Number Theory Test 44

Result

Number Theory Test 44

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Weekly Quiz Competition

Question 1
1 / -0

Given $$ z _ { 1 } + 3 z _ { 2 } - 4 z _ { 3 } = 0 $$ then $$ z _ { 1 } , z _ { 2 } , z _ { 3 } $$ are

A
collinear

B
can form sides of equilateral $$ \Delta $$

C
lie on circle

D
none of these

Solution
Question 2
1 / -0

If z be a complex number satisfying $$z^{4}+z^{3}+2z^{2}+z+1=0$$ then $$\left|z\right|=$$

A
$$\dfrac{1}{2}$$

B
$$\dfrac{3}{4}$$

C
$$1$$

D
none of these

Solution

$$z^{4}+z^{3}+2z^{2}+z+1=0$$
$$\Rightarrow z^{4}+z^{2}+z^{3}+z+z^{2}+1=0$$ by rearranging
$$\Rightarrow z^{2}(z^{2}+1)+z(z^{2}+1)+1(z^{2}+1)=0$$
$$\Rightarrow z^{2}(z^{2}+1)+(z^{2}+1)(z+1)=0$$
$$\Rightarrow (z^{2}+1)(z^{2}+z+1)=0$$
$$\Rightarrow z^{2}+1=0, z^{2}+2+1=0$$
$$\Rightarrow z=\pm i, z=\frac{-1\pm i\sqrt{3}}{2}$$
$$\therefore z=i, -i, \frac{-1+i\sqrt{3}}{2},\frac{-1-i\sqrt{3}}{2}$$
$$\therefore |z|=+1$$
Question 3
1 / -0

Which of the following is a prime number

A
391

B
899

C
621

D
199

Solution
Question 4
1 / -0

A number system with a base of two is referred as ______________.

A
Unary number system

B
Binary number system

C
Octal number system

D
None of these
Question 5
1 / -0

Which of the following is true?

A
Byte is a single digit in a binary number

B
Bit represents a grouping of digital numbers

C
Eight-digit binary number is called a bit

D
Eight-digit binary number is called a byte
Question 6
1 / -0

If a register containing data (11001100)2 is subjected to arithmetic shift left operation, then the content of the register after 'ashl' shall be _____________.

A
(11001100)2

B
(1101100)2

C
(10011001)2

D
(10011000)2
Question 7
1 / -0

C it refers to a _____________.

A
computer language.

B
CPU instruction.

C
0 or 1 value.

D
digital representation of an alphabetic character.
Question 8
1 / -0

Mark the correct alternative of the following.
Which of the following numbers is prime?

A
$$23$$

B
$$51$$

C
$$38$$

D
$$26$$

Solution
Question 9
1 / -0

Which of the following is a prime number?

A
$$203$$

B
$$139$$

C
$$115$$

D
$$161$$

Solution
Question 10
1 / -0

The least prime is?

A
$$1$$

B
$$2$$

C
$$3$$

D
$$5$$

Solution

The number $$2$$ is the least prime. It is the only even prime also.