MCQ Questions for Class 9 Maths Number Systems Quiz 11

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

0%
$0$
0%
$\dfrac {1}{10}$
0%
$1$
0%
$10$

Explanation

Using law of exponents,

$a^0=1$
where

$a\neq 1$

$\Rightarrow \ \left(\dfrac {1}{10}\right)^0 =1$

By solving

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

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$1$
0%
$0$
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$2$
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$-1$

Explanation

$0$

$(6^0 -7^0) \times (6^0+7^0)$

$=(1-1) \times (1+1)$

$=0\times 2=0$

State whether the following statement is true of false? Justify your answer.
The square of an irrational number is always rational.

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True
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False

Explanation

The given statement is false.

Because, consider an irrational number

$\sqrt [4]{2}$ . Then, its square

$(\sqrt [4]{2})^{2} = \sqrt {2}$ , which is not a rational number.

State whether the following statement is true of false? Justify your answer.

$\dfrac {\sqrt {15}}{\sqrt {3}}$ is written in the form

$\dfrac {p}{q}$ , where

$q \neq 0$ so its is rational number.

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True
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False

Explanation

Rational number is a number which can be written in form

$\cfrac pq$ , where

$p,q$ are both integers.

The given statement is false.

Because,

$\dfrac {\sqrt {15}}{\sqrt {3}} = \sqrt {\dfrac {15}{3}} = \sqrt {5} = \dfrac {\sqrt {5}}{1}$ , where

$p = \sqrt {5}$ is irrational number.

We, cannot write

$\sqrt5$ in

$\cfrac pq$ form with

$p,q$ both integers, so it is irrational number.

A rational number between

$\sqrt {2}$ and

$\sqrt {3}$ is

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$\dfrac {\sqrt {2} + \sqrt {3}}{2}$
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$\dfrac {\sqrt {2} \cdot \sqrt {3}}{2}$
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$1.5$
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$1.8$

Explanation

We know that

$\sqrt {2} = 1.4142135....$ and

$\sqrt {3} = 1.732050807 ...$

So, we can clearly see that

$1.5$ is a rational number and it lies between

$1.4142135...$ and

$1.732050807...$

Hence,

$(C)$ is the correct answer.

State whether the following statement is true (T) or false (F):

$5^0 \times 3^0 = 8^0$

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True
0%
False

Explanation

$5^0 \times 3^0 = 8^0$

$1 \times 1 =1$ (

$\because 5^0=1, 3^0 = 1, 8^0 =1$ )

Are the following statements true or false? Give reasons for your answers.
Every rational number is a whole number.

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True
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False

Explanation

False
Rational numbers- All numbers in the form p/q, where p and q are integers and

$\mathrm{q} \neq 0$ .
i.e., Rational numbers

$=0,19 / 30,2,9 /(-3),(-12) / 7 \ldots$
Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)
i.e., Whole numbers

$=0,1,2,3 \ldots$
Hence, we can say that integers includes whole numbers as well as negative numbers.

$\therefore$ Every whole numbers are rational, however, every rational number are not whole numbers.

Choose the correct alternative answer for the question given below.
Which one of the following is an irrational number?

0%
$\sqrt{\dfrac{16}{25}}$
0%
$\sqrt{5}$
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$\dfrac{3}{9}$
0%
$\sqrt{196}$

Explanation

Since,

$\sqrt{\dfrac{16}{25}}=\dfrac{4}{5}$ is a rational number;

$\dfrac{3}{9}$ is a rational number,

$\sqrt{196}=14$ is a rational number; and

$\sqrt{5}$ is an irrational number.

Choose the correct alternative answer for the question given below.
What is

$\sqrt{n}$ , if n is not a perfect square number?

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Natural number
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Rational number
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Irrational number
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Options A, B, C all are correct

Explanation

If n is not a perfect square number, then

$\sqrt{n}$ is an irrational number.

Every terminating decimal is:

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a natural number
0%
a rational number
0%
an integer
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a whole number

Which of the following is not an irrational number?

0%
$\sqrt{2}$
0%
$\sqrt{3}$
0%
$\sqrt{9}$
0%
$\sqrt{5}$

State whether the following statements are true or false. Give reasons for your answers :
Every rational number is a whole number.

0%
True
0%
False

Explanation

False.
Because

$\dfrac{1}{2}$ is a rational number but not a whole number.

Every integer can be identified with a rational number

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True
0%
False

$\sqrt{2}$ is

0%
a rational number
0%
an irrational number
0%
an integer
0%
a natural number

Explanation

${\textbf{Step - 1: Formation}}$

$\sqrt 2 {\text{ = }}\dfrac{{\text{p}}}{{\text{q}}}$

${{\text{Here p and q are coprime numbers and q}} \ne {\text{0}}}$

${\sqrt 2 {\text{ = }}\dfrac{{\text{p}}}{{\text{q}}}}$

${{\text{On squaring both the sides we get,}}}$

${{\Rightarrow \text{ 2 = }}{{\left( {\dfrac{{\text{p}}}{{\text{q}}}} \right)}^{\text{2}}}}$

${{\Rightarrow \text{ 2}}{{\text{q}}^{\text{2}}}{\text{ = }}{{\text{p}}^{\text{2}}}{{ \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots }}..\left( {\text{1}} \right)}$

${\Rightarrow} \dfrac{{{p^2}}}{2} = q$

${\textbf{Step - 2: Calculation}}$

${\text{So 2 divides p and p is multiple of 2}}$

$\Rightarrow {\text{p = 2m}}$

$\Rightarrow {{\text{p}}^2} = 4{m^2} ..........................(2)$

${\text{From equation (1) and (2), we get}}$

$\Rightarrow 2{q^2} = 4{m^2}$

$\Rightarrow {q^2} = 2{m^2}$

${q^2}\;{\text{is amultiple of 2}}$

${\text{So, q is multiple of 2}}$

${\text{Hence, p, q have a common factor 2. This contradicts our assumption that they are co-primes. }}$

${\text{Therefore, p/q is not a rational number}}$

$\sqrt 2{\text{ is an irrational number.}}$

${\textbf{Hence, the correct answer is option B.}}$

Choose correct answer (s) from given choice
An example of a rational number between

$\sqrt { 2 }$ and

$\sqrt { 15 }$ is

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3.9
0%
2.6
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$\dfrac { \sqrt { 2 } +\sqrt { 15 } }{ 2 }$
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$\dfrac { \sqrt { 2 } X\sqrt { 15 } }{ 2 }$

Which of the following is rational

0%
$\sqrt { 3 }$
0%
p
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$\dfrac { 4 }{ 0 }$
0%
$\dfrac { 0 }{ 4 }$

Which of the following numbers is a rational number?

0%
$x ^ { 2 } = 7$
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$x ^ { 2 } = \cfrac { 17 } { 4 }$
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$y ^ { 2 } = 16$
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$b ^ { 2 } = 0.4$

$x=\frac { 2 }{ \sqrt { 3 } -\sqrt { 5 } }\ and\quad y=\frac { 2 }{ \sqrt { 3 } +\sqrt { 5 } } \quad then\quad x+y=$

0%
3
0%
$4\sqrt { 3 }$
0%
$-2\sqrt { 3 }$
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6

Which of the following is a rational number ?

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$3^{ \dfrac { 29 }{ 27 } }.3^{ \dfrac { 27 }{ 29 } }$
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$\sqrt [ 6 ]{ \left( 3^{ \dfrac { 50 }{ 51 } }.3^{ \dfrac { 52 }{ 51 } } \right) } ^{ 3 }$
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$3^{ \dfrac { 15 }{ 8 } }-3^{ \dfrac { 7 }{ 8 } }$
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$\sqrt [ 15 ]{ (3^{ 3 })^{ 1/5 } }$

Which of the following pairs represent the same rational number? Tick

$\left( \surd \right)$ in the against them.

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$\dfrac { -4 }{ 9 } and\dfrac { 12 }{ -27 }$ ________
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$\dfrac { 7 }{ 3 } and\dfrac { -21 }{ -9 }$ __________
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$\dfrac { 15 }{ 11 } and\dfrac { 45 }{ -33 }$ __________
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$\dfrac { -3 }{ 5 } and\dfrac { -30 }{ -50 }$ _________

List five rational numbers between :

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-1 and 0
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-2 and -1
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$\dfrac { -4 }{ 5 } and\dfrac { -2 }{ 3 }$
0%
$\dfrac { 1 }{ 2 } and\dfrac { 2 }{ 3 }$

The simplest rationalising factor of

$\sqrt [ 3 ]{ 500 }$ is

0%
$\sqrt [ 3 ]{ 2 }$
0%
$\sqrt [ 3 ]{ 5 }$
0%
$\sqrt { 3 }$
0%
None

The value of $$\left( \sqrt { 2 } +1 \right) ^{ 6 }+\left( \sqrt { 2 } -1 \right) ^{ 6 }$4

0%
99
0%
182
0%
196
0%
198

Find whether the following statements are true or false.
Irrational numbers cannot be represented by points on the number line.

0%
True
0%
False

State whether the statements are true (T) or false (F).
The negative of a negative rational number is a positive rational number.

0%
True
0%
False

CBSE Questions for Class 9 Maths Number Systems Quiz 11 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Number Systems Quiz 11 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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