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Basic Maths: Test 39

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Question 1
The simplification of $\frac{4.8\times 64+4.8\times 36}{{{\left( 7.4 \right)}^{2}}-{{\left( 2.6 \right)}^{2}}}$ yields the result
A
7.2
B
8.5
C
10
D
12
Question 1 Explanation:
Expression
$\begin{align} & \frac{4.8\left( 64+36 \right)}{\left( 7.4+2.6 \right)\left( 7.4-2.6 \right)} \\ & =\frac{4.8\times 100}{10\times 4.8}=10 \\ \end{align}$
Question 2
$\left( 0.3\times 0.4+0.02 \right){{\left( 0.5\times 0.1+0.09 \right)}^{-1}}$ is equal to
A
1
B
$\frac{41}{12}$
C
$\frac{41}{4}$
D
$\frac{9}{5}$
Question 2 Explanation:
Expression
$\begin{align} & =\frac{\left( 0.12+0.02 \right)}{\left( 0.05+0.09 \right)} \\ & =\frac{0.14}{0.14}=1 \\ \end{align}$
Question 3
$5\frac{1}{5}-2\frac{1}{9}=?-7\frac{3}{5}-3\frac{1}{2}$
A
$13\frac{5}{63}$
B
$13\frac{107}{126}$
C
$14\frac{19}{90}$
D
$14\frac{17}{90}$
Question 3 Explanation:
$\begin{align} & 5\frac{1}{5}-2\frac{1}{9}=?-7\frac{3}{5}-3\frac{1}{2} \\ & \Rightarrow 5+\frac{1}{5}-2-\frac{1}{9}=?-7-\frac{3}{5}-3-\frac{1}{2} \\ & \Rightarrow ?=5+\frac{1}{5}-2-\frac{1}{9}+7+\frac{3}{5}+3+\frac{1}{2} \\ & =13+\left( \frac{1}{5}-\frac{1}{9}+\frac{3}{5}+\frac{1}{2} \right) \\ & =13+\left( \frac{18-10+54+45}{90} \right) \\ & =13+\frac{107}{90}=13+1\frac{17}{90} \\ & =14\frac{17}{90} \\ \end{align}$
Question 4
$\left( 0.125 \right)\div {{\left( 0.25 \right)}^{3}}\times \left( 0.0625 \right)={{\left( 0.5 \right)}^{?+1}}$
A
0
B
1
C
–1
D
–2
Question 4 Explanation:
Capture
Question 5
The value of $\frac{{{\left( 5.123 \right)}^{3}}+{{\left( 3.456 \right)}^{3}}-{{\left( 8.579 \right)}^{3}}}{\left( 5.123 \right)\,\left( 3.456 \right)\,\left( -8.579 \right)}$ lies between
A
–0.5 and 0
B
0 and 0.5
C
0.5 and 1
D
2.5 and 3.5
Question 5 Explanation:
$\begin{align} & If\,\,\,a+b+c=0,\,\,then\,\,\,{{a}^{3}}+{{b}^{3}}+{{c}^{3}}=3abc \\ & Here,\,\,\,\,5.123+3.456-8.579=0 \\ & Expression\, \\ & =\frac{3\times \left( 5.123 \right)\left( 3.456 \right)\left( -8.579 \right)}{\left( 5.123 \right)\left( 3.456 \right)\left( -8.579 \right)}=3 \\ \end{align}$
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