Rational Numbers Test

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Rational Numbers Test - 32

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Weekly Quiz Competition

Question 1
1 / -0

Given that $$Q$$ is a rational number:
(i) Difference of two $$Q$$s is $$Q$$.
(ii) Subtraction is commutative on $$Q$$.
(iii) Addition is not commutative on $$Q$$.
Which option is wrong?

A
(ii) and (iii)

B
(i) only

C
(i) and (iii)

D
All the above

Solution

Difference of two rational number will be rational number.
Commutative property applies only on addition and multiplication.
So (i) is correct but (ii) and (iii) are wrong
So correct answer will be option A
Question 2
1 / -0

Study the following statements.
Statement - 1 : Rational numbers are always closed under division.
Statement - 2 : Division by zero is not defined.
Which of the following options hold?

A
Both statement - 1 and statement - 2 are true.

B
Statement - 1 is true but statement -2 is false.

C
Statement - 1 is false but statement -2 is true.

D
Both statement - 1 and statement - 2 are false.

Solution

Statement $$1:$$ Rational number can even be simply integers which can be further represented as $$\cfrac {p}{q}$$ form. So, statement $$1$$ is false.
Statement $$2:$$ Any number divided by $$0$$ is not defined. So, statement $$2$$ is true.
Question 3
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If a, b, c are rational numbers, then associativity of rational numbers under addition is given by

A
$$a + b = b + a$$

B
$$a + (b + c) = (a + b) + c$$

C
$$a \times (b \times c) = (a \times b) \times c$$

D
$$a + (b - c) = (a + b) - c$$

Solution

Associative property of rational number under addition is given by following:
$$a+(b+c)=(a+b)+c$$
where, $$a,b$$ and $$c$$ are rational numbers.
Hence, B is the correct option.
Question 4
1 / -0

Find two rational numbers lying between $$\dfrac{-1}{3}$$ and $$\dfrac{1}{2}$$.

A
-1/6,1 /6

B
-2/3, 2/3

C
none

D
both

Solution
Question 5
1 / -0

If $$x$$ and $$y$$ are rational numbers then, then the following numbers:
$$x^{2}- y^{2}$$ is

A
rational number

B
irrational number

C
natural number

D
whole number

Solution

Given:$$x$$ and $$y$$ are rational numbers.
To Prove: $$x^2-y^2$$ are rational numbers.
Proof: Consider $$x^2-y^2$$
$$=(x-y)(x+y)$$ which is a rational number because we know addition, subtraction and product of two rational numbers is also a rational number.
So, $$A$$ is correct option.
Question 6
1 / -0

The rational number that lies between $$\dfrac{3}{7}$$ and $$\dfrac{2}{3}$$ is

A
$$\dfrac{2}{5}$$

B
$$\dfrac{4}{7}$$

C
$$\dfrac{3}{7}$$

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

Solution

$$ \dfrac{3}{7}\times \dfrac{3}{3} = \dfrac{9}{21},$$

$$\dfrac{2}{3}\times \dfrac{7}{7} = \dfrac{14}{21} $$

Rational numbers between $$ \dfrac{3}{7} $$ & $$ \dfrac{2}{3} $$ are $$ \dfrac{10}{21},\dfrac{11}{21},\dfrac{12}{21},\dfrac{13}{21} $$

$$ \dfrac{12}{21}= \dfrac{4}{7} $$

Hence, $$ \dfrac{4}{7} $$ lies between $$\dfrac37$$ and $$\dfrac23$$.
Question 7
1 / -0

which of the following is the insertion of three fractions in between $$\frac{7}{{12}}$$ and $$\frac{9}{{10}}$$ ?

A
$$\frac{8}{{11}},\frac{{15}}{{28}},\frac{{17}}{{21}}$$

B
$$\frac{4}{9},\frac{{23}}{{25}},\frac{7}{{24}}$$

C
$$\frac{{11}}{{18}},\frac{5}{{12}},\frac{{17}}{{19}}$$

D
$$\frac{{8}}{{11}},\frac{15}{{23}},\frac{{17}}{{21}}$$

Solution
Question 8
1 / -0

What is the additive inverse of $$-\dfrac { 3 }{ 13 } $$?

A
$$\dfrac{-13}{3} $$

B
$$\dfrac{3}{13} $$

C
$$1\dfrac{1}{3} $$

D
None of the above

Solution
Question 9
1 / -0

Which of the following is true for the number $$1$$?

A
It is identity for addition of rational numbers.

B
It is identity for subtraction of rational numbers.

C
It is identity for multiplication of rational numbers.

D
It is identity for division of rational numbers.

Solution

$${\textbf{Step-1: Identify for multiplication.}}$$
$${\text{If a is a rational number.}}$$
$$\Rightarrow a \times 1 =1 \times a =a$$
$$\therefore$$ $${\text{1 is the identity for multiplication of rational numbers.}}$$
$${\textbf{Hence, option C is the correct answer.}}$$
Question 10
1 / -0

Zero (0) is

A
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.

Solution

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Rational Numbers Test - 32

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Rational Numbers Test - 32

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Question 1

(ii) and (iii)

(i) only

(i) and (iii)

All the above

Solution

Question 2

Both statement - 1 and statement - 2 are true.

Statement - 1 is true but statement -2 is false.

Statement - 1 is false but statement -2 is true.

Both statement - 1 and statement - 2 are false.

Solution

Question 3

$$a + b = b + a$$

$$a + (b + c) = (a + b) + c$$

$$a \times (b \times c) = (a \times b) \times c$$

$$a + (b - c) = (a + b) - c$$

Solution

Question 4

-1/6,1 /6

-2/3, 2/3

none

both

Solution

Question 5

rational number

irrational number

natural number

whole number

Solution

Question 6

$$\dfrac{2}{5}$$

$$\dfrac{4}{7}$$

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

$$\dfrac{2}{3}$$

Solution

Question 7

$$\frac{8}{{11}},\frac{{15}}{{28}},\frac{{17}}{{21}}$$

$$\frac{4}{9},\frac{{23}}{{25}},\frac{7}{{24}}$$

$$\frac{{11}}{{18}},\frac{5}{{12}},\frac{{17}}{{19}}$$

$$\frac{{8}}{{11}},\frac{15}{{23}},\frac{{17}}{{21}}$$

Solution

Question 8

$$\dfrac{-13}{3} $$

$$\dfrac{3}{13} $$

$$1\dfrac{1}{3} $$

None of the above

Solution

Question 9

It is identity for addition of rational numbers.

It is identity for subtraction of rational numbers.

It is identity for multiplication of rational numbers.

It is identity for division of rational numbers.

Solution

Question 10

The identity for addition of rational numbers.

The identity for subtraction of rational numbers.

The identity for multiplication of rational numbers.

The identity for division of rational numbers.

Solution

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