====== MCQs: Ch 01 Number Systems ======
High quality MCQs of Chapter 01 Number System of Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. The answers are given at the end of the page.

====MCQs====
  - 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

====Answers====
1-b, 2-b, 3-d, 4-a, 5-b, 6-b, 7-c, 8-c, 9-a, 10-d, 11-a, 12-a, 13-d, 14-c, 15-a, 16-c, 17-d, 18-b, 19-d, 20-d, 21-b, 22-b, 23-c, 24-c, 25-c, 26-b, 27-c, 28-d, 29-b, 30-d, 31-c, 32-b, 33-d, 34-a, 35-c, 36-c, 37-c, 38-d, 39-a, 40-d, 41-b, 42-d, 43-c, 44-d, 45-c, 46-b, 47-b, 48-c, 49-b, 50-c, 51-c, 52-c, 53-b, 54-a, 55-b, 56-c, 57-c, 58-a, 59-b, 60-c, 61-c, 62-c, 63-b, 64-b, 65-a, 66-c