Rational Numbers Test

Result

Rational Numbers Test - 21

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Weekly Quiz Competition

Question 1
1 / -0

If $$y$$ be the reciprocal of rational number $$x$$, then the reciprocal of $$y$$ will be

A
$$x$$

B
$$y$$

C
$$\dfrac{x}{y}$$

D
$$\dfrac{y}{x}$$

Solution

Given $$y$$ is reciprocal of $$x$$.
$$y =\dfrac{1}{x}$$
$$\implies x=\dfrac{1}{y}$$
Therefore $$x$$ is reciprocal of $$y$$.
Question 2
1 / -0

The reciprocal of $$0$$ is

A
$$1$$

B
$$-1$$

C
$$0$$

D
Not defined

Solution
Question 3
1 / -0

The reciprocal of any rational number $$\dfrac{p}{q}$$ where $$p$$ and $$q$$ are integers and $$p,q \neq 0.$$

A
$$\dfrac{p}{q}$$

B
$$1$$

C
$$0$$

D
$$\dfrac{q}{p}$$

Solution

Reciprocal of rational number $$\dfrac{p}{q}$$,
$$\dfrac{1}{{\dfrac{p}{q}}} = \dfrac{q}{p}$$

Hence, $$D$$ is correct.
Question 4
1 / -0

Which of the following statements is always true ?

A
$$\dfrac{x - y}{2}$$ is a rational number between x and y

B
$$\dfrac{x + y}{2}$$ is a rational number between x and y

C
$$\dfrac{x \times y}{2}$$ is a rational number between x and y

D
$$\dfrac{x \div y}{2}$$ is a rational number between x and y

Solution
Question 5
1 / -0

$$\left(-5 \dfrac{1}{3}\right) \times\left(-1 \dfrac{7}{8}\right)$$ is equal to

A
10

B
-10

C
$$5 \dfrac{7}{24}$$

D
$$-5 \dfrac{7}{24}$$

Solution

$$ \left(-5 \dfrac{1}{3}\right) \times \left(-1 \dfrac{7}{8}\right)= \dfrac{-16}{3}\times\dfrac{-15}{8}=10$$
Question 6
1 / -0

$$\dfrac{-3}{15}-\left(\dfrac{-2}{15}\right)$$
is equal to

A
$$\dfrac{-11}{5}$$

B
$$\dfrac{-1}{15}$$

C
$$\dfrac{-7}{15}$$

D
$$\dfrac{7}{15}$$

Solution

$$\dfrac{-3}{5}-\left(\dfrac{-2}{15}\right)=\dfrac{-3}{5}+\dfrac{2}{15}$$
$$=\dfrac{-3+2}{15}=\dfrac{-1}{15}$$
Question 7
1 / -0

$$\left(-2 \dfrac{1}{3}\right) \div 2 \dfrac{11}{12}$$ is
equal to

A
$$-\dfrac{4}{5}$$

B
$$\dfrac{4}{5}$$

C
$$\dfrac{4}{11}$$

D
$$-\dfrac{4}{11}$$

Solution

$$\left(-2 \dfrac{1}{3}\right) \div 2 \dfrac{11}{12}$$

$$\left(-2 \dfrac{1}{3}\right)=\dfrac {-7}3$$

$$2 \dfrac{11}{12}=\dfrac {35}{12}$$

$$\left(-2 \dfrac{1}{3}\right) \div 2 \dfrac{11}{12}=\dfrac {-7}{3} \times \dfrac {12}{35}=\dfrac {-4}5$$
Question 8
1 / -0

Which of the following numbers lie on the right of $$\dfrac{2}{3}$$

A
$$0$$

B
$$\dfrac{-1}{3}$$

C
$$\dfrac{4}{3}$$

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

Solution
Question 9
1 / -0

Let $$a$$ and $$b$$ are rational numbers and $$a > b$$. Then, on the number line,

A
$$-a$$ is on the right of $$-b$$

B
$$-a$$ is on the left of $$-b$$

C
$$a$$ is on the left of $$b$$

D
None of the above.
Question 10
1 / -0

Which of the following numbers is a rational number?

A
$$x ^ { 2 } = 7$$

B
$$x ^ { 2 } = \cfrac { 17 } { 4 }$$

C
$$y ^ { 2 } = 16$$

D
$$b ^ { 2 } = 0.4$$

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Re-Attempt Weekly Quiz Competition

Rational Numbers Test - 21

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Rational Numbers Test - 21

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Question 1

$$x$$

$$y$$

$$\dfrac{x}{y}$$

$$\dfrac{y}{x}$$

Solution

Question 2

$$1$$

$$-1$$

$$0$$

Not defined

Solution

Question 3

$$\dfrac{p}{q}$$

$$1$$

$$0$$

$$\dfrac{q}{p}$$

Solution

Question 4

$$\dfrac{x - y}{2}$$ is a rational number between x and y

$$\dfrac{x + y}{2}$$ is a rational number between x and y

$$\dfrac{x \times y}{2}$$ is a rational number between x and y

$$\dfrac{x \div y}{2}$$ is a rational number between x and y

Solution

Question 5

10

-10

$$5 \dfrac{7}{24}$$

$$-5 \dfrac{7}{24}$$

Solution

Question 6

$$\dfrac{-11}{5}$$

$$\dfrac{-1}{15}$$

$$\dfrac{-7}{15}$$

$$\dfrac{7}{15}$$

Solution

Question 7

$$-\dfrac{4}{5}$$

$$\dfrac{4}{5}$$

$$\dfrac{4}{11}$$

$$-\dfrac{4}{11}$$

Solution

Question 8

$$0$$

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

$$\dfrac{4}{3}$$

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

Solution

Question 9

$$-a$$ is on the right of $$-b$$

$$-a$$ is on the left of $$-b$$

$$a$$ is on the left of $$b$$

None of the above.

Question 10

$$x ^ { 2 } = 7$$

$$x ^ { 2 } = \cfrac { 17 } { 4 }$$

$$y ^ { 2 } = 16$$

$$b ^ { 2 } = 0.4$$

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