Number Theory Test 5

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Number Theory Test 5

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Weekly Quiz Competition

Question 1
1 / -0

All prime numbers are

A
even numbers

B
odd numbers

C
composite numbers

D
odd numbers except 2

Solution

Prime numbers are $$2,3,5,7,11,13,....$$

Only $$2$$ is an even number and others are odd numbers.

So, all prime numbers are odd numbers except for $$2$$.

Hence, correct answer is option D.
Question 2
1 / -0

The prime number that comes just after 47 is ......

A
57

B
51

C
53

D
none of these

Solution

After $$47$$,
$$48,49,50,51,52$$ are composite numbers; but, $$53$$ is a prime number, as it has no factor other than 1 and itself.
So correct answer will be option C
Question 3
1 / -0

The number which is neither prime nor composite is

A
$$0$$

B
$$1$$

C
$$2$$

D
$$5$$

Solution

$$1$$ is the number which is neither prime nor composite.
Because $$1$$ has only $$1$$ divisor which is $$1$$ only.
Question 4
1 / -0

Which prime number which comes just after $$43$$ ?

A
$$49$$

B
$$45$$

C
$$47$$

D
none of these

Solution

Numbers after $$ 43 $$ are $$ 43, 44, 45, 46, 47, 48... $$

$$ 44 $$ is a composite number as it has more than two factors $$ 1, 2, 11, 22, 44 $$
Similarly, $$ 45, 46 $$ has more than two factors.

However $$ 47 $$ has only two factors $$ 1, 47 $$.
Thus the next prime number after $$ 43 $$ is $$ 47. $$
Question 5
1 / -0

Number of prime numbers between $$50$$ to $$60$$ is

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

Prime numbers between 50 and 60 are 53 and 59.
Question 6
1 / -0

Every prime number is $$.......$$

A
a even number

B
an odd number

C
a composite number

D
none of these

Solution

Prime numbers have only two factors $$ 1 $$ and the number itself.

For example, $$ 2, 3, 5, 7, 11.. $$

From this, we notice that all prime numbers cannot be put to one category except being non-composite.
Question 7
1 / -0

A prime number

A
has exactly one factor.

B
has exactly two factors.

C
is not divisible by $$2$$.

D
is an odd number.

Solution

A prime number has only two factors.
For eg. $$11, 17$$, etc..
Each of these numbers is divisible by $$1$$ and itself.
Hence, option B is correct.
Question 8
1 / -0

Which of the following are prime numbers?

A
$$137$$

B
$$143$$

C
$$396$$

D
Both A and B

Solution

$$143=11\times 13$$
$$396=2\times198$$
Only $$137$$ is a prime number.
Question 9
1 / -0

Number of prime numbers between $$50$$ to $$60$$ is

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

The prime numbers between $$50$$ and $$60$$ are $$53$$ and $$59.$$
Hence, number of prime numbers between $$50$$ and $$60$$ is $$2.$$
Question 10
1 / -0

$$\displaystyle \frac{\displaystyle i^{4n + 3} + (-i)^{8n - 3}}{\displaystyle(i)^{12 n- 1} - i^{2 - 16 n}}, n \varepsilon N$$ is equal to

A
1 + i

B
2i

C
-2i

D
-1 - i

Solution

Given expression
$$= \displaystyle \frac{\displaystyle i^3 + (-1) (i)^{-3}}{(-i)^{-1} - (i)^2} = \frac{\displaystyle -i - i}{\displaystyle i + 1}$$
$$=\displaystyle \frac{\displaystyle -2i}{1 + i} \times \frac{1 - i}{1 - i} = \frac{\displaystyle -2i - 2}{\displaystyle 1 + 1} = - 1 - i$$

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Re-Attempt Weekly Quiz Competition

Number Theory Test 5

Result

Number Theory Test 5

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SHARING IS CARING

Question 1

even numbers

odd numbers

composite numbers

odd numbers except 2

Solution

Question 2

57

51

53

none of these

Solution

Question 3

$$0$$

$$1$$

$$2$$

$$5$$

Solution

Question 4

$$49$$

$$45$$

$$47$$

none of these

Solution

Question 5

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 6

a even number

an odd number

a composite number

none of these

Solution

Question 7

has exactly one factor.

has exactly two factors.

is not divisible by $$2$$.

is an odd number.

Solution

Question 8

$$137$$

$$143$$

$$396$$

Both A and B

Solution

Question 9

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 10

1 + i

2i

-2i

-1 - i

Solution

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