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• These tests focus on the basics of Maths and are meant to indicate your preparation level for the subject.
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## Basic Maths: Test 42

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 Question 1
${{\left( 0.16 \right)}^{-1.5}}$ on simplification gives:
 A 64 B 125 C 14.625 D 12.5
Question 1 Explanation:
\begin{align} & {{\left( 0.16 \right)}^{-1.5}}=\frac{1}{{{\left( 0.16 \right)}^{1.5}}} \\ & =\frac{1}{{{\left[ {{\left( 0.4 \right)}^{2}} \right]}^{\frac{3}{2}}}}=\frac{1}{{{\left( 0.4 \right)}^{2\times \frac{3}{2}}}}=\frac{1}{{{\left( 0.4 \right)}^{3}}} \\ & =\frac{1}{0.064}=\frac{1000}{64}=14.625 \\ \end{align}
 Question 2
$\frac{{{\left( 0.16 \right)}^{3}}-{{\left( 0.04 \right)}^{3}}}{{{\left( 0.16 \right)}^{2}}+0.0064+{{\left( 0.04 \right)}^{2}}}$is simplified to:
 A 1.2 B 0.04 C 0.12 D 0.16
Question 2 Explanation:
Let 0.16= a and 0.04 = b,
Therefore Expression
\begin{align} & \frac{{{a}^{3}}-{{b}^{3}}}{{{a}^{2}}+ab+{{b}^{2}}}=\frac{\left( a-b \right)\left( {{a}^{2}}+ab+{{b}^{2}} \right)}{{{a}^{2}}+ab+{{b}^{2}}} \\ & =a-b=0.16-0.04=0.12 \\ \end{align}
 Question 3
$\sqrt{\frac{0.49}{0.0025}}\times \sqrt{\frac{0.16}{0.64}}$ is equal to:
 A 7 B 8 C 9 D 11
Question 3 Explanation:
Expression
\begin{align} & =\sqrt{\frac{0.49}{0.0025}}\times \sqrt{\frac{0.16}{0.64}} \\ & =\sqrt{\frac{\frac{49}{100}\times \frac{16}{100}}{\frac{25}{10000}\times \frac{64}{100}}} \\ & =\sqrt{\frac{49\times 16\times 1000000}{25\times 64\times 10000}} \\ & =\frac{7\times 4\times 10}{5\times 8} \\ & =7 \\ \end{align}
 Question 4
$\frac{-\frac{3}{2}-\frac{2}{3}+\frac{3}{5}-\frac{3}{3}+\frac{7}{5}+\frac{3}{4}}{\frac{3}{2}+\frac{7}{4}-\frac{4}{3}+\frac{5}{3}-\frac{1}{5}-\frac{4}{5}}$ is simplified to
 A $-\frac{1}{3}$ B $-\frac{3}{10}$ C $-\frac{1}{30}$ D $-\frac{1}{5}$
Question 4 Explanation:
Expression
\begin{align} & \frac{\frac{-90-40+36-60+84+45}{60}}{\frac{90+75-80+100-12-48}{60}} \\ & =\frac{165-190}{265-140}=-\frac{25}{125}=-\frac{1}{5} \\ \end{align}
 Question 5
The simplification of $\left( 0.\overline{65}+.0\overline{35}+0.\overline{87} \right)$ yields the result
 A $1.\overline{98}$ B $1.\overline{81}$ C $1.\overline{79}$ D 1.99
Question 5 Explanation:
Expression
\begin{align} & \left( 0.\overline{65}+.0\overline{35}+0.\overline{87} \right) \\ & =\frac{65}{99}+\frac{35}{99}+\frac{87}{99} \\ & =\frac{65+35+87}{99}=\frac{187}{99} \\ & =1\frac{98}{99} \\ & =1.\overline{98} \\ \end{align}
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