- 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 54

Congratulations - you have completed *Basic Maths: Test 54*.

You scored %%SCORE%% out of %%TOTAL%%.

Your performance has been rated as %%RATING%%

Your answers are highlighted below.

Question 1 |

${{\left( 2457\div 91 \right)}^{\frac{1}{3}}}+{{\left( \frac{12.5\times 100}{50} \right)}^{\frac{1}{2}}}={{\left( ? \right)}^{\frac{1}{3}}}$

512 | |

64 | |

256 | |

16 |

Question 1 Explanation:

$\begin{align}
& {{\left( \frac{2457}{91} \right)}^{\frac{1}{3}}}+{{\left( 12.5\times 2 \right)}^{\frac{1}{2}}}={{\left( ? \right)}^{\frac{1}{3}}} \\
& \Rightarrow {{\left( 27 \right)}^{\frac{1}{3}}}+{{\left( 25 \right)}^{\frac{1}{2}}}={{\left( ? \right)}^{\frac{1}{3}}} \\
& \Rightarrow {{\left( {{3}^{3}} \right)}^{\frac{1}{3}}}+{{\left( {{5}^{2}} \right)}^{\frac{1}{2}}}={{\left( ? \right)}^{\frac{1}{3}}} \\
& \Rightarrow 3+5={{\left( ? \right)}^{\frac{1}{3}}} \\
& \Rightarrow {{\left( ? \right)}^{\frac{1}{3}}}=8={{\left( {{8}^{3}} \right)}^{\frac{1}{3}}} \\
& \Rightarrow ?={{8}^{3}}=512 \\
\end{align}$

Question 2 |

$\sqrt{{{12}^{2}}+32\div 2-{{\left( 5 \right)}^{2}}+154}={{\left( ? \right)}^{2}}$

18 | |

$\sqrt{17}$ | |

289 | |

17 |

Question 2 Explanation:

$\begin{align}
& {{?}^{2}}=\sqrt{{{12}^{2}}+32\times \frac{1}{2}-{{\left( 5 \right)}^{2}}+154} \\
& =\sqrt{144+16-25+154} \\
& =\sqrt{289}=17 \\
& \Rightarrow ?=\sqrt{17} \\
\end{align}$

Question 3 |

${{\left( 0.25 \right)}^{4}}\times {{\left( 0.125 \right)}^{4}}\div {{\left( 0.0625 \right)}^{4}}={{\left( 50\div 100 \right)}^{?+3}}$

3 | |

1 | |

4 | |

7 |

Question 3 Explanation:

$\begin{align}
& {{\left( {{\left( 0.5 \right)}^{2}} \right)}^{4}}\times {{\left( {{\left( 0.5 \right)}^{3}} \right)}^{4}}\div {{\left( {{\left( 0.5 \right)}^{4}} \right)}^{4}}={{\left( \frac{50}{100} \right)}^{?+3}} \\
& \Rightarrow {{0.5}^{8}}\times {{.5}^{12}}\div {{\left( 0.5 \right)}^{16}}={{\left( 0.5 \right)}^{?+3}} \\
& \Rightarrow {{\left( 0.5 \right)}^{8+12-16}}={{\left( 0.5 \right)}^{?+3}}={{\left( 0.5 \right)}^{4}} \\
& \Rightarrow ?+3=4\, \\
& \Rightarrow ?=4-3=1 \\
\end{align}$

Question 4 |

1/2 | |

43/196 | |

196/43 | |

1 |

Question 4 Explanation:

Question 5 |

$\sqrt{\frac{0.049\times 0.576}{0.0036\times 7.84}}$ is equal to

1 | |

1.1 | |

10 | |

1.11 |

Question 5 Explanation:

$\begin{align}
& =\sqrt{\frac{0.049\times 0.576}{0.0036\times 7.84}} \\
& =\sqrt{\frac{49\times 576}{36\times 784}} \\
& =\frac{7\times 24}{6\times 28} \\
& =1 \\
\end{align}$

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