CBSE Questions for Class 11 Commerce Applied Mathematics Number Theory Quiz 3 - MCQExams.com

Which one of the following is not a prime number?
  • $$31$$
  • $$61$$
  • $$71$$
  • $$91$$
What is the modulus of $$\cfrac { \sqrt { 2 } +i }{ \sqrt { 2 } -i } $$ where $$i=\sqrt { -1 } $$
  • $$3$$
  • $$\dfrac{1}{2}$$
  • $$1$$
  • None of the above
If $$\cos { \left( \log { { i }^{ 4i } }  \right)  } =a+ib$$, then
  • $$a=1,b=-1$$
  • $$a=-1,b=1$$
  • $$a=1,b=0$$
  • $$a=1,b=2$$
Which of the following numbers is prime?
  • $$119$$
  • $$187$$
  • $$247$$
  • $$179$$
$$( 7 \times 11 \times 13 + 13 )$$ is a/an
  • Composite number
  • Prime number
  • Irrational number
  • Imaginary number.
The reciprocal of the smallest prime number is _______.
  • $$0$$
  • $$\dfrac {1}{2}$$
  • $$1$$
  • $$2$$
Which of the following is not a prime number?
  • $$23$$
  • $$29$$
  • $$43$$
  • $$21$$
Instructions and memory address are represented by 
  • Character code
  • Binary codes
  • Binary word
  • parity bit
Bit stands for
  • Binary digits
  • bit of system
  • a part of byte
  • All of above
A byte is made up of
  • Eight bytes
  • Eight binary digits
  • Two binary digits
  • Tow decimal points
The roots of the equation $${ \left( z+\alpha \beta  \right)  }^{ 3 }={ \alpha  }^{ 3 }$$ represent the vertices of a triangle, one of whose sides is of length
  • $$\sqrt { 3 } \left| \alpha \beta \right|$$
  • $$\sqrt { 3 } \left| \alpha \right|$$
  • $$\sqrt { 3 } \left| \beta \right|$$
  • $$None\ of\ these$$
How many options doe a BINARY choice offer
  • None
  • One
  • Two
  • it depends on the amount of memory on the computer
  • It depends on the speed of the computer's processor
Which number system is usually followed in a typical 32-bit computer?
  • Binary
  • Decimal
  • Hexadecimal
  • Octal
Put the following in the form of A + iB :
$$\dfrac{(3 \, - \, 2i)(2 \, + \, 3i)}{(1 \, + \, 2i)(2 \, - \, i)}$$
  • $$\dfrac{3}{4} \, + \, \dfrac{9}{4} \, i$$
  • $$\dfrac{63}{25} \, - \, \dfrac{16}{25} \, i$$
  • $$\dfrac{5}{4} \, + \, \dfrac{9}{4} \, i$$
  • $$\dfrac{1}{4} \, + \, \dfrac{7}{4} \, i$$
............... code is used to implement data transparency in the binary synchronous protocol.
  • $$DLE$$
  • $$NAK$$
  • $$EOH$$
  • $$EOT$$
The number $$111111111$$ is a
  • Prime number
  • Composite number
  • Divisible by $$\frac{10^7-1}{9}$$
  • None of these
In the complex numbers, where $$i = \sqrt {-1}$$, the conjugate of any value $$a + bi$$ is $$a -ib$$. What is the result when you multiply $$2 + 7i$$ by its conjugate?
  • $$45$$
  • $$-45$$
  • $$45i$$
  • $$53$$
  • $$53i$$
Evaluate:
$$\left| \left( 1+i \right) \dfrac { \left( 2+i \right)  }{ \left( 3+i \right)  }  \right| =$$ ?
  • $$\dfrac{-1}{2}$$
  • $$\dfrac{1}{2}$$
  • $$1$$
  • $$-1$$
If $$(1+i)^{-20}=a+ib$$, then the values of $$a$$ and $$b$$ are
  • $$a=2^{-10}, b=-2^{-10}$$
  • $$a=-2^{-10}, b=0$$
  • $$a=2^{-10}, b=0$$
  • $$none\ of\ these$$
The maximum value of $$\left| {{\rm{3z + 9 - 7i}}\left| {{\rm{if}}} \right|{\rm{z + 2 - i}}\left. {} \right|} \right.{\rm{ = 5}}$$is
  • $$20$$
  • $$15$$
  • $$25$$
  • $$5$$
Find the modulus of the complex number $$-2+2\sqrt{3}i$$.
  • 2
  • 4
  • 6
  • 8
Find the which of the complex number has greatest modulus.
  • $$7-5i$$
  • $$\sqrt{3}+\sqrt{2}i$$
  • $$-8+15i$$
  • $$-3(1-i)$$
If $$\dfrac {z-1}{z+1}$$ is purely imaginary then 
  • $$|z|=1$$
  • $$|z|>1$$
  • $$|z|<1$$
  • $$|z|<2$$
 For any complex number $$z$$ the minimum value of $$|z|+|z-2013i|$$ is...
  • $$2010$$
  • $$2011$$
  • $$2013$$
  • $$2012$$
If $$z=x+iy(x,y\epsilon R,x\neq -1/2),$$ the number of values of z satisfying $$\left | z \right |^{n}=z^{2}\left | z \right |^{n-2}+1.(n\epsilon N,n> 1)$$is
  • 0
  • 1
  • 2
  • 3
Which of the following is true
  • $$(3 + \sqrt{-5})(3 - \sqrt{-5}) = 14$$
  • $$(-2 + \sqrt{-3})(-3 + 2\sqrt{-3}) = -7\sqrt{3}i$$
  • $$(2 + 3i)^2 = (-5 + 12i)$$
  • $$(\sqrt{5} - 7i)^2 = -44 - 14\sqrt{5}i$$
$$z_{1}$$ and $$z_{2}$$ are two non-zero complex numbers such that $$|z_{1}|=|z_{2}|$$ and $$argz_{1}+argz_{2}=\pi$$, then $$z_{2}$$ equals 
  • $$\bar{z_{1}}$$
  • $$-\bar{z_{1}}$$
  • $$z_{1}$$
  • $$-z_{1}$$
If $$ z=1+i\sqrt { 3, } \left| arg\left( z \right)  \right| +\left| arg\left( \overline { z }  \right)  \right|$$
  • $$\dfrac{\pi}{3}$$
  • $$\dfrac{2\pi}{3}$$
  • $$0$$
  • $$\dfrac{\pi}{2}$$
If $$\alpha $$ and $$\beta $$ are real then $$\left| \dfrac { \alpha +i\beta  }{ \beta +i\alpha  }  \right|=$$ 
  • Lies betwen 0 and 1
  • = 1
  • >1
  • 2
If arg $$\left( {{Z_1} + {Z_2}} \right) = 0\;$$ and $$|{z_1}|\; = \;|{z_2}|\; = 1.$$ then.
  • $${z_1} + {z_2} = 0$$
  • $${z_1}{\overline z _2} = 1$$
  • $${z_1} = {\overline z _2}$$
  • none
The value of $${\left( {1 + i} \right)^5} \times {\left( {1 - i} \right)^5}$$ is
  • $$-8$$
  • $$8i$$
  • $$8$$
  • $$32$$
How many two-digit prime numbers are there having the digit $$3$$ in their units place?
  • $$10$$
  • $$8$$
  • $$6$$
  • $$5$$
Argument and modulus of $$\left[\dfrac {1+i}{1-i}\right]^{2013}$$ are respectively ____
  • $$\dfrac {-\pi}{2}$$ and $$1$$
  • $$\dfrac {\pi}{2}$$ and $$\sqrt {2}$$
  • $$0$$ and $$\sqrt {2}$$
  • $$\dfrac {\pi}{2}$$ and $$1 $$
 If $$z_1=\sqrt { 3 } -i,z_2=1+i\sqrt { 3 } ,$$ then amp$$(z_1+z_2)=$$ 
  • $$\dfrac { \pi }{ 12 } $$
  • $$\dfrac { \pi }{ 15 } $$
  • $$\dfrac { \pi }{ 6 } $$
  • $$\dfrac { \pi }{ 4 } $$
If $$z=\dfrac {1+2i}{1-2i}$$  and.consider $$z=x+iy$$ then which of the following relationship is correct:
  • $$x^{2}+y^{2}=1$$
  • $$x^{2}+y^{2}=4$$
  • $$x^{2}+y^{2}=2$$
  • $$x^{2}+y^{2}=3$$
Find the least positive value of n, if $$(\dfrac{1+i}{1-i})^n=1$$
  • 1
  • 2
  • 3
  • 4
Inequality  $$a + i b > c + i d$$  can be explained only when :
  • $$b=0,c=0$$
  • $$b=0,d=0$$
  • $$a=0,c=0$$
  • $$a=0,d=0$$
If $$z_1=3+4i\\z_2=4-5i$$ Then find $$z_1+z_2$$
  • 7-i
  • 7+i
  • 7+9i
  • None of these
If $$z_1=3+4i,z_2=2-i$$ find $$z_2-z_1$$
  • -1-5i
  • 2-5i
  • 1+5i
  • 1-5i
The complex numbers $$z_1=8+9i, z_2=4-6i$$ then $$z_1-z_2$$
  • $$4+15i$$
  • $$4-3i$$
  • $$12+3i$$
  • $$12-15i$$
If $$z$$ is a complex number such that $$|z|=1$$, then $$\left|\dfrac 1{\bar z}\right|$$ is 
  • $$0$$
  • $$-1$$
  • $$\sqrt{2}$$
  • $$1$$
The sum of prime numbers, out of the numbers $$17, 8, 21, 13, 41, 2, 27, 31, 51$$ is:
  • $$125$$
  • $$102$$
  • $$104$$
  • $$155$$
If $$z_1=4+i,z_2=4-i $$ find $$z_1z_2$$
  • $$17$$
  • $$16$$
  • $$17-i$$
  • $$16i$$
$$z_1=9+8i\ \ \  |z|=$$
  • $$\sqrt {145}$$
  • $$\sqrt {163}$$
  • $$\sqrt {117}$$
  • $$\sqrt {137}$$
Mark against the correct answer in each of the following .
$$i^{-38}=$$?
  • $$i$$
  • $$-i$$
  • $$1$$
  • $$-1$$
Mark against the correct answer in each of the following .
$$i^{-75}=$$?
  • $$1$$
  • $$-1$$
  • $$i$$
  • $$-i$$
Mark against the correct answer in each of the following .
$$i^{124}=$$?
  • $$-1$$
  • $$1$$
  • $$i$$
  • $$-i$$
If $$(x+iy)(2-3i)=4+i\left ( \dfrac{1}{2} \right )$$ then $$x + y =$$
  • $$\dfrac{3}{2}$$
  • $$\dfrac{1}{2}$$
  • $$0$$
  • $$\dfrac{2}{3}$$
In the complex numbers, where $$i^{2} = -1$$, what is the value of $$5 + 6i$$ multiplied by $$3-  2i$$?
  • $$27$$
  • $$27i$$
  • $$27 + 8i$$
  • $$15 + 8i$$
  • $$15 - 18i$$
If $$m_1$$, $$m_2$$, $$m_3$$ and $$m_4$$ respectively denote the moduli of the complex numbers $$1 + 4i, 3 + i, 1 – i \ and\  2 – 3i$$ then the correct order among the following is :
  • $$m_1$$<$$m_2$$<$$m_3$$<$$m_4$$
  • $$m_4$$<$$m_3$$<$$m_2$$<$$m_1$$
  • $$m_3$$<$$m_2$$<$$m_4$$<$$m_1$$
  • $$m_3$$<$$m_1$$<$$m_2$$<$$m_4$$
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