If $*$ is a binary operation in a set $A$, then for all $a, b \in A$
$a+b \in A$
$a-b \in A$
$a \times b \in A$
$a * b \in A$
If $z=(1,3)$ then $z^{-1}= $
$(\displaystyle{\frac{1}{10}},\displaystyle{\frac{3}{10}})$
$(-\displaystyle{\frac{1}{10}},\displaystyle{\frac{3}{10}})$
$(\displaystyle{\frac{1}{10}},-\displaystyle{\frac{3}{10}})$
$(-\displaystyle{\frac{1}{10}},-\displaystyle{\frac{3}{10}})$
$\displaystyle{\frac{3}{2+2i}}=$
$1-i$
$1+i$
$-2i$
$\displaystyle{\frac{3-3i}{4}}$
$\overline{z_1+z_2}=$
$\overline{z_1}+\overline{z_2}$
$\overline{z_1}-\overline{z_2}$
$\overline{z_1}+z_2$
$z_1+\overline{z_2}$
$|z_1+z_2|$
$>|z_1|+|z_2|$
$\leq|z_1|+|z_2|$
$\leq z_1+z_2$
$>z_1+z_2$
If $z_1=2+i$, $z_2=1+3i$, then $z_1-z_2=$
$1-7i$
$-1+7i$
$1-2i$
$3+4i$
If $z_1=2+i$, $z_2=1+3i$, then $-i lm (z_1-z_2)=$
$2i$
$-2i$
$2$
$3$
Which of the following sets has closure property with respect to multiplication?
$\{-1,1\}$
$\{-1\}$
$\{-1,0\}$
$\{0,2\}$
The multiplicative inverse of $2$ is
$0$
$1$
$-2$
$\displaystyle{\frac{1}{2}}$
$\displaystyle{\frac{4}{2-2i}}=$
$1-i$
$1+i$
$-2i$
$i$
The simplified form of $i^{101}$ is
$-1$
$1$
$i$
$-i$
$\overline{\overline{z}}=$ is
$\overline{z}$
$-\overline{z}$
$z$
$-z$
If $z_1=2+i$, $z_2=1+3i$, then $i \Re (z_1-z_2)=$
$1$
$i$
$-2i$
$2$
$\sqrt{2}$ is ——- number.
natural
complex
irrational
$\displaystyle{\frac{p}{q}}$ form
A rational number is a number which can be expressed in the form ——-
$\displaystyle{\frac{p}{q}}$ where $p,q \in z \wedge q \neq 0$
$\displaystyle{\frac{q}{p}}$ where $p,q \in z \wedge q \neq 0$
$\displaystyle{\frac{p}{q}}$ where $p,q \in Z \wedge q = 0$
$\displaystyle{\frac{q}{p}}$ where $p,q \in N \wedge q \neq 0$
$\mathbb{R}=$
$\mathbb{Q} \cup \mathbb{N}'$
$\mathbb{Q}$
$\mathbb{Q} \cup \mathbb{Q}'$
$\mathbb{Q}$
$\{1,2,3,...\}$
set of irrational number
set of real number
set of rational number
set of natural number
The set of integers is —–
$\{\pm1,\pm2,\pm3,...\}$
$\{0,\pm1,\pm2,\pm3,...\}$
$\{+1,+2,+3,...\}$
$\{-1,+1,-2,+2\}$
$0.333...=(\approx \displaystyle{\frac{1}{3}})$ is a ——– decimal.
Terminating
non-recurring
recurring
non-terminating and recurring
$2.\overline{3}(=2.333...)$ is a —– number.
irrational
complex
real
rational
For all $a, b, c \in \mathbb{R}$
(i) $a>b \wedge b>c \Rightarrow a>c$
(ii) $a<b \wedge b<c \Rightarrow a<c$
is called —– property.
Translative
Transitive
Trichotomy
Trigonometric
For all $ a, b, c \in \mathbb{R}$
(i) $a>b \Rightarrow a+c>b+c$
(ii) $a<b \Rightarrow a+c<b+c$
is called —– property.
Additional
Advantage
Advance
Additive
The number of the form $x+iy$, where $x,y \in \mathbb{R}$ is called ——- number.
real
conjugate
complex
imaginative
Every real number is a complex number with $0$ as its ——— part.
conjugate
complex
imaginary
real
Every complex number $(a,b)$ has a multiplicative identity equal to ———–
$(0,1)$
$(0,0)$
$(1,0)$
$(1,1)$
Every complex number $(a,b)$ has a additive inverse equal to ———–
$(-a,0)$
$(-a,-b)$
$(o,-b)$
$(a,b)$
Every complex number $(a,b)$ has a additive identity equal to ———–
$0$
$(0,1)$
$(0,0)$
$(1,0)$
The conjugate of a complex number $(a,b)$ is equal to ———–
$(-a,-b)$
$(-a,+b)$
$(a,b)$
$(a,-b)$
The modulus of a complex number $(a,b)$ is equal to ———–
$\sqrt{a+b}$
$\sqrt{a^2+b^2}$
$\sqrt{a^3+b^3}$
$\sqrt{a^2-b^2}$
The figure representing one or more complex numbers on the complex plane is called ——– diagram.
an artistic
an organd
an imaginative
an argand
The geometrical plane on which coordinate system has been specified is called the ——– plane.
complex
complex conjugate
real
realistic
The Cartesian product $\mathbb{R} \times \mathbb{R}$ where $\mathbb{R}$ is the set of real numbers is called the ——– plane.
ordered
cartesian
classical
an argand
If a point $A$ of the coordinate plane correspond to the ordered pair $(a,b)$ then $a,b$ are called the —— of $A$.
ordinates
abscissas
coefficients
coordinates
Around $``5000 $ BC'' the Egyptians had a number system based on
$5$
$50$
$10$
$100$
If $n$ is a prime number, then $\sqrt{n}$ is
complex number
rational number
irrational number
none of these
A recurring decimal represents
real number
natural number
rational number
none of these
$\pi$ is
rational number
an integer
an irrational number
natural number
$0$ is
positive number
negative number
natural number
none of these
A prime number can be a factor of a square only if it occurs in the square at least
twice
once
thrice
none of these
$\sqrt{-1}$ is
real number
natural number
rational number
imaginary number
The multiplicative inverse of a complex number $(a,b)$ is
$(\displaystyle{\frac{a}{a^2+b^2}},\displaystyle{\frac{b}{a^2+b^2}})$
$(\displaystyle{\frac{a}{a^2+b^2}},-\displaystyle{\frac{b}{a^2+b^2}})$
$(-\displaystyle{\frac{a}{a^2+b^2}},\displaystyle{\frac{b}{a^2+b^2}})$
$(-\displaystyle{\frac{a}{a^2+b^2}},-\displaystyle{\frac{b}{a^2+b^2}})$
Every real number is a
rational number
natural number
prime number
complex number
The Cartesian product of two non-empty sets $A$ and $B$ denoted by
$AB$
$BA$
$A \times B$
none of these
Conjugate of complex number $x+iy$ is
$-x+iy$
$-x-iy$
$x+y$
$x-iy$
Polar form of a complex number $x+iy$ is ……, where $r=|z|$ and $\theta = arg z$
$\cos \theta+i \sin \theta$
$r \cos \theta-ir \sin \theta$
$r \cos \theta+ir \sin \theta$
none of these
If $z=x+iy$ then $|\overline{z}|$ is
$\sqrt{x^2-y^2}$
$\sqrt{x^2+y^2}$
$\sqrt{2xy}$
none of these
If $-x-iy$ is a complex number then modulus of a complex number is
$\sqrt{x^2-y^2}$
$\sqrt{x^2+y^2}$
$\sqrt{2xy}$
none of these
If $z_1$ and $z_2$ are two complex numbers then $\overline{z_1+z_2}$ is
$z_1+z_2$
$\overline{z_1}-\overline{z_2}$
$\overline{z_1}+\overline{z_2}$
none of these
If $z_1$ and $z_2$ are two complex numbers then $\overline{z_1-z_2}$ is
$z_1+z_2$
$\overline{z_1}-\overline{z_2}$
$\overline{z_1}+\overline{z_2}$
none of these
If $z_1$ and $z_2$ are two complex numbers then $\overline{z_1z_2}$ is
$z_1z_2$
$\displaystyle{\frac{z_1}{z_2}}$
$\overline{z_1}\times \overline{z_2}$
none of these
If $z_1$ and $z_2$ are two complex numbers then $\overline{\displaystyle{\frac{z_1}{z_2}}}$ is
$\displaystyle{\frac{z_1}{z_2}}$
$z_1z_2$
$\displaystyle{\overline{z_2}}$
none of these
If $z_1$ and $z_2$ are two complex numbers then $|z_1z_2|$ is
$z_1z_2$
$\displaystyle{\frac{|z_1|}{|z_2|}}$
$|z_1||z_2|$
none of these
If $z$ and $\overline{z}$ is a conjugate then $|z \overline{z}|$ is equal to
$|z||\overline{z}|$
$|z|^2$
$\displaystyle{\frac{|z|}{\overline{|z|}}}$
none of these
If $z-3-5i$ then $z^{-1}$ ———-
$-\displaystyle{\frac{3}{34}}+\displaystyle{\frac{5}{34}i}$
$\displaystyle{\frac{3}{34}}-\displaystyle{\frac{5}{34}i}$
$\displaystyle{\frac{3}{34}}+\displaystyle{\frac{5}{34}i}$
none of these
If $(x+iy)^2=-----$
$x^2+y^2+2xyi$
$x^2-y^2-2xyi$
$x^2-y^2+2xyi$
none of these
If $(x-iy)^2=-----$
$x^2+y^2+2xyi$
$x^2-y^2-2xyi$
$x^2+y^2-2xyi$
none of these
If $z^2+\overline{z}^2$ is a
Complex number
Real number
Both A and B
None of these
If $(z-\overline{z})^2$ is a
Real number
Complex number
Both A and B
None of these
If $(z+\overline{z})^2$ is a
Complex number
Real number
Both A and B
None of these
$i$ can be written in th form of an ordered pair as
$(1,0)$
$(1,1)$
$(0,1)$
None of these
If $z=3-4i$ then $|\overline{z}|$ is
$4$
$3$
$5$
None of these
For all $\ a, b, c \in R$, $a=b \wedge b=c\Rightarrow a=c$ is called
Reflexive property
Symmetric property
Transitive property
None of these
For all $ a, b, c \in R$, $a+c=b+c \Rightarrow a=b$ is called
Additive property
Cancellation property w.r.t addition
Cancellation property w.r.t multiplication
None of these
For all $a, b, c \in R$, $ac=bc \Rightarrow a=b,c \neq 0$ is called
Cancellation property w.r.t addition
Cancellation property w.r.t multiplication
Symmetric property
None of these
$-(-a)$ should be read as
Negative of negative
Minus minus a
Both A and B
None of these
If a point $A$ of the coordinate plane correspond to the order pair $(a,b)$ then $b$ is called
Abscissa
x-coordinate
Ordinate
None of these