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• This is an assessment test.
• These tests focus on the basics of Maths and are meant to indicate your preparation level for the subject.
• Kindly take the tests in this series with a pre-defined schedule.

## Basic Maths: Test 46

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 Question 1
$\left[ \frac{{{\left( 0.54 \right)}^{3}}+{{\left( 0.45 \right)}^{3}}}{{{\left( 0.54 \right)}^{2}}+{{\left( 0.45 \right)}^{2}}-\left( 0.54 \right)\times \left( 0.45 \right)} \right]$ Simplifies to:
 A 1 B 0.4087 C 0.73 D 0.27
Question 1 Explanation:
Let 0.54= a and 0.45 = b
Therefore expression
\begin{align} & =\frac{{{a}^{3}}+{{b}^{3}}}{{{a}^{2}}+{{b}^{2}}-ab} \\ & =\frac{\left( a+b \right)\left( {{a}^{2}}+{{b}^{2}}-ab \right)}{{{a}^{2}}+{{b}^{2}}-ab} \\ & =a+b=0.54+0.45=1 \\ \end{align}
 Question 2
$\left( 79\times 21+25\times 17+7\times 3 \right)$ equals
 A 2450 B 2405 C 2150 D 2105
Question 2 Explanation:
Expression
\begin{align} & =\left( 79\times 21+25\times 17+7\times 3 \right) \\ & =1659+425+21=2105 \\ \end{align}
 Question 3
$\left( 0.06\times 6-0.006\times 6 \right)$ is equal to:
 A 3.24 B 0.366 C 0.324 D 0.342
Question 3 Explanation:
Expression
\begin{align} & =0.06\times 6-0.006\times 6 \\ & =0.36-0.036=0.324 \\ \end{align}
 Question 4
The value of $\sqrt[3]{\frac{0.3\times 0.3\times 0.3+0.05\times 0.05\times 0.05}{0.6\times 0.6\times 0.6+0.1\times 0.1\times 0.1}}$ is
 A 0.5 B 0.25 C 0.75 D 0.125
Question 4 Explanation:
Let 0.3= a and 0.05= b
Therefore 0.6 = 2a and 0.1 = 2b
Therefore expression
 Question 5
$\frac{{{\left( 2.25 \right)}^{\frac{1}{2}}}\times {{\left( 0.0196 \right)}^{\frac{1}{2}}}+1-0.01}{{{\left( 0.064 \right)}^{\frac{1}{3}}}\times {{\left( 16 \right)}^{\frac{1}{4}}}}$ is simplified to
 A 0.15 B 1.5 C 1 D $1.\overline{5}$
Question 5 Explanation:
Expression
\begin{align} & =\frac{{{\left( 2.25 \right)}^{\frac{1}{2}}}\times {{\left( 0.0196 \right)}^{\frac{1}{2}}}+1-0.01}{{{\left( 0.064 \right)}^{\frac{1}{3}}}\times {{\left( 16 \right)}^{\frac{1}{4}}}} \\ & =\frac{{{\left( 1.5 \right)}^{2\times \frac{1}{2}}}\times {{\left( 0.14 \right)}^{2\times \frac{1}{2}}}+1-0.01}{{{\left( 0.4 \right)}^{3\times \frac{1}{3}}}\times {{\left( 2 \right)}^{4\times \frac{1}{4}}}} \\ & =\frac{1.5\times 0.14+1-0.01}{0.4\times 2}=\frac{0.21+1-0.01}{0.8} \\ & =\frac{1.20}{0.8}=\frac{120}{80} \\ & =1.5 \\ \end{align}
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