MCQ Questions for Class 9 Maths Number Systems Quiz 10

$\sqrt 7$ is irrational.

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True
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False

Which of the following is irrational

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$\sqrt {\dfrac {4}{9}}$
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$\dfrac {4}{5}$
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$\sqrt {7}$
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$\sqrt {81}$

Explanation

${\textbf{Step-1: Identify rational and irrational}}$

$\text{A = }\sqrt{4/9}$

$\text{=}\sqrt{\text2/3}$ ${\text{Rational}}$

${\text{B = 4/5}}$ ${\text{Rational}}$

$\text{C = }\sqrt {\text{7}}$ ${\text{Irrational}}$

$\text{D = }\sqrt {{\text{81}}}$ = 9 ${\text{Rational}}$

${\textbf{Hence option C is correct}}$

Simplify

$2\sqrt{5}$ +

$10\sqrt{5}$ +

$25\sqrt{5}$ +

$31\sqrt{5}$ .

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$68\sqrt{5}$
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$28\sqrt{5}$
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$48\sqrt{5}$
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$\sqrt{5}$

Explanation

$2\sqrt{5}+10\sqrt{5}+25\sqrt{5}+31\sqrt{5}$

$=(2+10+25+31)\sqrt5$

$=68\sqrt{5}$

The product of

$6\sqrt {5}$ and

$2\sqrt {5}$ is

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$30$
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$60$
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$50$
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$12$

Find one irrational number between 0.2101 and 0.2222.

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$0.2$
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$0.25$
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$0.22010010001..$
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None of these

Explanation

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

$0.2222....$

1523747_1668362_ans_8a76b548ab774b4dbb31c192209c734c.png

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

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$2\sqrt{5},-2\sqrt{5}$
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$\sqrt{5},-\sqrt{5}$
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$2\sqrt{5},3\sqrt{5}$
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None of the above

Explanation

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

$2\sqrt{5}+3\sqrt{5} = 5 \sqrt 5$ is an irrational number.

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

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$\sqrt{3},\sqrt{5}$
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$\sqrt{5},\sqrt{6}$
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$\sqrt{5}, -\sqrt{5}$
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None of the above

Explanation

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

$\sqrt{5}-\sqrt{5}=0$ is a rational number

State whether the following statement is true of false? Justify your answer.
There are numbers which can be written in the form

$\dfrac {p}{q}, q\neq 0, p, q$ both are not integers.

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True
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False

Explanation

The given statement is true.

For example,

$\dfrac {\sqrt {3}}{\sqrt {5}}$ is of the form

$\dfrac {p}{q}$ but

$p = \sqrt {3}$ and

$q = \sqrt {5}$ are not integers.

Simplify:

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

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$\sqrt{15}$
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$\sqrt{5}$
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$\sqrt{7}$
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None of the above

Explanation

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

$(a+b)(a-b)=a^2-b^2$

$=\dfrac{4\sqrt 5}{4}=\sqrt 5$

State whether the statement is true/false.

$8$ can be written as a rational number with any integer as denominator.

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True
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False

State whether the statement is true/false.

Two rational numbers with different numerators cannot be equal.

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True
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False

State whether the statement is true/false.

Every rational number is a whole number.

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True
0%
False

State whether the given statement is true or false.
The sum of two irrational numbers is irrational.

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True
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False

Explanation

False. Sum of two irrational numbers can be rational if the irrational parts have the sum as zero so the result is rational.

For example,

$\sqrt{3}$ and

$-\sqrt{3}$

The sum is

$0$ , which is a rational number.

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

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$a^2b^3$
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$a^3b^2$
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$a^3b^3$
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$a^5b^5$

Explanation

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

$a^2b^3$

Which of the following rational numbers is negative?

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$-\left(\dfrac{-3}{7}\right)$
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$\dfrac{-5}{-8}$
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$\dfrac{9}{8}$
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$\dfrac{3}{-7}$

Explanation

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

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

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

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

$\therefore -\dfrac{3}{7}$ is a negative rational number.

State whether the statements given are True or False
Every negative integer is not a negative rational number

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True
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False

State whether the statements given are True or False

Every rational number is a whole number.

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True
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False

Explanation

As we know, whole numbers are 0,1,2,3... Where

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

State whether the statements given are True or False
Every integer is a rational number but not every rational number need be an integer.

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True
0%
False

State whether the statements given are True or False

In a rational number, denominator always has to be a non-zero integer.

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True
0%
False

Explanation

According to the definition of rational number, It can be written in the form of

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

$q$ is not equal to zero.Because any number divided by zero is not defined.

State whether the statements given are True or False
Every natural number is a rational number but not every rational number need to be natural number.

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True
0%
False

Explanation

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

State whether the statements given are True or False

If $\dfrac{p}{q}$ is a rational number and m is a non-zero integer, then $\dfrac{p}{q}=\dfrac{p\times m}{q\times m}$

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True
0%
False

Explanation

Let

$m=1,2...$
When

$m=1$ ,

$\dfrac{p}{q}=\dfrac{p\times1}{1\times q}=\dfrac{p}{q}$

$\dfrac{p}{q}=\dfrac{p\times2}{p\times 2}=\dfrac{p}{q}$

When

$m=2$
Hence,

$\dfrac{p}{q}=\dfrac{p\times m}{q\times m}$

State whether the statements given are True or False

Every fraction is a rational number.

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True
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False

State whether the statements given are True or False
Zero is a rational number

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True
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False

Explanation

It can be written as

$\dfrac{0}{1},$ which is a rational number in the form of

$\dfrac{p}{q},$ where q is not equal to zero.

State whether the statements are true (T) or false (F).
The population of India in

$2004-05$ is a rational number.

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True
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False

State whether the statements are true (T) or false (F).
Every whole number is a rational number.

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True
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False

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

$0$ is a whole number but it is not a rational number.

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True
0%
False

Explanation

$0$ is a whole number as well as a rational number.

Hence the given statemet is false

State whether the statements are true (T) or false (F).
0 is a rational number.

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True
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False

A number of the form

$\dfrac{p}{q}$ is said to be a rational number if

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

$(-4)^{4}\times (4)^{1}=(4)^{5}$

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True
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False

Explanation

False

$LHS=(-4)^{4}\times (4)^{1}$
Using law of exponents

$a^{m}\times a^{n}=a^{m+n}$

$(-4)^{4}\times (4)^{1}=(4)^{4+1} =(4)^{5}$

$\left(-\dfrac{8}{2}\right)^{0}=0$

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True
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False

Explanation

$LHS=\left(-\dfrac{8}{2}\right)^{0}$
Using law of exponent

$=a^{0}=1$

$\Rightarrow \left(-\dfrac{8}{2}\right)^{0}=1$

$LHS\neq RHS$

CBSE Questions for Class 9 Maths Number Systems Quiz 10 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Number Systems Quiz 10 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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