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

  1. If $*$ is a binary operation in a set $A$, then for all $a, b \in A$
    1. $a+b \in A$
    2. $a-b \in A$
    3. $a \times b \in A$
    4. $a * b \in A$
  2. If $z=(1,3)$ then $z^{-1}= $
    1. $(\displaystyle{\frac{1}{10}},\displaystyle{\frac{3}{10}})$
    2. $(-\displaystyle{\frac{1}{10}},\displaystyle{\frac{3}{10}})$
    3. $(\displaystyle{\frac{1}{10}},-\displaystyle{\frac{3}{10}})$
    4. $(-\displaystyle{\frac{1}{10}},-\displaystyle{\frac{3}{10}})$
  3. $\displaystyle{\frac{3}{2+2i}}=$
    1. $1-i$
    2. $1+i$
    3. $-2i$
    4. $\displaystyle{\frac{3-3i}{4}}$
  4. $\overline{z_1+z_2}=$
    1. $\overline{z_1}+\overline{z_2}$
    2. $\overline{z_1}-\overline{z_2}$
    3. $\overline{z_1}+z_2$
    4. $z_1+\overline{z_2}$
  5. $|z_1+z_2|$
    1. $>|z_1|+|z_2|$
    2. $\leq|z_1|+|z_2|$
    3. $\leq z_1+z_2$
    4. $>z_1+z_2$
  6. If $z_1=2+i$, $z_2=1+3i$, then $z_1-z_2=$
    1. $1-7i$
    2. $-1+7i$
    3. $1-2i$
    4. $3+4i$
  7. If $z_1=2+i$, $z_2=1+3i$, then $-i lm (z_1-z_2)=$
    1. $2i$
    2. $-2i$
    3. $2$
    4. $3$
  8. Which of the following sets has closure property with respect to multiplication?
    1. $\{-1,1\}$
    2. $\{-1\}$
    3. $\{-1,0\}$
    4. $\{0,2\}$
  9. The multiplicative inverse of $2$ is
    1. $0$
    2. $1$
    3. $-2$
    4. $\displaystyle{\frac{1}{2}}$
  10. $\displaystyle{\frac{4}{2-2i}}=$
    1. $1-i$
    2. $1+i$
    3. $-2i$
    4. $i$
  11. The simplified form of $i^{101}$ is
    1. $-1$
    2. $1$
    3. $i$
    4. $-i$
  12. $\overline{\overline{z}}=$ is
    1. $\overline{z}$
    2. $-\overline{z}$
    3. $z$
    4. $-z$
  13. If $z_1=2+i$, $z_2=1+3i$, then $i \Re (z_1-z_2)=$
    1. $1$
    2. $i$
    3. $-2i$
    4. $2$
  14. $\sqrt{2}$ is ——- number.
    1. natural
    2. complex
    3. irrational
    4. $\displaystyle{\frac{p}{q}}$ form
  15. A rational number is a number which can be expressed in the form ——-
    1. $\displaystyle{\frac{p}{q}}$ where $p,q \in z \wedge q \neq 0$
    2. $\displaystyle{\frac{q}{p}}$ where $p,q \in z \wedge q \neq 0$
    3. $\displaystyle{\frac{p}{q}}$ where $p,q \in Z \wedge q = 0$
    4. $\displaystyle{\frac{q}{p}}$ where $p,q \in N \wedge q \neq 0$
  16. $\mathbb{R}=$
    1. $\mathbb{Q} \cup \mathbb{N}'$
    2. $\mathbb{Q}$
    3. $\mathbb{Q} \cup \mathbb{Q}'$
    4. $\mathbb{Q}$
  17. $\{1,2,3,\ldots\}$
    1. set of irrational number
    2. set of real number
    3. set of rational number
    4. set of natural number
  18. The set of integers is —–
    1. $\{\pm1,\pm2,\pm3,\ldots\}$
    2. $\{0,\pm1,\pm2,\pm3,\ldots\}$
    3. $\{+1,+2,+3,\ldots\}$
    4. $\{-1,+1,-2,+2\}$
  19. $0.333\ldots=(\approx \displaystyle{\frac{1}{3}})$ is a ——– decimal.
    1. Terminating
    2. non-recurring
    3. recurring
    4. non-terminating and recurring
  20. $2.\overline{3}(=2.333\ldots)$ is a —– number.
    1. irrational
    2. complex
    3. real
    4. rational
  21. 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.
    1. Translative
    2. Transitive
    3. Trichotomy
    4. Trigonometric
  22. 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.
    1. Additional
    2. Advantage
    3. Advance
    4. Additive
  23. The number of the form $x+iy$, where $x,y \in \mathbb{R}$ is called ——- number.
    1. real
    2. conjugate
    3. complex
    4. imaginative
  24. Every real number is a complex number with $0$ as its ——— part.
    1. conjugate
    2. complex
    3. imaginary
    4. real
  25. Every complex number $(a,b)$ has a multiplicative identity equal to ———–
    1. $(0,1)$
    2. $(0,0)$
    3. $(1,0)$
    4. $(1,1)$
  26. Every complex number $(a,b)$ has a additive inverse equal to ———–
    1. $(-a,0)$
    2. $(-a,-b)$
    3. $(o,-b)$
    4. $(a,b)$
  27. Every complex number $(a,b)$ has a additive identity equal to ———–
    1. $0$
    2. $(0,1)$
    3. $(0,0)$
    4. $(1,0)$
  28. The conjugate of a complex number $(a,b)$ is equal to ———–
    1. $(-a,-b)$
    2. $(-a,+b)$
    3. $(a,b)$
    4. $(a,-b)$
  29. The modulus of a complex number $(a,b)$ is equal to ———–
    1. $\sqrt{a+b}$
    2. $\sqrt{a^2+b^2}$
    3. $\sqrt{a^3+b^3}$
    4. $\sqrt{a^2-b^2}$
  30. The figure representing one or more complex numbers on the complex plane is called ——– diagram.
    1. an artistic
    2. an organd
    3. an imaginative
    4. an argand
  31. The geometrical plane on which coordinate system has been specified is called the ——– plane.
    1. complex
    2. complex conjugate
    3. real
    4. realistic
  32. The Cartesian product $\mathbb{R} \times \mathbb{R}$ where $\mathbb{R}$ is the set of real numbers is called the ——– plane.
    1. ordered
    2. cartesian
    3. classical
    4. an argand
  33. If a point $A$ of the coordinate plane correspond to the ordered pair $(a,b)$ then $a,b$ are called the —— of $A$.
    1. ordinates
    2. abscissas
    3. coefficients
    4. coordinates
  34. Around $``5000 $ BC'' the Egyptians had a number system based on
    1. $5$
    2. $50$
    3. $10$
    4. $100$
  35. If $n$ is a prime number, then $\sqrt{n}$ is
    1. complex number
    2. rational number
    3. irrational number
    4. none of these
  36. A recurring decimal represents
    1. real number
    2. natural number
    3. rational number
    4. none of these
  37. $\pi$ is
    1. rational number
    2. an integer
    3. an irrational number
    4. natural number
  38. $0$ is
    1. positive number
    2. negative number
    3. natural number
    4. none of these
  39. A prime number can be a factor of a square only if it occurs in the square at least
    1. twice
    2. once
    3. thrice
    4. none of these
  40. $\sqrt{-1}$ is
    1. real number
    2. natural number
    3. rational number
    4. imaginary number
  41. The multiplicative inverse of a complex number $(a,b)$ is
    1. $(\displaystyle{\frac{a}{a^2+b^2}},\displaystyle{\frac{b}{a^2+b^2}})$
    2. $(\displaystyle{\frac{a}{a^2+b^2}},-\displaystyle{\frac{b}{a^2+b^2}})$
    3. $(-\displaystyle{\frac{a}{a^2+b^2}},\displaystyle{\frac{b}{a^2+b^2}})$
    4. $(-\displaystyle{\frac{a}{a^2+b^2}},-\displaystyle{\frac{b}{a^2+b^2}})$
  42. Every real number is a
    1. rational number
    2. natural number
    3. prime number
    4. complex number
  43. The Cartesian product of two non-empty sets $A$ and $B$ denoted by
    1. $AB$
    2. $BA$
    3. $A \times B$
    4. none of these
  44. Conjugate of complex number $x+iy$ is
    1. $-x+iy$
    2. $-x-iy$
    3. $x+y$
    4. $x-iy$
  45. Polar form of a complex number $x+iy$ is ……, where $r=|z|$ and $\theta = arg z$
    1. $\cos \theta+i \sin \theta$
    2. $r \cos \theta-ir \sin \theta$
    3. $r \cos \theta+ir \sin \theta$
    4. none of these
  46. If $z=x+iy$ then $|\overline{z}|$ is
    1. $\sqrt{x^2-y^2}$
    2. $\sqrt{x^2+y^2}$
    3. $\sqrt{2xy}$
    4. none of these
  47. If $-x-iy$ is a complex number then modulus of a complex number is
    1. $\sqrt{x^2-y^2}$
    2. $\sqrt{x^2+y^2}$
    3. $\sqrt{2xy}$
    4. none of these
  48. If $z_1$ and $z_2$ are two complex numbers then $\overline{z_1+z_2}$ is
    1. $z_1+z_2$
    2. $\overline{z_1}-\overline{z_2}$
    3. $\overline{z_1}+\overline{z_2}$
    4. none of these
  49. If $z_1$ and $z_2$ are two complex numbers then $\overline{z_1-z_2}$ is
    1. $z_1+z_2$
    2. $\overline{z_1}-\overline{z_2}$
    3. $\overline{z_1}+\overline{z_2}$
    4. none of these
  50. If $z_1$ and $z_2$ are two complex numbers then $\overline{z_1z_2}$ is
    1. $z_1z_2$
    2. $\displaystyle{\frac{z_1}{z_2}}$
    3. $\overline{z_1}\times \overline{z_2}$
    4. none of these
  51. If $z_1$ and $z_2$ are two complex numbers then $\overline{\displaystyle{\frac{z_1}{z_2}}}$ is
    1. $\displaystyle{\frac{z_1}{z_2}}$
    2. $z_1z_2$
    3. $\displaystyle{\overline{z_2}}$
    4. none of these
  52. If $z_1$ and $z_2$ are two complex numbers then $|z_1z_2|$ is
    1. $z_1z_2$
    2. $\displaystyle{\frac{|z_1|}{|z_2|}}$
    3. $|z_1||z_2|$
    4. none of these
  53. If $z$ and $\overline{z}$ is a conjugate then $|z \overline{z}|$ is equal to
    1. $|z||\overline{z}|$
    2. $|z|^2$
    3. $\displaystyle{\frac{|z|}{\overline{|z|}}}$
    4. none of these
  54. If $z-3-5i$ then $z^{-1}$ ———-
    1. $-\displaystyle{\frac{3}{34}}+\displaystyle{\frac{5}{34}i}$
    2. $\displaystyle{\frac{3}{34}}-\displaystyle{\frac{5}{34}i}$
    3. $\displaystyle{\frac{3}{34}}+\displaystyle{\frac{5}{34}i}$
    4. none of these
  55. If $(x+iy)^2=-----$
    1. $x^2+y^2+2xyi$
    2. $x^2-y^2-2xyi$
    3. $x^2-y^2+2xyi$
    4. none of these
  56. If $(x-iy)^2=-----$
    1. $x^2+y^2+2xyi$
    2. $x^2-y^2-2xyi$
    3. $x^2+y^2-2xyi$
    4. none of these
  57. If $z^2+\overline{z}^2$ is a
    1. Complex number
    2. Real number
    3. Both A and B
    4. None of these
  58. If $(z-\overline{z})^2$ is a
    1. Real number
    2. Complex number
    3. Both A and B
    4. None of these
  59. If $(z+\overline{z})^2$ is a
    1. Complex number
    2. Real number
    3. Both A and B
    4. None of these
  60. $i$ can be written in th form of an ordered pair as
    1. $(1,0)$
    2. $(1,1)$
    3. $(0,1)$
    4. None of these
  61. If $z=3-4i$ then $|\overline{z}|$ is
    1. $4$
    2. $3$
    3. $5$
    4. None of these
  62. For all $\ a, b, c \in R$, $a=b \wedge b=c\Rightarrow a=c$ is called
    1. Reflexive property
    2. Symmetric property
    3. Transitive property
    4. None of these
  63. For all $ a, b, c \in R$, $a+c=b+c \Rightarrow a=b$ is called
    1. Additive property
    2. Cancellation property w.r.t addition
    3. Cancellation property w.r.t multiplication
    4. None of these
  64. For all $a, b, c \in R$, $ac=bc \Rightarrow a=b,c \neq 0$ is called
    1. Cancellation property w.r.t addition
    2. Cancellation property w.r.t multiplication
    3. Symmetric property
    4. None of these
  65. $-(-a)$ should be read as
    1. Negative of negative
    2. Minus minus a
    3. Both A and B
    4. None of these
  66. If a point $A$ of the coordinate plane correspond to the order pair $(a,b)$ then $b$ is called
    1. Abscissa
    2. x-coordinate
    3. Ordinate
    4. 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

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