- 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 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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