CBSE Questions for Class 11 Commerce Applied Mathematics Number Theory Quiz 1 - MCQExams.com

If $$(\dfrac{3-z_{1}}{2-z_{1}})(\dfrac{2-z_{2}}{3-z_{2}})=k$$, then point $$A(z_{1}, z_{2}),  C(3, 0)$$ and $$D(2, 0)$$ (taken in clockwise sense ) will
  • lie on a circle only for $$k>0$$
  • lie on a circle only for $$k=0$$
  • lie on a circle $$\forall k\in R$$
  • be vertices of a square $$\forall k\in (0, 1)$$
If $$\tan^{-1}(\alpha+ i\beta) = x+iy,$$ then $$x$$ is equal to
  • $$\frac{1}{2}\tan^{-1}\left ( \dfrac{2\alpha}{1-\alpha^2-\beta^2}\right)$$
  • $$\frac{1}{2}\tan^{-1}\left ( \dfrac{2\alpha}{1+\alpha^2+\beta^2}\right)$$
  • $$\tan^{-1}\left ( \dfrac{2\alpha}{1-\alpha^2-\beta^2}\right)$$
  • None of the above
The complex numbers $${ z }_{ 1 },{ z }_{ 2 },{ z }_{ 2 }$$ satisfying $$\dfrac { { z }_{ 1 }+{ z }_{ 3 } }{ { z }_{ 2 }-{ z }_{ 3 } } =\dfrac { 1-i\sqrt { 3 }  }{ 2 } $$
  • If area zero
  • right angled isosceles
  • equilateral
  • obtuse angled
If $$z$$ is a complex number such that $$| z | = 1 , z \neq 1 ,$$ then the real part of $$\frac { z - 1 } { z + 1 }$$ is
  • $$\frac { 1 } { | z + 1 | ^ { 2 } }$$
  • $$\frac {- 1 } { | z + 1 | ^ { 2 } }$$
  • $$\frac { \sqrt 2 } { | z + 1 | ^ { 2 } }$$
  • 0
Evaluate:
$$\dfrac {3+2 i\sin \theta}{1-2i \sin \theta},\theta \epsilon \left(-\dfrac {\pi}{2},\pi\right)$$ is 
  • $$2\pi/3$$
  • $$\pi/3$$
  • $$4\pi/3$$
  • $$\pi$$
Find the modules and amplitude for each of the following complex numbers
  • 7-5i
  • $$\sqrt { 3 } +\sqrt { 2 } i$$
  • -8+15i
  • -3(1-i)
Let $$\alpha,\ \beta$$ be real and $$\mathrm{z}$$ be a complex number. If $$\mathrm{z}^{2}+\alpha \mathrm{z}+\beta=0$$ has two distinct roots on the line $$Re(z) =1$$, then it is necessary that: 
  • $$\beta\in(0,1)$$
  • $$\beta\in(-1,0)$$
  • $$|\beta|=1$$
  • $$\beta\in(1, \infty)$$
Which of the following is/are not twin prime(s)?
  • $$(2, 3)$$
  • $$(41,43)$$
  • $$(17, 19)$$
  • $$(59, 61)$$
Sum of first three prime numbers which end at 3 is: 
  • 20
  • 16
  • 39
  • 40
Which of the following is the factor of all prime numbers?
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
What is the sum of the smallest prime and the largest prime less than $$10$$?
  • $$7$$
  • $$9$$
  • $$10$$
  • $$11$$
  • $$12$$
For $$i=\sqrt{-1}$$, what is the sum $$\left(7+3i\right) + \left(-8+9i\right)$$?
  • $$-1+12i$$
  • $$-1-6i$$
  • $$15+12i$$
  • $$15-6i$$
Perform the indicated operations:
$$(8-2i)-(-2-6i)$$
  • $$6+4i$$
  • $$10+4i$$
  • $$10+8i$$
  • $$10-8i$$
If $$|\mathrm{z}^{2}-1|=|\mathrm{z}|^{2}+1$$, then $$\mathrm{z}$$ lies on
  • the real axis
  • the imaginary axis
  • a circle
  • an ellipse
If $$z = x + iy$$ and $$\omega = \dfrac{(1 -iz)}{(z-i)}$$, then $$\left|\omega\right| = 1$$ implies that in the complex plane
  • z lies on the imaginary axis
  • z lies on the real axis
  • z lies on the unit circle
  • none of these
If $$(x+iy)(2-3i)=4+i$$ then (x, y) =
  • $$\left ( 1,\dfrac{1}{13} \right )$$
  • $$\left ( -\dfrac{5}{13},\dfrac{14}{13} \right )$$
  • $$\left ( \dfrac{5}{13},\dfrac{14}{13} \right )$$
  • $$\left ( -\dfrac{5}{13},-\dfrac{14}{13} \right )$$
If $$z =3+5i$$, then $$z^3+z+198=$$
  • $$3 - 15i$$
  • $$-3 - 15i$$
  • $$-3 + 15i$$
  • $$3 + 15i$$
The modulus of $$\sqrt{2}i-\sqrt{-2}i$$ is:
  • 2
  • $$\sqrt{2}$$
  • 0
  • $$2\sqrt{2}$$
If $$z=2-3i$$ then $$z^2-4z+13=$$
  • $$0$$
  • $$1$$
  • $$2$$
  • $$3$$
The complex number $$\displaystyle \frac{1+2i}{1-i}$$ lies in the quadrant :
  • I
  • II
  • III
  • IV
$$\sqrt{-3}\sqrt{-75}=$$
  • $$15$$
  • $$15i$$
  • $$-15$$
  • $$-15i$$
The sum of two complex numbers $$a + ib$$ and $$c +id$$ is a real number if
  • $$a + c = 0$$
  • $$b + d = 0$$
  • $$a + b= 0$$
  • $$b + c = 0$$
The locus of complex number z such that z is purely real and real part is equal to - 2 is
  • Negative y-axis
  • Negative x-axis
  • The point (-2, 0)
  • The point (2, 0)
$$\dfrac{1}{i-1}+\dfrac{1}{i+1}$$ is
  • positive rational number
  • purely imaginary
  • positive Integer
  • negative integer
The sum of two complex numbers $$a + ib$$ and $$c+ id$$ is purely imaginary if
  • $$a + c = 0$$
  • $$a + d = 0$$
  • $$b + d = 0$$
  • $$b + c = 0$$
Which of the following is not a prime number ?
  • 5
  • 7
  • 8
  • 11
Which of the following is not a composite number?
  • $$4$$
  • $$6$$
  • $$7$$
  • $$8$$
The number of prime numbers between 0 and 20 is
  • 7
  • 8
  • 6
  • 9
The units digit of every prime number (other than $$2$$ and $$5$$) must be necessarily
  • $$1, 3$$ or $$5$$
  • $$1, 3, 7$$ or $$9$$
  • $$7$$ or $$9$$
  • $$1$$ or $$7$$
Which of the following is not a composite number?
  • $$352+6$$
  • $$357+7$$
  • $$352+7$$
  • $$353+1$$
The total number of prime numbers between $$120$$ and $$140$$ is
  • $$7$$
  • $$6$$
  • $$5$$
  • $$4$$
If the square of $$(a + ib)$$ is real, then $$ ab=$$
  • $$0$$
  • $$1$$
  • $$-1$$
  • $$2$$
Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique apart from the order in which the prime factors occur.
  • True
  • False
  • Neither
  • Either
The number of composite numbers between $$101$$ and $$120$$
(excluding both) are
  • $$11$$
  • $$12$$
  • $$13$$
  • $$14$$
What is the remainder obtained when a prime number greater than $$6$$ is divided by $$6$$? 
  • $$1 \ or\  3$$
  • $$1 \ or\  5$$
  • $$3\  or\  5$$
  • $$4 \ or\  5$$
A number other than one which is either divisible by $$1$$ or itself is called a
  • composite number
  • prime number
  • comprime number
  • none of these
Write two pairs of twin primes between $$20$$ and $$50.$$
  • $$16$$ and $$26, 19$$ and $$29$$
  • $$29$$ and $$31, 41$$ and $$43$$
  • $$11$$ and $$21, 61$$ and $$71$$
  • $$15$$ and $$17, 37$$ and $$39$$
Find the value of $$x$$ of the equation $${ \left( 1-i \right)  }^{ x }={ 2 }^{ x }$$ 
  • $$1$$
  • $$2$$
  • $$0$$
  • none of these
Which of the following is a prime number?
  • $$889$$
  • $$997$$
  • $$899$$
  • $$1147$$
Write all prime numbers between $$20$$ and $$50.$$
  • $$21, 29, 33, 37, 41, 43$$ and $$47$$
  • $$29, 33, 37, 39, 41, 43$$ and $$47$$
  • $$23, 29, 31, 37, 41, 43$$ and $$47$$
  • None of these
Solve $$\displaystyle \left ( 1-i \right )x+\left ( 1+i \right )y= 1-3i,$$
  • $$\displaystyle x= -1, y= 2.$$
  • $$\displaystyle x= 2, y= -1.$$
  • $$\displaystyle x= 2, y= 1.$$
  • $$\displaystyle x= 1, y= 2.$$
Evaluate :
 $$\sqrt{-25} + 3 \sqrt{-4} +2 \sqrt{-9}$$
  • $$-17i$$
  • $$5i$$
  • $$17i$$
  • $$6i$$
How many prime numbers are there between $$0$$ and $$30$$?
  • $$9$$
  • $$10$$
  • $$8$$
  • $$11$$
An example for twin primes is
  • $$5, 11$$
  • $$3, 5$$
  • $$11, 17$$
  • $$3, 7$$
The number which is neither prime nor composite is
  • $$3$$
  • $$1$$
  • $$2$$
  • $$5$$
The two consecutive prime numbers with difference $$2$$ are called
  • co-primes
  • twin primes
  • composite
  • none of these
Number of prime numbers from 1 to 50 are
  • $$18$$
  • $$12$$
  • $$15$$
  • $$20$$
The numbers which have more than two factors are called
  • even
  • prime
  • composite
  • none of these
All prime numbers are
  • even numbers
  • odd numbers
  • composite numbers
  • odd numbers except 2
The prime number that comes just after 47 is ......
  • 57
  • 51
  • 53
  • none of these
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers