Number Systems Test

Result

Number Systems Test - 17

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

The value of $2\sqrt {3} + \sqrt {3}$ is equal to

A
$2\sqrt {6}$

B
$3\sqrt {3}$

C
$4\sqrt {6}$

D
$6$

Solution

$2\sqrt { 3 } +\sqrt { 3 } =\left( 2+1 \right) \sqrt { 3 } =3\sqrt { 3 }$
Question 2
1 / -0

Two rational numbers between $\dfrac{2}{3}$ and $\dfrac{5}{3}$ are :

A
$\dfrac{1}{6}$ and $\dfrac{2}{6}$

B
$\dfrac{1}{2}$ and $\dfrac{2}{1}$

C
$\dfrac{5}{6}$ and $\dfrac{7}{6}$

D
$\dfrac{2}{3}$ and $\dfrac{4}{3}$

Solution

Changing the denominators of both numbers to 6, we get
$\dfrac { 2 }{ 3 } =\dfrac { 4 }{ 6 } \quad \& \quad \dfrac { 5 }{ 3 } =\dfrac { 10 }{ 6 }$
Numbers between the given rational numbers from the options are
$\dfrac { 5 }{ 6 } \quad \& \quad \dfrac { 7 }{ 6 }$
So, correct answer is option C.
Question 3
1 / -0

A number is an irrational if and only if its decimal representation is:

A
non terminating

B
non terminating and repeating

C
non terminating and non repeating

D
terminating

Solution

According to definition of irrational number, If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without recurring digits.
Hence, a number having non terminating and non repeating decimal representation is an irrational number.
So, option C is correct.
Question 4
1 / -0

Every rational number is

A
A natural number

B
An integer

C
A real number

D
A whole number

Solution

Real number is a value that represents a quantity along the number line.
Real number includes all rational and irrational numbers.
Rational numbers are numbers which can be represented in the form $\dfrac { p }{ q }$ where, $q\neq 0$ and $p,q$ are integers.
Therefore, rational number is a subset of real number.

We know that rational and irrational numbers taken together are known as real numbers. Therefore, every real number is either a rational number or an irrational number. Hence, every rational number is a real number. Therefore, (c) is the correct answer.
Question 5
1 / -0

Between any two rational numbers,

A
there is no rational number

B
there is exactly one rational number

C
there are infinitely many rational numbers

D
there are only rational numbers and no irrational numbers

Solution

Recall that to find a rational number between $r$ and $s,$ you can add

$r$ and $s$ and divide the sum by $2,$ that is $\displaystyle \frac { r+s }{ 2 }$ lies between r and s.
For example, $\displaystyle \frac { 5 }{ 2 }$ is a number between $2$ and

$3.$ We can proceed in this manner to find many more rational numbers between $2$ and $3.$
Hence, we can conclude that there are infinitely many rational numbers between any two given rational numbers.
Question 6
1 / -0

The decimal expansion of $\pi$ is :

A
terminating

B
non-terminating and non-recurring

C
non-terminating and recurring

D
doesnt exist

Solution

We know that $\pi$ is irrational number and Irrational numbers have decimal expansions that neither terminate nor become periodic.
So, correct answer is option $B$ .
Question 7
1 / -0

The rationalizing factor of $(a+\sqrt{b})$ is

A
$a-\sqrt{b}$

B
$\sqrt{a}-b$

C
$\sqrt{a}-\sqrt{b}$

D
None of these

Solution

The rationalizing factor of a+ $\sqrt { b }$ is a- $\sqrt { b }$ as the product of these two expressions give a rational number.
Question 8
1 / -0

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

A
Whole numbers

B
Rational numbers

C
Irrational numbers

D
Integers

Solution

$\sqrt{2}, \sqrt{3}$ are irrational numbers.
Because these two values cannot be written in the form of p/q where p and q both are integers and q should not be equal to zero .
Question 9
1 / -0

The value of $(6 + \sqrt{27}) - (3 + \sqrt{3}) + (1 - 2\sqrt{3})$ when simplified is :

A
positive and irrational

B
negative and rational

C
positive and rational

D
negative and irrational

Solution

$6+\sqrt { 27 } -(3+\sqrt { 3 } )+(1-2\sqrt { 3 } )=6+3\sqrt { 3 } -3-\sqrt { 3 } +1-2\sqrt { 3 } \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad =4$
$4$ is a positive rational number
Hence, correct answer is option C.
Question 10
1 / -0

Two rational numbers between $\dfrac{1}{5}$ and $\dfrac{4}{5}$ are :

A
1 and $\dfrac{3}{5}$

B
$\dfrac{2}{5}$ and $\dfrac{3}{5}$

C
$\dfrac{1}{2}$ and $\dfrac{2}{1}$

D
$\dfrac{3}{5}$ and $\dfrac{6}{5}$

Solution

Since the denominator of both rational numbers are same. So, for getting the rational numbers between the given rational numbers, we only have to consider the numerators of the rational numbers.
Two numbers between 1 & 4 are 2 and 3.
So, two rational numbers between the given rational numbers will be $\dfrac { 2 }{ 5 }$ and $\dfrac { 3 }{ 5 }$
So, correct answer is option B.

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Number Systems Test - 17

Result

Number Systems Test - 17

Score

-

Rank

-

SHARING IS CARING

Question 1

262\sqrt {6}26​

333\sqrt {3}33​

464\sqrt {6}46​

666

Solution

Question 2

16\dfrac{1}{6}61​ and 26\dfrac{2}{6}62​

12\dfrac{1}{2}21​ and 21\dfrac{2}{1}12​

56\dfrac{5}{6}65​ and 76\dfrac{7}{6}67​

23\dfrac{2}{3}32​ and 43\dfrac{4}{3}34​

Solution

Question 3

non terminating

non terminating and repeating

non terminating and non repeating

terminating

Solution

Question 4

A natural number

An integer

A real number

A whole number

Solution

Question 5

there is no rational number

there is exactly one rational number

there are infinitely many rational numbers

there are only rational numbers and no irrational numbers

Solution

Question 6

terminating

non-terminating and non-recurring

non-terminating and recurring

doesnt exist

Solution

Question 7

a−ba-\sqrt{b}a−b​

a−b\sqrt{a}-ba​−b

a−b\sqrt{a}-\sqrt{b}a​−b​

None of these

Solution

Question 8

Whole numbers

Rational numbers

Irrational numbers

Integers

Solution

Question 9

positive and irrational

negative and rational

positive and rational

negative and irrational

Solution

Question 10

1 and 35\dfrac{3}{5}53​

25\dfrac{2}{5}52​ and 35\dfrac{3}{5}53​

12\dfrac{1}{2}21​ and 21\dfrac{2}{1}12​

35\dfrac{3}{5}53​ and 65\dfrac{6}{5}56​

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.

$2\sqrt {6}$

$3\sqrt {3}$

$4\sqrt {6}$

$6$

$\dfrac{1}{6}$ and $\dfrac{2}{6}$

$\dfrac{1}{2}$ and $\dfrac{2}{1}$

$\dfrac{5}{6}$ and $\dfrac{7}{6}$

$\dfrac{2}{3}$ and $\dfrac{4}{3}$

$a-\sqrt{b}$

$\sqrt{a}-b$

$\sqrt{a}-\sqrt{b}$

1 and $\dfrac{3}{5}$

$\dfrac{2}{5}$ and $\dfrac{3}{5}$

$\dfrac{1}{2}$ and $\dfrac{2}{1}$

$\dfrac{3}{5}$ and $\dfrac{6}{5}$