{5(-8+16 i)}{(1+i)^2}$ :
  • $40,20$
  • B
    $-40,-20$
  • C
    $20, 40$
  • D
    $-20,-40$
Answer
Correct option: A.
$40,20$
(A)
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MCQ 171 Mark
If $z=x+i y$ and $\left|\frac{z-5 i}{z+5 i}\right|=1$ then $z$ lies :
  • at $x-$ axis
  • B
    at $y -$ axis
  • C
    at line $y=5$
  • D
    None of these
Answer
Correct option: A.
at $x-$ axis
(A)
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MCQ 181 Mark
If $z_1, z_2 \in C$ then which is true statement:
  • A
    $\left|z_1-z_2\right|=\left|z_1\right|+\left|z_2\right|$
  • B
    $\left|z_1-z_2\right|>\left|z_1\right|+\left|z_2\right|$
  • $\left|z_1+z_2\right| \leq\left|z_1\right|+\left|z_2\right|$
  • D
    $\left|z_1+z_2\right|=\left|z_1-z_2\right|$
Answer
Correct option: C.
$\left|z_1+z_2\right| \leq\left|z_1\right|+\left|z_2\right|$
(C )
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MCQ 191 Mark
If $\left[\frac{1-i}{1+i}\right]^{100}=a+i b$, then :
  • A
    $a=2, b=-1$
  • B
    $a=1, b=0$
  • $a=0, b=1$
  • D
    $a=-1, b=2$
Answer
Correct option: C.
$a=0, b=1$
(C )
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