Number Theory Test 7

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Number Theory Test 7

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Weekly Quiz Competition

Question 1
1 / -0

The number which have more than two factors is called _____.

A
Even

B
Prime

C
Odd

D
None of these

Solution

The number with more than two factors is called a composite number.
So option C is the correct answer.
Question 2
1 / -0

If i = $$\sqrt {-1}, then 1 + i^2 + i^3 -i^6 + i^8 $$ is equal to -

A
2- i

B
1

C
-3

D
-1

Solution

Given, $$i= \sqrt {-1}$$
$$\therefore 1+i^{ 2 }+i^{ 3 }-i^{ 6 }+i^{ 8 }=1-1-i+1+1$$
$$=2-i$$
Question 3
1 / -0

($$i^{10}+1) (i^9 + 1)(i^8 +1).......(i+1)$$ equal to

A
-1

B
1

C
0

D
i

Solution

$$(i^{10}+1) (i^9 + 1)(i^8 +1).......(i+1)$$
$$=(i^{10}+1) (i^9 + 1)(i^8 +1).......(i^3+1)(i^2+1)(i+1)$$
$$=(i^{10}+1) (i^9 + 1)(i^8 +1).......(i^3+1)(-1+1)(i+1)[\because i^2=-1]$$
$$=(i^{10}+1) (i^9 + 1)(i^8 +1).......(i^3+1)(0)(i+1) =0$$
Question 4
1 / -0

Twin primes consist of

A
composite numbers

B
prime numbers

C
even numbers

D
none of these

Solution

Twin primes are prime numbers which differ by $$2.$$
So, options $$B$$ is correct.
Question 5
1 / -0

The two consecutive prime numbers with difference 2 are called

A
co-primes

B
twin primes

C
composite

D
none

Solution

Twin prime numbers are two consecutive prime numbers with a difference of $$2$$.
For eg. $$\{3,5\}$$ and $$\{5,7\}$$ are twin prime numbers.
Hence, option B is correct.
Question 6
1 / -0

Identify the prime number among the following options.

A
$$11$$

B
$$15$$

C
$$18$$

D
$$20$$

Solution

$$11$$ is a prime number because it has only two factors that are $$1$$ and $$11$$.
So, option A is correct.
Question 7
1 / -0

Which of the following is/are not twin prime(s)?

A
$$(2, 3)$$

B
$$(41,43)$$

C
$$(17, 19)$$

D
$$(59, 61)$$

Solution

$$3 - 2 = 1$$
They don't differ by $$2$$.
Rest other options are prime numbers that differ by $$2.$$
So, option $$A$$ is correct.
Question 8
1 / -0

Sum of first three prime numbers which end at 3 is:

A
20

B
16

C
39

D
40

Solution

First three prime numbers which end with $$3$$ are $$3,13,23$$.
$$Sum=3+13+23=39$$
Question 9
1 / -0

Which of the following is the factor of all prime numbers?

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

Option $$A$$ is correct because $$1$$ is the factor of all prime numbers.
Question 10
1 / -0

The product of $$2 \times 7 \times 3 \times 5$$ is a .........

A
composite number

B
prime number

C
negative number

D
none of the above

Solution

Composite numbers are numbers which have more then $$2$$ factors. They have at least $$1$$ factor more than $$1$$ and the number itself.
The given expression has more than $$2$$ factors. So, it is a Composite number.
Therefore, $$A$$ is the correct answer.

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Re-Attempt Weekly Quiz Competition

Number Theory Test 7

Result

Number Theory Test 7

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SHARING IS CARING

Question 1

Even

Prime

Odd

None of these

Solution

Question 2

2- i

1

-3

-1

Solution

Question 3

-1

1

0

i

Solution

Question 4

composite numbers

prime numbers

even numbers

none of these

Solution

Question 5

co-primes

twin primes

composite

none

Solution

Question 6

$$11$$

$$15$$

$$18$$

$$20$$

Solution

Question 7

$$(2, 3)$$

$$(41,43)$$

$$(17, 19)$$

$$(59, 61)$$

Solution

Question 8

20

16

39

40

Solution

Question 9

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 10

composite number

prime number

negative number

none of the above

Solution

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