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CBSE Questions for Class 8 Maths Rational Numbers Quiz 10 - MCQExams.com
CBSE
Class 8 Maths
Rational Numbers
Quiz 10
Find
$$\dfrac { 2 }{ 5 } \times \dfrac { -3 }{ 7 } -\dfrac { 1 }{ 14 } -\dfrac { 3 }{ 7 } \times \dfrac { 3 }{ 5 }$$
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$$2$$
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$$\dfrac { 1 }{ 2 }$$
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$$-2$$
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$$\dfrac { -1 }{ 2 }$$
State which property is used in following operation-
$$\dfrac { -19 }{ 29 } \times \dfrac { 29 }{ -19 } =1$$
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Additive inverse
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multiplicative inverse
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commutative
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Associative
Name the property which is used in following operation-
$$\dfrac { -4 }{ 5 } \times 1=1\times \dfrac { -4 }{ 5 } =\dfrac { -4 }{ 5 }$$
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Distributive
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Associative
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Commutative
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None of the above
Find the value of following expression-
$$\dfrac { -4 }{ 5 } \times \dfrac { 3 }{ 7 } \times \dfrac { 15 }{ 16 } \times \dfrac { -14 }{ 9 }$$
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$$\dfrac { 1 }{ 2 }$$
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$$\dfrac { 1 }{ 4 }$$
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$$\dfrac { 1 }{ 3 }$$
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$$\dfrac { 3 }{ 4 }$$
Solve
$$\dfrac { 2 }{ 5 } \times \left( \dfrac { -3 }{ 7 } \right) -\dfrac { 1 }{ 6 } \times \dfrac { 3 }{ 2 } +\dfrac { 1 }{ 14 } \times \dfrac { 2 }{ 5 }$$
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$$\dfrac { 28 }{ 11 }$$
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$$\dfrac { 11 }{ 28 }$$
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$$\dfrac { -28 }{ 11 }$$
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$$\dfrac { -11 }{ 28 }$$
Find the additive inverse of $$\dfrac { -7 }{ 9 }$$
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$$\dfrac { -9 }{ 7 }$$
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$$\dfrac { 7 }{ 9 }$$
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$$\dfrac { 9 }{ 7 }$$
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$$0$$
For any two real number, an operation defined by $$a* b= 1 +ab$$ is.
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Commutative but not associative
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Associative but not commutative
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Neither Commutative nor associative
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Both commutative and associative
Explanation
A binary operation $$∗$$ on $$A$$ is associative if
$$∀a, b, c ∈ A$$,
$$(a ∗ b) ∗ c = a ∗ (b ∗ c)$$ and
A binary operation $$∗$$ on $$A$$ is commutative if
$$∀a, b ∈ A$$
,
$$a ∗ b = b ∗ a$$
$$a∗b=1+ab$$ is commutative as:
$$a∗b=b∗a\\ \Rightarrow 1+ab =1+ba \\ \Rightarrow 1+ab =1+ab$$
which is true.
$$a∗b=1+ab$$
is not associative as:
$$(a∗b)∗c=a∗(b∗c)\\ \Rightarrow \left( 1+ab \right) ∗c=a∗\left( 1+bc \right) \\ \Rightarrow 1+(1+ab)c=1+a(1+bc)\\ \Rightarrow 1+c+abc=a+a+abc$$
which is not true.
Hence, the binary operation
$$∗$$
is commutative but not associative.
What is the multiplicative inverse of $$\dfrac { 8 }{ 21 } ?$$
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$$-\frac { 8 }{ 21 } $$
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1
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0
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$$\frac { 21 }{ 8 } $$
State whether the statements are true (T) or false (F).
If $$\dfrac{x}{y}$$ is the additive inverse of $$\dfrac{c}{d},$$ then $$\dfrac{x}{y} - \dfrac{c}{d} = 0.$$
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True
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False
The value of $$\left( \sqrt { 2 } +1 \right) ^{ 6 }+\left( \sqrt { 2 } -1 \right) ^{ 6 }$4
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99
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182
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196
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198
State whether the statements are true (T) or false (F).
The additive inverse of $$\dfrac{1}{2}$$ is $$-2.$$
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True
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False
An example of a rational number between $$\sqrt { 2 } $$ and $$\sqrt { 15 } $$ is
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3.9
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2.6
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$$\dfrac { \sqrt { 2 } +\sqrt { 15 } }{ 2 } $$
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$$\dfrac { \sqrt { 2 } X\sqrt { 15 } }{ 2 } $$
which of the following is the insertion of three fractions in between $$\frac{7}{{12}}$$ and
$$\frac{9}{{10}}$$ ?
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$$\frac{8}{{11}},\frac{{15}}{{28}},\frac{{17}}{{21}}$$
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$$\frac{4}{9},\frac{{23}}{{25}},\frac{7}{{24}}$$
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$$\frac{{11}}{{18}},\frac{5}{{12}},\frac{{17}}{{19}}$$
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$$\frac{{8}}{{11}},\frac{15}{{23}},\frac{{17}}{{21}}$$
State whether the statements are true (T) or false (F).
If $$\dfrac{x}{y}$$ is the additive inverse of $$\dfrac{c}{d},$$ then $$\dfrac{x}{y} + \dfrac{c}{d} = 0.$$
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True
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False
State whether the statement is true (T) or false (F).
If $$x + y = 0,$$ then $$-y$$ is known as the negative of x, where x and y are rational numbers.
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True
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False
State whether the statements are true (T) or false (F).
Subtraction of rational number is commutative.
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True
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False
State whether the statements are true (T) or false (F).
For all rational numbers $$a, b$$ and $$c, a (b + c) = ab + bc.$$
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True
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False
State whether the statements are true (T) or false (F).
If x and y are negative rational numbers, then so is $$x + y.$$
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True
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False
State whether the statements are true (T) or false (F).
The negative of the negative of any rational number is the number itself.
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True
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False
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