CBSE Questions for Class 11 Commerce Applied Mathematics Number Theory Quiz 2 - MCQExams.com

The number which is neither prime nor composite is
  • $$0$$
  • $$1$$
  • $$2$$
  • $$5$$
Which prime number which comes just after $$43$$ ?
  • $$49$$
  • $$45$$
  • $$47$$
  • none of these
Number of prime numbers between $$50$$ to $$60$$ is
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
Every prime number is $$.......$$
  • a even number
  • an odd number
  • a composite number
  • none of these
A prime number 
  • has exactly one factor.
  • has exactly two factors.
  • is not divisible by $$2$$.
  • is an odd number.
Which of the following are prime numbers?
  • $$137$$
  • $$143$$
  • $$396$$
  • Both A and B
Number of prime numbers between $$50$$ to $$60$$ is 
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
$$\displaystyle \frac{\displaystyle i^{4n + 3} + (-i)^{8n - 3}}{\displaystyle(i)^{12 n- 1} - i^{2 - 16 n}}, n    \varepsilon N$$ is equal to
  • 1 + i
  • 2i
  • -2i
  • -1 - i
Which is the least prime number ?
  • $$1$$
  • $$0$$
  • $$2$$
  • $$3$$
If $$i^2 = - 1$$, then the value of $$\displaystyle \sum^{200}_{n = 1} i^n $$ is
  • 50
  • -50
  • 0
  • 100
If $$z = \displaystyle \frac{(3 + 4i)(5 - 7 i)}{(7 + 5i)(4 - 3i)}$$ then $$|z| = ?$$
  • 5
  • 4
  • 1
  • None of these
By Goldbach's conjecture, every even number greater than 4 can be expressed as a sum of
  • Two even numbers
  • Two odd prime numbers
  • Two composite numbers
  • Two co-prime numbers
How many prime numbers are there between 10 and 30?
  • $$6$$
  • $$5$$
  • $$7$$
  • $$8$$
Which of the following is not a composite number ?
  • $$4$$
  • $$6$$
  • $$7$$
  • $$10$$
If 2009 = $$\displaystyle p^{a}.q^{b}$$ where p and q are prime numbers then find the value of p + q
  • 3
  • 48
  • 51
  • 2009
1+$$i^2 + i^4 + i^6 + ........+ i^{2n}$$ is
  • Positive
  • Negative
  • Zero
  • Cannot be determined
Which of the following is not a composite number?
  • 5
  • 6
  • 7
  • 8
The number of prime numbers between $$0$$ and $$20$$ is
  • $$7$$
  • $$8$$
  • $$6$$
  • $$9$$
If i = $$\sqrt {-1}, then  1 + i^2 + i^3 -i^6 + i^8 $$ is equal to -
  • 2- i
  • 1
  • -3
  • -1
($$i^{10}+1) (i^9 + 1)(i^8 +1).......(i+1)$$  equal to 
  • -1
  • 1
  • 0
  • i
Twin primes consist of 
  • composite numbers
  • prime numbers
  • even numbers
  • none of these
Which of the following are twin primes?
  • $$(2, 3)$$
  • $$(5, 7)$$
  • $$(3, 5)$$
  • $$(11, 13)$$
Identify prime numbers among the following options.
  • $$2$$
  • $$5$$
  • $$6$$
  • $$8$$
The two consecutive prime numbers with difference 2 are called
  • co-primes
  • twin primes
  • composite
  • none
The number which have more than two factors is called _____. 
  • Even
  • Prime
  • Odd
  • None of these
The product of $$2 \times 7 \times 3 \times 5$$ is a .........
  • composite number
  • prime number
  • negative number
  • none of the above
When $$(3-2i)$$ is subtracted from $$(4 + 7i)$$, then the result is
  • $$1 + 5i$$
  • $$1 + 9i$$
  • $$7 + 5i$$
  • $$7 + 9i$$
Fundamental theorem of arithmetic is when any .......... greater than $$1$$ is either a prime number or can be written as a unique product of prime numbers.
  • decimal number
  • fraction
  • irrational number
  • integer
If $$u = 3 - 5i$$ and $$v = -6 + i$$, then the value of $$(u+v)^2$$ is
  • $$-7 + 24i$$
  • $$9 + 8i$$
  • $$9 + 16i$$
  • $$25 - 24i$$
Every ........ number can be expressed as a product of prime numbers.
  • composite
  • prime
  • natural
  • irrational
Identify the prime number among the following options.
  • $$11$$
  • $$15$$
  • $$18$$
  • $$20$$
Addition of prime number
  • gives a prime number
  • gives a composite number
  • may give a prime number or composite number
  • none of these
The value of $$-i^{48}$$ is
  • $$-i$$
  • $$i$$
  • $$-1$$
  • $$1$$
For any complex number $$z$$, the minimum value of $$\left| z \right| +\left| z-1 \right| $$ is
  • $$0$$
  • $$1$$
  • $$2$$
  • $$-1$$
The composite numbers _________ .
  • has atleast one factors other than itself and 1 
  • has no factor other than 1
  • only A
  • none
Select the right statement.
  • Zero is not even and not positive
  • Zero is even and positive
  • The largest factor of $$28$$ is $$14$$
  • The sum of the smallest prime and the greatest negative even integer is zero
  • None
What is the product of the smallest prime number that is greater than $$50$$ and the greatest prime number that is less than $$50$$ ? 
  • $$2400$$
  • $$2491$$
  • $$2450$$
  • $$2241$$
The simplest form of the expression $$\dfrac {10 - \sqrt {-12}}{1 - \sqrt {-27}} $$ is
  • $$-\dfrac {2}{7}$$
  • $$\dfrac {28}{3}$$
  • $$-\dfrac {2}{7} + i\sqrt {3}$$
  • $$1 + i \sqrt {3}$$
If $$i^2$$ $$= -1$$, then find the odd one out of the following expressions.
  • $$-i^2$$
  • $$(-i)^2$$
  • $$i^4$$
  • $$(-i)^4$$
  • $$-i^6$$
Find the number of prime numbers between $$20$$ and $$40$$, both inclusive.
  • Three
  • Four
  • Five
  • Six
  • Seven
What is the sum of the least prime number and the greatest negative even integer?
  • $$10$$
  • $$0$$
  • $$1$$
  • $$2$$
  • $$3$$
What is the least positive integer that is the product of $$3$$ different prime numbers greater than $$2$$?
  • $$27$$
  • $$45$$
  • $$63$$
  • $$75$$
  • $$105$$
How many prime numbers are less than $$50$$?
  • $$16$$
  • $$15$$
  • $$14$$
  • $$18$$
What is the value of $$x$$ for which $$x, x + 1, x + 3$$ are all prime numbers?
  • $$0$$
  • $$1$$
  • $$2$$
  • $$101$$
The smallest 3 digit prime number is:
  • $$101$$
  • $$103$$
  • $$109$$
  • $$113$$
Which of the following number is a prime?
  • $$667$$
  • $$861$$
  • $$481$$
  • $$331$$
The complex number $$e^{i\theta }$$ can be expressed in vector form by
  • $$\sin \theta + i\cos \theta $$
  • $$\cos \theta + i\sin \theta $$
  • both $$(a)$$ and $$(b)$$
  • none of these
Which of the following is a prime number?
  • $$33$$
  • $$81$$
  • $$93$$
  • $$97$$
Consider the following numbers.
$$247$$
$$203$$
Which of the above number is/are prime?
  • $$1$$ only
  • $$2$$ only
  • Both $$1$$ and $$2$$
  • Neither $$1$$ nor $$2$$
Which one of the following is a prime number?
  • $$184$$
  • $$171$$
  • $$173$$
  • $$221$$
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