Number Systems Test

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Number Systems Test - 23

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Question 1
1 / -0

The value of $$(10)^{0} \times (20)^{0}\times (30)^{0}$$ is:

A
$$1$$

B
$$3$$

C
$$60$$

D
$$0$$

Solution

$$(10)^{0} \times (20)^{0} \times (30)^{0} = 1\times 1\times 1 = 1$$

So, option $$A$$ is correct.
Question 2
1 / -0

The expression $$((2)^{0} + (3)^{0} + (5)^{0})^{0}$$ is equal to _____

A
$$3$$

B
$$1$$

C
$$10$$

D
$$0$$

Solution

$$((2)^{0} + (3)^{0} + (5)^{0})^{0} = (1 + 1 + 1)^{0}$$
$$= 3^{0}$$
$$= 1$$

So, option $$B$$ is the correct answer.
Question 3
1 / -0

Which of the following is equal to $$1$$?

A
$$(3)^{0} + (3)^{0}$$

B
$$(3)^{0} - (3)^{0}$$

C
$$(3)^{0}$$

D
$$(3^{3})^{0} + (3^{0})^{3}$$

Solution

$$\textbf{Step 1: Simplify the following expressions.}$$

$$(a)\ 3^0+3^0=1+1=2\neq 1$$

$$(b)\ 3^0-3^0=1-1=0\neq 1$$

$$(c)\ 3^0=1$$

$$(d)\ (3^3)^0+(3^0)^3=9^0+1^3=1+1=2\neq 1$$

$$\textbf{Hence, Option C is correct.}$$
Question 4
1 / -0

Simplify: $$\left((9)^{0} + (11)^{0} + (13)^{0}\right) \div (23)^{0}$$

A
$$1$$

B
$$3$$

C
$$0$$

D
$$2$$

Solution

$$\left((9)^{0} + (11)^{0} + (13)^{0}\right) \div (23)^{0}$$
$$= (1 + 1 + 1) \div 1$$
$$= 3\div 1$$
$$= 3$$
So, option $$B$$ is correct.
Question 5
1 / -0

What are rational numbers?

A
A number of the form $$\dfrac {p}{q}$$ where $$p$$ and $$q$$ are any positive integers and $$q\neq 0$$ is called a rational number.

B
A number of the form $$\dfrac {p}{q}$$ where $$p$$ and $$q$$ are any negative integers and $$q\neq 0$$ is called a rational number.

C
A number of the form $$\dfrac {p}{q}$$ where $$p$$ and $$q$$ are integers is called a rational number.

D
A number of the form $$\dfrac {p}{q}$$ where $$p$$ and $$q$$ are any integers and $$q\neq 0$$ is called a rational number.

Solution

A number of the form $$\dfrac {p}{q}$$ where $$p$$ and $$q$$ are any integers and $$q\neq 0$$ is called a rational number.

Ex:- Consider $$\dfrac{2}{3}$$ here $$2,3$$ are co-primes so the number $$\dfrac{2}{3}$$ is a rational number
Question 6
1 / -0

The value of $$((6)^{0} + (16)^{0}) \div ((7)^{0} + (17)^{0})$$ is _____

A
$$2$$

B
$$4$$

C
$$1$$

D
$$0$$

Solution

$$((6)^{0} + (16)^{0}) \div ((7)^{0} + (17)^{0})$$
$$ = (1 + 1)\div (1 + 1)$$
$$= 2\div 2$$
$$= 1$$
So, option $$C$$ is correct.
Question 7
1 / -0

The value of $$(100)^{0}$$ is _____.

A
$$1$$

B
$$0$$

C
$$100$$

D
$$1000$$

Solution

According to the law of power of $$0$$,
$$(100)^{0} = 1$$.

So, option $$A$$ is correct.
Question 8
1 / -0

Evaluate: $$({(10)^0} + (12)^{0})\times (18)^{0}$$

A
$$1$$

B
$$0$$

C
$$2$$

D
$$18$$

Solution

$$((10)^{0} + (12)^{0})\times (18)^{0} = (1 + 1) \times 1$$
$$= (2)\times 1$$
$$= 2$$
So. option $$C$$ is correct.
Question 9
1 / -0

$$\dfrac {7}{9}$$ is a/an _______ number.

A
rational

B
composite

C
irrational

D
prime

Solution

$$\dfrac{7}{9}$$ is of the form $$\dfrac {p}{q}$$ form , hence it is rational no.
Question 10
1 / -0

$$\sqrt {23}$$ is not a ...... number.

A
irrational

B
co-prime

C
composite

D
rational

Solution

As per the theorem, the square root of any prime number is irrational. $$\sqrt {23}$$ is a prime number, so is not a rational number. It is irrational.
Therefore, $$D$$ is the correct answer.

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Number Systems Test - 23

Result

Number Systems Test - 23

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SHARING IS CARING

Question 1

$$1$$

$$3$$

$$60$$

$$0$$

Solution

Question 2

$$3$$

$$1$$

$$10$$

$$0$$

Solution

Question 3

$$(3)^{0} + (3)^{0}$$

$$(3)^{0} - (3)^{0}$$

$$(3)^{0}$$

$$(3^{3})^{0} + (3^{0})^{3}$$

Solution

Question 4

$$1$$

$$3$$

$$0$$

$$2$$

Solution

Question 5

A number of the form $$\dfrac {p}{q}$$ where $$p$$ and $$q$$ are any positive integers and $$q\neq 0$$ is called a rational number.

A number of the form $$\dfrac {p}{q}$$ where $$p$$ and $$q$$ are any negative integers and $$q\neq 0$$ is called a rational number.

A number of the form $$\dfrac {p}{q}$$ where $$p$$ and $$q$$ are integers is called a rational number.

A number of the form $$\dfrac {p}{q}$$ where $$p$$ and $$q$$ are any integers and $$q\neq 0$$ is called a rational number.

Solution

Question 6

$$2$$

$$4$$

$$1$$

$$0$$

Solution

Question 7

$$1$$

$$0$$

$$100$$

$$1000$$

Solution

Question 8

$$1$$

$$0$$

$$2$$

$$18$$

Solution

Question 9

rational

composite

irrational

prime

Solution

Question 10

irrational

co-prime

composite

rational

Solution

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