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