CBSE Questions for Class 11 Commerce Applied Mathematics Number Theory Quiz 7 - MCQExams.com

The number which have only two factors $$(1$$ and the number itself) are called as ________.
  • Composite
  • Even
  • Prime
  • None of these
Computers use the .... number system to store data and perform calculations.
  • binary
  • octal
  • decimal
  • hexadecimal
If $$z_1, z_2$$ are two complex numbers such that $$arg(z_1+z_2)=0$$ and $$Im(z_1z_2)=0$$, then.
  • $$z_1=-z_2$$
  • $$z_1=z_2$$
  • $$z_1=\vec{z_2}$$
  • none of these
If $$z + \sqrt {2}|z + 1| + i = 0$$ and $$z = x + iy$$, then
  • $$x = -2$$
  • $$x = 2$$
  • $$y = -2$$
  • $$y = 1$$
If $${z}_{1}=-3+5i;{z}_{2}=-5-3i$$ and $$z$$ is a complex number lying on the line segment joining $${z}_{1}$$ and $${z}_{2}$$, then $$arg(z)$$ can be:
  • $$-\cfrac { 3\pi }{ 4 } $$
  • $$-\cfrac { \pi }{ 4 } $$
  • $$\cfrac { \pi }{ 6 } $$
  • $$\cfrac { 5\pi }{ 6 } $$
The complex numbers $$z=x+iy$$ which satisfy the equation
$$\left| \cfrac { z-5i }{ z+5i }  \right| =1$$ lie on:
  • the x-axis
  • straight line $$y=5$$
  • a circle through the origin
  • none of these
Which of the following is not a binary number?
  • 001
  • 101
  • 202
  • 110
The memory of a computer is commonly expressed in terms of Kilobytes or Megabytes. A byte is made up of
  • eight decimal digits
  • eight binary digits
  • two binary digits
  • two decimal digits
What is the byre capacity of a drum which is $$5$$ inch high, $$10$$ inch diameter, and which has $$60$$ tracks per inch and bit density of $$800$$ bits per inch?
  • $$942000$$ bytes
  • $$9712478$$ bytes
  • $$192300$$ bytes
  • $$14384$$ bytes
  • None of the above
What digits are representative of all binary numbers?
  • $$0$$
  • $$1$$
  • Both (a) and (b)
  • $$3$$
  • None of the above
If $$\left| {z - \dfrac{4}{z}} \right| = 2$$ , then the maximum value of$$\left| z \right|$$ is
  • $$\sqrt 5 $$
  • $$\sqrt 5 + 1$$
  • $$\sqrt 5 - 1$$
  • $$1 - \sqrt 5 $$
If $$z_1, z_2, z_3$$ are three points lying on the circle |z| =2, then the minimum value of $$|z_1 + z_2|^2 + | z_2 + z_3|^2 + | z_3 + z_1|^2$$ is equal to
  • $$6$$
  • $$12$$
  • $$15$$
  • $$24$$
An output device that converts data from a binary format in main storage to coded hole patterns punched into a paper tape is?
  • Paper tape punch
  • Punched paper tape
  • Magnetic disk
  • Magnetic tape
  • None of the above
The $$2$$'s complement number of $$110010$$ is?
  • $$001101$$
  • $$110011$$
  • $$010011$$
  • All of the above
  • None of the above
Instructions and memory addresses are represented by.
  • Character codes
  • Binary codes
  • Binary word
  • Parity bit
  • None of the above
What is the highest address possible if $$16$$ bits are used for each address?
  • $$65536$$
  • $$12868$$
  • $$16556$$
  • $$643897$$
  • None of the above
Multiplication of $$111_2$$ by $$101_2$$ is?
  • $$110011_2$$
  • $$100011_2$$
  • $$111100_2$$
  • $$000101_2$$
  • None of the above
The $$0$$ and $$1$$ in the binary numbering system are called binary digits or ____________.
  • Bytes
  • Kilobytes
  • Decimal bytes
  • Bits
  • Nibbles
The real and imaginary part of the complex number $$1 + \sqrt {i}$$ where $$i = \sqrt {-1}$$ are
  • $$1 - \dfrac {1}{\sqrt {2}}$$ and $$-\dfrac {1}{\sqrt {2}}$$ respectively
  • $$1 - \dfrac {1}{\sqrt {2}}$$ and $$\dfrac {1}{\sqrt {2}}$$ respectively
  • $$1 + \dfrac {1}{\sqrt {2}}$$ and $$\dfrac {1}{\sqrt {2}}$$ respectively
  • $$1 + \dfrac {1}{\sqrt {2}}$$ and $$-\dfrac {1}{\sqrt {2}}$$ respectively
Find a complex number z satisfying the equation $$z+\sqrt{2}|z+1|+i=0$$
  • $$2-i$$
  • $$-2-i$$
  • $$\sqrt{2}-i$$
  • None of these
If $${ a }^{ 2 }+{ b }^{ 2 }=1$$, then $$\dfrac {\left( 1+b+ia \right) }{\left( 1+b-ia \right)} $$ is
  • $$1$$
  • $$2$$
  • $$b+ia$$
  • $$a+ib$$
If $$\left| {z - 1} \right| = 2$$, then the value of $$z\overline z  - z - \overline z $$ is equal to: 
  • $$-3$$
  • $$4$$
  • $$3$$
  • $$-4$$
The total number of even prime numbers is?
  • $$0$$
  • $$1$$
  • $$2$$
  • Unlimited
The real part of $$(1-\cos\theta +2i \sin\theta)^{-1}$$ is?
  • $$\displaystyle\frac{1}{3+5\cos\theta}$$
  • $$\displaystyle\frac{1}{5-3\cos\theta}$$
  • $$\displaystyle\frac{1}{3-5\cos\theta}$$
  • $$\displaystyle\frac{1}{5+3\cos\theta}$$
If $$\dfrac {lz_{2}}{mz_{1}}$$ is purely imaginary number, then $$\left |\dfrac {\lambda z_{1} + \mu z_{2}}{\lambda z_{1} - \mu z_{2}}\right |$$ is equal to
  • $$\dfrac {l}{m}$$
  • $$\dfrac {\lambda}{\mu}$$
  • $$\dfrac {-\lambda}{\mu}$$
  • $$1$$
The complex number  $$\dfrac{1+2i}{1-i}$$ lies in which quadrant of the compiles plan
  • First
  • Second
  • Third
  • Fourth
In binary synchronous, communication ............code is used by the receiver to check the validity of the message recovered. 
  • $$OK$$
  • $$ACK$$
  • $$BCC$$
  • $$SOH$$
Binary number are used because:
  • Decimal system can not be represented on motherboard
  • Binary data needs just 2 wires for the transmission, one for 1 & other for 0
  • Binary data is easier to represent using 'on'(1) & 'off' (0) states of switches.
  • All of these
Which of the following is NOT a binary system?
  • EBCDIC
  • ASCII
  • HEX
  • None of these
..............is a binary synchronous data transmission. 
  • Each bit is sent over a separate wire
  • Sequence numbers are sent in numbered frames
  • Each character is prefixed with DLE
  • Character are used for control purpose
Which are not property of Binary relations
  • reflexive relation, symmetric relation, anti symmetrical relation
  • reflexive, transitive, equivalence relations
  • transitive, partial ordering relation, symmetric
  • reflexive, partial, chain relation
............are the Pentium binary program that can be embedded in a web page. 
  • Servlets
  • Hyperlink
  • Hypertext
  • Active X controls
If Z satisfied   the equation  $$\left ( \dfrac{Z- 2}{Z + 2} \right ) \, \left ( \dfrac {{\bar Z} - 2}{{\bar Z} + 2} \right )$$then minimum, value of$$ |Z| $$is equal to 
  • 0
  • 2
  • 4
  • 6
If $$\mid{z_1}\mid=2$$, $$\mid{z_2}\mid=3$$, $$\mid{z_3}\mid=4$$ and $$\mid{z_1+z_2+z_3}\mid=2$$, then the value of $$\mid{4z_2z_3+9z_3z_1+16z_1z_2}\mid$$.
  • 24
  • 48
  • 96
  • 120
Evaluate:
$${ \left( \dfrac { cos\dfrac { \pi  }{ 8 } -isin\dfrac { \pi  }{ 8 }  }{ cos\dfrac { \pi  }{ 8 } +isin\dfrac { \pi  }{ 8 }  }  \right)  }^{ 4 }$$
  • $$1$$
  • $$-1$$
  • $$2$$
  • $$\dfrac { 1 }{ 2 } $$
$$ | \frac{z_1 - 2z_2}{2 - z_1\bar{z}_2} | = 1$$ and $$|z_2| \neq 1$$ then the value of $$|z_1|$$ is
  • 4
  • 2
  • 1
  • $$\frac{1}{2}$$
The complex number $$x+iy$$ whose modulus is unity, $$y\neq 0$$, can be represented as $$x+iy=\dfrac { a+i }{ a-i }$$,  where $$a$$ is real number.
  • True
  • False
Simplify $$\left ( \dfrac{2i}{1 \, + \, i} \right )^2$$
  • $$i$$
  • $$2i$$
  • $$1 - i$$
  • $$1 - 2i$$
If $$z_1 \, z_2$$ be two distinct complex numbers and let z = (1 - t) $$z_1$$ + t$$z_2$$ for some real number t with 0 < t <If arg $$(\omega)$$ denotes the principal argument of a non-zero complex number $$(\omega)$$, then
  • $$|z \, - \, z_1| \, + \, |z \, - \, z_2| \, = \, |z_2\, - \, z_1|$$
  • $$arg(z \, - \, z_1) \, = \, arg (z \, - \, z_2)$$
  • $$\begin{vmatrix}

    z \, - \, z_1 & \bar z \, - \, \bar{z_1}\\

    z_2 \, - \, z_1 & \bar{z_2} \, - \, \bar{z_1}

    \end{vmatrix}$$
  • $$arg(z \, - \, z_1) \, = \, arg (z_2 \, - \, z_1)$$
If z is a complex number such that $$\left|\dfrac{z-3i}{z+3i}\right|=1$$ then z lies on?
  • The real axis
  • The line Im(z)$$=3$$
  • A circle
  • None of these

Let $$z$$ be a complex number such that $$\left| z+\dfrac { 1 }{ z }  \right| =2$$. 

If $$\left| z \right| ={ r }_{ 1 }$$ and $$\left| \dfrac { 1 }{ z }  \right| =$$ $${r}_{2}$$ for $$\arg z=\dfrac { \pi  }{ 4 }$$ then 

$$\left| { r }_{ 1 }-{ r }_{ 2 } \right| =$$
  • $$\dfrac { 1 }{ \sqrt { 2 } }$$
  • $$1$$
  • $$\sqrt { 2 }$$
  • $$2$$
If $${z}_{1}=1+2i,\ {z}_{2}=2+3i,\ {z}_{3}=3+4i$$, then $${z}_{1},\ {z}_{2}$$ and $${z}_{3}$$ are collinear.
  • True
  • False
If $$\dfrac{2z_1}{3z_2}$$ is a purely imaginary number,then $$\left|\dfrac{z_1-z_2}{z_1+z_2}\right|=$$
  • $$3/2$$
  • $$1$$
  • $$2/3$$
  • $$4/9$$
If z satisfies $$\left| {z - 1} \right| < \left| {z + 3} \right|$$ then $$w = 2z + 3 - i$$ , ( where $$w = 2z + 3 - i$$ ) satisfies:
  • $$\left| {w - 5 - i} \right| < \left| {w + 3i} \right|$$
  • $$\left| {w - 5} \right| < \left| {w + 3} \right|$$
  •  $$\left( {iw} \right) > 1$$
  • $$\left| {\arg \left( {w - 1} \right)} \right| < {\pi  \over 2}$$
Find the real number $$x$$ if $$(x-2i)(1+i)$$ is purely imaginary.
  • $$2$$
  • $$-2$$
  • $$4$$
  • $$-4$$
Real part of  $$\dfrac{(1 + i)^2}{3 - i} =$$
  • $$-1/5$$
  • $$1/5$$
  • $$1/10$$
  • $$-1/10$$
$$i \, \log \left(\dfrac{x - i}{x + i}\right)$$ is equal to
  • $$2i\log (x-i)-i\log (x^2+1)$$
  • $$2i\log (x-i)+i\log (x^2+1)$$
  • $$2i\log (x+i)-3i\log (x^2+1)$$
  • $$2i\log (x-i)-i\log (x^2+i)$$
On the complex plane locus of a point $$z$$ satisfy inequality
$$2\le \left| z-1 \right| <3$$ denotes
  • region between, the concentric circles of radii $$3$$ and $$1$$ centered at $$(1,0)$$
  • region between the concentric circles of radii $$3$$ and $$2$$ centered at $$(1,0)$$ excluding the inner and outer boundaries.
  • region between the concentric circles of radii $$3$$ and $$2$$ centered at $$(1,0)$$ including the inner and outer boundaries.
  • region between, the concentric circles of radii $$3$$ and $$2$$ centered at $$(1,0)$$ including he inner boundary and excluding the outer boundary.
The value of $$\dfrac{1}{i} + \dfrac{1}{{{i^2}}} + \dfrac{1}{{{i^3}}} + ... + \dfrac{1}{{i^{102}}}$$ is equal to 
  • $$ - 1 - i$$
  • $$ - 1 + i$$
  • $$ 1 - i$$
  • $$1 + i$$
If $$i^2= -1$$, then $$1+ i^2+ i^4 +i^6+i^8 +.............to ( 2n +1)$$ terms is equal to
  • $$0$$
  • $$1$$
  • $$3i$$
  • $$4i$$
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