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Maths M.C.Q. [1 Marks Each]

Rational Numbers · Jharkhand Board (JAC) STD 8 (Jharkhand - English Medium). 25 questions.

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M.C.Q. [1 Marks Each]

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25 questions · auto-graded multiple-choice test.

MCQ 11 Mark
Between two given rational numbers, we can find:
  • A
    One and only one rational number.
  • B
    Only two rational numbers.
  • C
    Only ten rational numbers.
  • ✓
    Infinitely many rational numbers.
Answer
Correct option: D.
Infinitely many rational numbers.
We can find infinite many rational numbers between two given rational numbers.
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MCQ 21 Mark
The numerical expression $\frac{3}{8}+\frac{(-5)}{7}=\frac{-19}{56}$ shows that:
  • A
    Rational numbers are closed under addition.
  • ✓
    Rational numbers are not closed under addition.
  • C
    Rational numbers are closed under multiplication.
  • D
    Addition of rational numbers is not commutative.
Answer
Correct option: B.
Rational numbers are not closed under addition.
We have $\frac{3}{8}+\frac{(-5)}{7}=\frac{-19}{56}$
Show that rational numbers are closed under addition.
$\Big[\frac{3}{8}$ and $\frac{-5}{7}$ are rational numbers and their addition is $\frac{-19}{56}$ which is also rational number$\Big]$
Note The sun of any two rational numbers is always a rational number.
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MCQ 31 Mark
The reciprocal of $\frac{-3}{8}\times\Big(\frac{-7}{13}\Big)$ is:
  • ✓
    $\frac{104}{21}$
  • B
    $\frac{-104}{21}$
  • C
    $\frac{21}{104}$
  • D
    $\frac{-21}{104}$
Answer
Correct option: A.
$\frac{104}{21}$
Given number is $\frac{-3}{8}\times\Big(\frac{-7}{13}\Big)$
The product of $-\frac{3}{8}\times\Big(\frac{-7}{13}\Big)=\frac{21}{104}.$
Hence, the multiplicative inverse of $\frac{21}{104}$ is $\frac{104}{21}.$
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MCQ 41 Mark
The multiplicative inverse of $-1\frac{1}{7}$ is:
  • A
    $\frac{8}{7}$
  • B
    $\frac{-8}{7}$
  • C
    $\frac{7}{8}$
  • ✓
    $\frac{7}{-8}$
Answer
Correct option: D.
$\frac{7}{-8}$
We know that, if the product of two rational numbers is $1,$
Then they are multiplicative inverse of each other.
Given number is $-1\frac{1}{7},$ i.e. $\frac{-8}{7}.$
Let the multiplicative inverse of $-\frac{8}{7}$ be x.
$\Rightarrow\frac{-8}{7}\times\text{x}=1$
$\Rightarrow\text{x}=1\times\Big(-\frac{7}{8}\Big)$
$=\frac{7}{-8}$
Hence, $\frac{7}{-8}$ is the multiplication inverse of $-\frac{8}{7}.$
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MCQ 51 Mark
To get the product $1$, we should multiply $\frac{8}{21}$ by:
  • A
    $\frac{8}{21}$
  • B
    $\frac{-8}{21}$
  • ✓
    $\frac{21}{8}$
  • D
    $\frac{-21}{8}$
Answer
Correct option: C.
$\frac{21}{8}$
Let we should multiply $\frac{8}{21}$ by x.
Then according to question, $\text{x}\times\frac{8}{21}=1$
Hence, we should multiply $\frac{8}{21}$ by $\frac{21}{8},$ for getting the product $1.$
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MCQ 61 Mark
If $x + 0 = 0 + x = x$, which is rational number, then $0$ is called:
  • ✓
    Identity for addition of rational numbers.
  • B
    Additive inverse of $x.$
  • C
    Multiplicative inverse of $x.$
  • D
    Reciprocal of $x.$
Answer
Correct option: A.
Identity for addition of rational numbers.
We know that, the sum of any rational number and zero $(0)$ is the rational number itself.
Now, $x + 0 = 0 + x = x,$ which is a rational number, then $0$ is called identity for addition of rational numbers.
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MCQ 71 Mark
A number which can be expressed as $\frac{\text{p}}{\text{q}}$ where p and q are integers and $\text{q}\neq0$ is:
  • A
    Natural number.
  • B
    Whole number.
  • C
    Integer.
  • ✓
    Rational number.
Answer
Correct option: D.
Rational number.
A number Which can be experssed as $\frac{\text{p}}{\text{q}},$ where p and q are integers $\text{q}\neq0$ is a rational number.
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MCQ 81 Mark
The reciprocal of $1$ is:
  • ✓
    $1$
  • B
    $-1$
  • C
    $0$
  • D
    Not defined.
Answer
Correct option: A.
$1$
The reciprocal of $1$ is the number itself.
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MCQ 91 Mark
One $(1)$ is:
  • A
    The identity for addition of rational numbers.
  • B
    The identity for subtraction of rational numbers.
  • ✓
    The identity for multiplication of rational numbers.
  • D
    The identity for division of rational numbers.
Answer
Correct option: C.
The identity for multiplication of rational numbers.
One $(1)$ is the identity for multiplication of rational numbers.
That means,
If a is a rational number.
Then, $a - 1 = 1 - a = a$
Note: One $(1)$ is the multiplication identity for integers and whole number also.
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MCQ 101 Mark
Which of the following is an example of distributive property of multiplication over addition for rational numbers.
  • ✓
    $-\frac{1}{4}\times\bigg\{\frac{2}{3}+\Big(\frac{-4}{7}\Big)\bigg\}=\Big[-\frac{1}{4}\times\frac{2}{3}\Big]+\bigg[-\frac{1}{4}\times\Big(\frac{-4}{7}\Big)\bigg]$
  • B
    $-\frac{1}{4}\times\bigg\{\frac{2}{3}+\Big(\frac{-4}{7}\Big)\bigg\}=\Big[\frac{1}{4}\times\frac{2}{3}\Big]-\Big(\frac{-4}{7}\Big)$
  • C
    $-\frac{1}{4}\times\bigg\{\frac{2}{3}+\Big(\frac{-4}{7}\Big)\bigg\}=\frac{2}{3}+\Big(-\frac{1}{4}\Big)\times\frac{-4}{7}$
  • D
    $-\frac{1}{4}\times\bigg\{\frac{2}{3}+\Big(\frac{-4}{7}\Big)\bigg\}=\bigg\{\frac{2}{3}+\Big(\frac{-4}{7}\Big)\bigg\}-\frac{1}{4}$
Answer
Correct option: A.
$-\frac{1}{4}\times\bigg\{\frac{2}{3}+\Big(\frac{-4}{7}\Big)\bigg\}=\Big[-\frac{1}{4}\times\frac{2}{3}\Big]+\bigg[-\frac{1}{4}\times\Big(\frac{-4}{7}\Big)\bigg]$
We know that, the distributive property of multiplication over addition for rational numbers can be expressed as $a x (b + c) = ab + ac,$ where $a, b$ and $c$ are rational numbers.
Here, $-\frac{1}{4}\times\bigg\{\frac{2}{3}+\Big(\frac{-4}{7}\Big)\bigg\}=\Big[-\frac{1}{4}\times\frac{2}{3}\Big]+\bigg[-\frac{1}{4}\times\Big(\frac{-4}{7}\Big)\bigg]$
Is the example of distributive property of multiplication over addition for rational numbers.
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MCQ 111 Mark
If $x$ be any rational number then $x + 0$ is equal to:
  • ✓
    $x$
  • B
    $0$
  • C
    $-x$
  • D
    Not defined.
Answer
Correct option: A.
$x$
If $x$ is any rational number,
Then $x + 0 = x [0$ is the additive identity]
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MCQ 121 Mark
The reciprocal of any rational number $p$ and $q$, where $p$ and $q$ are integers and $\text{q}\neq0,$ is:
  • A
    $\frac{\text{p}}{\text{q}}$
  • B
    $1$
  • C
    $0$
  • ✓
    $\frac{\text{q}}{\text{p}}$
Answer
Correct option: D.
$\frac{\text{q}}{\text{p}}$
The reciprocal of any rational number $\frac{\text{p}}{\text{q}},$
Where p and q are integers and $\text{q}\neq0$ is $\frac{\text{q}}{\text{p}}.$
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MCQ 131 Mark
A number of the form $\frac{\text{p}}{\text{q}}$ is said to be a rational number if:
  • A
    $p$ and $q$ are integers.
  • ✓
    $p$ and $q$ are integers and $\text{q}\neq0$
  • C
    $p$ and $q$ are integers and $\text{p}\neq0$
  • D
    $p$ and $q$ are integers and $\text{p}\neq0$ also $\text{q}\neq0$
Answer
Correct option: B.
$p$ and $q$ are integers and $\text{q}\neq0$
A number of the form $\frac{\text{p}}{\text{q}}$ is said to be a rational number, if $p$ and $q$ are integers.
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MCQ 141 Mark
$-(-x)$ is same as:
  • A
    $-\text{x}$
  • ✓
    $\text{x}$
  • C
    $\frac{1}{\text{x}}$
  • D
    $\frac{-1}{\text{x}}$
Answer
Correct option: B.
$\text{x}$
$-(-x) = x$
Negative of negative rational number is equal to positive rational number.
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MCQ 151 Mark
Multiplicative inverse of a negative rational number is:
  • A
    A positive rational number.
  • ✓
    A negative rational number.
  • C
    $0$
  • D
    $1$
Answer
Correct option: B.
A negative rational number.
We know that, the product of two rational numbers is $1$, taken they are multiplication inverse of each other, e.g.
Suppose, $p$ is negative rational number, i.e.
$\frac{1}{\text{p}}$ is the multiplicative inverse of $-p,$
Then, $-\text{p}\times\frac{1}{-\text{p}}= 1$
Hence, multiplicative inverse of a negative rational number is a negative rational number.
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MCQ 161 Mark
$\frac{\text{x}+\text{y}}{2}$ is a rational number.
  • ✓
    Between $x$ and $y.$
  • B
    Less than $x$ and $y$ both.
  • C
    Greater than $x$ and $y$ both.
  • D
    Less than $x$ but greater than $y.$
Answer
Correct option: A.
Between $x$ and $y.$
Let $x$ and $y$ be two numbers.
Case-I If $x < y$
Then, $\frac{\text{x}+\text{y}}{2}$ lies in between $x$ and such that

Case-II If x < y
Then, $\frac{\text{x}+\text{y}}{2}$ lies in between $x$ and $y$ such that
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MCQ 171 Mark
$-\frac{3}{8}+\frac{1}{7}=+\Big(\frac{-3}{8}\Big)$ is an example to show that:
  • ✓
    Addition of rational numbers is commutative.
  • B
    Rational numbers are closed under addition.
  • C
    Addition of rational number is associative.
  • D
    Rational numbers are distributive under addition.
Answer
Correct option: A.
Addition of rational numbers is commutative.
Given, $-\frac{3}{8}+\frac{1}{7}=+\Big(\frac{-3}{8}\Big)$
Let two rational number, $\text{a}=\frac{-3}{8},\ \text{b}=\frac{1}{7}$
$\therefore\text{a}+\text{b}=\frac{-3}{8}+\frac{1}{7}$
$=\frac{-21+8}{56}$
$=\frac{-13}{56}$
and
$\text{b}+\text{a}=\frac{1}{7}+\frac{-3}{8}$
$=\frac{8-21}{56}$
$=\frac{-13}{56}$
Clearly, $a + b = b + a$
So, addition is communucation for rational numbers.
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MCQ 181 Mark
The reciprocal of $-1$ is:
  • A
    $1$
  • ✓
    $-1$
  • C
    $0$
  • D
    Not defined.
Answer
Correct option: B.
$-1$
The reciprocal of $-1$ is the number itself.
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MCQ 191 Mark
Which of the following is not true?
  • A
    Rational numbers are closed under addition.
  • B
    Rational numbers are closed under subtraction.
  • C
    Rational numbers are closed under multiplication.
  • ✓
    Rational numbers are closed under division.
Answer
Correct option: D.
Rational numbers are closed under division.
Rational numbers are not not closed under division.
As, $1$ and $0$ are the rational number but $\frac{1}{0}$ is not defined.
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MCQ 201 Mark
The reciprocal of $0$ is:
  • A
    $1$
  • B
    $-1$
  • C
    $0$
  • ✓
    Not defined.
Answer
Correct option: D.
Not defined.
The reciprocal of $0$ is not defined.
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MCQ 211 Mark
Zero $(0)$ is:
  • ✓
    The identity for addition of rational numbers.
  • B
    The identity for subtraction of rational numbers.
  • C
    The identity for multiplication of rational numbers.
  • D
    The identity for division of rational numbers.
Answer
Correct option: A.
The identity for addition of rational numbers.
Zero $(0)$ is the identity for addition of rational numbers.
That means,
If a is a rational number.
Then, $a + 0 = 0 + a = a$
Note: Zero $(0)$ is also the additive identity for integers and whole number as well.
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MCQ 221 Mark
The additive inverse of $\frac{-7}{19}$ is:
  • A
    $\frac{-7}{19}$
  • ✓
    $\frac{7}{19}$
  • C
    $\frac{19}{7}$
  • D
    $\frac{-19}{7}$
Answer
Correct option: B.
$\frac{7}{19}$
We know that, if a and b are the additive inverse of each other,
Then $a + b = 0$
Suppose, x is the additive inverse of $\frac{-7}{19}$
Then, $\text{x}-\frac{7}{19}=0$
$\Rightarrow\text{x}=\frac{7}{19}$
Hence, additive inverse of $\frac{-7}{19}$ is $\frac{7}{19}.$
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MCQ 231 Mark
Which of the following statements is always true?
  • A
    $\frac{\text{x}-\text{y}}{2}$ is a rational number between $x$ and $y.$
  • ✓
    $\frac{\text{x}+\text{y}}{2}$ is a rational number between $x$ and $y.$
  • C
    $\frac{\text{x}\times\text{y}}{2}$ is a rational number between $x$ and $y.$
  • D
    $\frac{\text{x}\div\text{y}}{2}$ is a rational number between $x$ and $y.$
Answer
Correct option: B.
$\frac{\text{x}+\text{y}}{2}$ is a rational number between $x$ and $y.$
Here, $\frac{\text{x}+\text{y}}{2}$ is a rational number.
Then, it always lies in between $x$ and $y$ either $x < y$ or $y < x.$
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MCQ 241 Mark
If $y$ be the reciprocal of rational number $x$, then the reciprocal of $y$ will be:
  • ✓
    $\text{x}$
  • B
    $\text{y}$
  • C
    $\frac{\text{x}}{\text{y}}$
  • D
    $\frac{\text{y}}{\text{x}}$
Answer
Correct option: A.
$\text{x}$
If $y$ be the reciprocal of rational number x, i.e. $\text{y}=\frac{1}{\text{x}}$ or $\text{x}=\frac{1}{\text{y}}.$
Hence, the reciprocal of $y$ will be $x.$
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MCQ 251 Mark
Which of the following expressions shows that rational numbers are associative under multiplication:
  • ✓
    $\frac{2}{3}\times\Big(\frac{-6}{7}\times\frac{3}{5}\Big)=\Big(\frac{2}{3}\times\frac{-6}{7}\Big)\times\frac{3}{5}$
  • B
    $\frac{2}{3}\times\Big(\frac{-6}{7}\times\frac{3}{5}\Big)=\frac{2}{3}\times\Big(\frac{3}{5}\times\frac{-6}{7}\Big)$
  • C
    $\frac{2}{3}\times\Big(\frac{-6}{7}\times\frac{3}{5}\Big)=\Big(\frac{3}{5}\times\frac{2}{3}\Big)\times\frac{-6}{7}$
  • D
    $\Big(\frac{2}{3}\times\frac{-6}{7}\Big)\times\frac{3}{5}=\Big(\frac{-6}{7}\times\frac{2}{3}\Big)\times\frac{3}{5}$
Answer
Correct option: A.
$\frac{2}{3}\times\Big(\frac{-6}{7}\times\frac{3}{5}\Big)=\Big(\frac{2}{3}\times\frac{-6}{7}\Big)\times\frac{3}{5}$
$\frac{2}{3}\times\Big(\frac{-6}{7}\times\frac{3}{5}\Big)=\Big(\frac{2}{3}\times\frac{-6}{7}\Big)\times\frac{3}{5}$
[by associative property under multiplication, $a \times (b \times c) = (a \times b) \times c]$
$\Rightarrow\frac{2}{3}\times\frac{-18}{35}=\frac{-12}{21}\times\frac{3}{5}$
So, $a \times (b \times c) = (a \times b) \times c$
Hence, the given expression shows that rational numbers are associative under multiplication.
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