Number Systems Test

Result

Number Systems Test - 36

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Find one irrational number between 0.2101 and 0.2222.

A
$$0.2$$

B
$$0.25$$

C
$$0.22010010001..$$

D
None of these

Solution

Given Numbers are $$0.2101$$ which is terminating decimal and $$0.22222$$__ which is non terminating recurring decimal.

$$\Rightarrow$$ Irrational Numbers are non terminating and nonrecurring decimals

In between $$0.2101$$ and $$0.2222 ...$$, we can find $$0.220$$

Now,
We can write the irrational number as given in the above figure $$\rightarrow $$
REF. IMAGE

Hence $$0.2201001000100001....$$ is an irrational number that lies in between $$0.2101$$ and $$0.2222....$$
Question 2
1 / -0

Give an example of two irrational numbers whose sum is an irrational number.

A
$$2\sqrt{5},-2\sqrt{5}$$

B
$$\sqrt{5},-\sqrt{5}$$

C
$$2\sqrt{5},3\sqrt{5}$$

D
None of the above

Solution

$$2\sqrt{5},3\sqrt{5}$$ are the irrational numbers and their sum,

$$2\sqrt{5}+3\sqrt{5} = 5 \sqrt 5$$ is an irrational number.
Question 3
1 / -0

Give an example of two irrational numbers whose sum is a rational number.

A
$$\sqrt{3},\sqrt{5}$$

B
$$\sqrt{5},\sqrt{6}$$

C
$$\sqrt{5}, -\sqrt{5}$$

D
None of the above

Solution

$$\sqrt{5},-\sqrt{5}$$ are the irrational numbers, their sum

$$\sqrt{5}-\sqrt{5}=0$$ is a rational number
Question 4
1 / -0

Simplify:$$\dfrac{7+3\sqrt{5}}{3+\sqrt{5}}-\dfrac{7-3\sqrt{5}}{3-\sqrt{5}}$$

A
$$ \sqrt{15} $$

B
$$ \sqrt{5} $$

C
$$ \sqrt{7} $$

D
None of the above

Solution

Given,

$$\dfrac{7+3\sqrt{5}}{3+\sqrt{5}}-\dfrac{7-3\sqrt{5}}{3-\sqrt{5}}$$

$$=\dfrac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)-\left(7-3\sqrt{5}\right)\left(3+\sqrt{5}\right)}{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}$$
$$=\dfrac{21-7\sqrt5+9\sqrt5-15-21-7\sqrt5+9\sqrt5+15}{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}$$
$$=\dfrac{4\sqrt{5}}{3^2-(\sqrt 5)^2}$$ By using $$(a+b)(a-b)=a^2-b^2$$

$$=\dfrac{4\sqrt 5}{4}=\sqrt 5$$
Question 5
1 / -0

$$a\times a\times b\times b\times b$$ can be written as

A
$$a^2b^3$$

B
$$a^3b^2$$

C
$$a^3b^3$$

D
$$a^5b^5$$

Solution

we have, $$a\times a\times b\times b\times b$$
$$=a^2 \times b^3 =a^2b^3$$

Hence, $$a\times a\times b\times b\times b$$ can be written as $$a^2b^3$$
Question 6
1 / -0

Which of the following rational numbers is positive?

A
$$-\dfrac{8}{7}$$

B
$$\dfrac{19}{-13}$$

C
$$\dfrac{-3}{-4}$$

D
$$\dfrac{-21}{12}$$

Solution

$$\Rightarrow \dfrac{-3}{-4}= \dfrac{3}{4}$$
The numerator and denominator both are negative, it will cancel out each other and gives a positive rational number.
Question 7
1 / -0

Which of the following rational numbers is negative?

A
$$-\left(\dfrac{-3}{7}\right)$$

B
$$\dfrac{-5}{-8}$$

C
$$\dfrac{9}{8}$$

D
$$\dfrac{3}{-7}$$

Solution

$$(a) \Rightarrow -\left(\dfrac{-3}{7}\right)=\dfrac{3}{7}$$

$$(b) \Rightarrow \dfrac{-5}{-8}=\dfrac{5}{8}$$

$$(c) \Rightarrow \dfrac{9}{8}=\dfrac{9}{8}$$

$$(d) \Rightarrow \dfrac{3}{-7}=-\dfrac{3}{7}$$

$$\therefore -\dfrac{3}{7}$$ is a negative rational number.
Question 8
1 / -0

A number of the form $$\dfrac{p}{q}$$ is said to be a rational number if

A
p and q are integers

B
p and q are integers and $$q \neq 0$$

C
p and q are integers and $$p \neq 0$$

D
p and q are integers and $$p \neq 0$$ also $$q \neq 0$$

Solution
Question 9
1 / -0

$$\left(\dfrac {1}{10}\right)^0$$ is equal to

A
$$0$$

B
$$\dfrac {1}{10}$$

C
$$1$$

D
$$10$$

Solution

Using law of exponents, $$a^0=1$$
where $$a\neq 1$$
$$\Rightarrow \ \left(\dfrac {1}{10}\right)^0 =1$$
Question 10
1 / -0

By solving $$(6^0 -7^0) \times (6^0+7^0)$$, we get ________.

A
$$1$$

B
$$0$$

C
$$2$$

D
$$-1$$

Solution

$$0$$
$$(6^0 -7^0) \times (6^0+7^0)$$
$$=(1-1) \times (1+1)$$
$$=0\times 2=0$$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Number Systems Test - 36

Result

Number Systems Test - 36

Score

-

Rank

-

SHARING IS CARING

Question 1

$$0.2$$

$$0.25$$

$$0.22010010001..$$

None of these

Solution

Question 2

$$2\sqrt{5},-2\sqrt{5}$$

$$\sqrt{5},-\sqrt{5}$$

$$2\sqrt{5},3\sqrt{5}$$

None of the above

Solution

Question 3

$$\sqrt{3},\sqrt{5}$$

$$\sqrt{5},\sqrt{6}$$

$$\sqrt{5}, -\sqrt{5}$$

None of the above

Solution

Question 4

$$ \sqrt{15} $$

$$ \sqrt{5} $$

$$ \sqrt{7} $$

None of the above

Solution

Question 5

$$a^2b^3$$

$$a^3b^2$$

$$a^3b^3$$

$$a^5b^5$$

Solution

Question 6

$$-\dfrac{8}{7}$$

$$\dfrac{19}{-13}$$

$$\dfrac{-3}{-4}$$

$$\dfrac{-21}{12}$$

Solution

Question 7

$$-\left(\dfrac{-3}{7}\right)$$

$$\dfrac{-5}{-8}$$

$$\dfrac{9}{8}$$

$$\dfrac{3}{-7}$$

Solution

Question 8

p and q are integers

p and q are integers and $$q \neq 0$$

p and q are integers and $$p \neq 0$$

p and q are integers and $$p \neq 0$$ also $$q \neq 0$$

Solution

Question 9

$$0$$

$$\dfrac {1}{10}$$

$$1$$

$$10$$

Solution

Question 10

$$1$$

$$0$$

$$2$$

$$-1$$

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.