- 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 41

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*Basic Maths: Test 41*. You scored %%SCORE%% out of %%TOTAL%%. Your performance has been rated as %%RATING%% Your answers are highlighted below.

Question 1 |

$\frac{\frac{1}{7}.\frac{1}{7}.\frac{1}{7}+\frac{1}{2}.\frac{1}{2}.\frac{1}{2}-3.\frac{1}{7}.\frac{1}{2}.\frac{1}{5}.+\frac{1}{5}.\frac{1}{5}.\frac{1}{5}}{\frac{1}{7}.\frac{1}{7}+\frac{1}{2}.\frac{1}{2}+\frac{1}{5}.\frac{1}{5}-\left( \frac{1}{7}.\frac{1}{2}+\frac{1}{2}.\frac{1}{5}+\frac{1}{5}.\frac{1}{7} \right)}$
is equal to:

$\frac{2}{3}$ | |

$\frac{39}{40}$ | |

$\frac{59}{60}$ | |

$\frac{59}{70}$ |

Question 1 Explanation:

$\begin{align}
& Let\,\,\frac{1}{7}\,\,=a,\frac{1}{2}\,=b\,\,\,and\,\frac{1}{5}\,\,=c \\
& Therefore\,\,\,\,\,\exp ression \\
& =\frac{{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc}{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-ac-bc} \\
& =\frac{\left( a+b+c \right)\left( {{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-ac-bc \right)}{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-ac-bc}=a+b+c \\
& =\frac{1}{7}+\frac{1}{2}+\frac{1}{5} \\
& =\frac{10+35+14}{70} \\
& =\frac{59}{70} \\
\end{align}$

Question 2 |

The value of $\frac{27-0.064}{9+1.2+0.16}$is:

3.6 | |

3.4 | |

2.6 | |

2.4 |

Question 2 Explanation:

$\begin{align}
& =\frac{{{\left( 3 \right)}^{3}}-{{\left( 0.4 \right)}^{3}}}{{{\left( 3 \right)}^{2}}+3\times 0.4+{{\left( 0.4 \right)}^{2}}} \\
& Let\,\,3\,\,=a,\,0.4\,=b \\
& Therefore\,\,\,\,\exp ression \\
& =\frac{{{a}^{3}}-{{b}^{3}}}{{{a}^{2}}+ab+{{b}^{2}}} \\
& =\frac{\left( a-b \right)\left( {{a}^{2}}+ab+{{b}^{2}} \right)}{{{a}^{2}}+ab+{{b}^{2}}} \\
& =a-b=3-0.4=2.6 \\
\end{align}$

Question 3 |

$10.9-\left[ 9.8-\left\{ 8.7-\left( 7.6-\overline{6.5-4} \right)\, \right\}\, \right]$is simplified to:

2.7 | |

3.7 | |

4.7 | |

5.7 |

Question 3 Explanation:

$\begin{align}
& =10.9-\left[ 9.8-\left\{ 8.7-\left( 7.6-\overline{6.5-4} \right)\, \right\}\, \right] \\
& =10.9-\left[ 9.8-\left\{ 8.7-\left( 7.6-2.5 \right)\, \right\}\, \right] \\
& =10.9-\left[ 9.8-\left\{ 8.7-4.1\, \right\}\, \right] \\
& =10.9-\left[ 9.8-4.6\, \right] \\
& =10.9-5.2 \\
& =5.7 \\
\end{align}$

Question 4 |

$\frac{1\frac{1}{10}\div 1\frac{1}{5}}{\left( \frac{11}{12}+1-\frac{5}{6} \right)}$
is equal to:

11/15 | |

13/11 | |

11/13 | |

15/17 |

Question 4 Explanation:

$\begin{align}
& =\frac{1\frac{1}{10}\div 1\frac{1}{5}}{\left( \frac{11}{12}+1-\frac{5}{6} \right)} \\
& =\frac{\frac{11}{10}\times \frac{5}{6}}{\left( \frac{11+12-10}{12} \right)} \\
& =\frac{\frac{11}{10}\times \frac{5}{6}}{\frac{13}{12}}=\frac{11}{12}\times \frac{12}{13}=\frac{11}{13} \\
\end{align}$

Question 5 |

The greatest number among $0.9+\sqrt{.09,}\,\,1.4\,\,-\frac{1.2}{24},\,\,1.5\times 0.89\,\,and\,\,\sqrt{1.21}$ is:

$0.9+\sqrt{0.09}$ | |

$\sqrt{1.21}$ | |

$1.5\times 0.89$ | |

$1.4-\frac{1.2}{24}$ |

Question 5 Explanation:

$\begin{align}
& 0.9+\sqrt{0.09} \\
& =0.9+0.3=1.2 \\
& 1.4-\frac{1.2}{24} \\
& =1.4-0.05 \\
& =1.35 \\
& 1.5\times 0.89=1.335 \\
& \sqrt{1.21}=1.1 \\
& Hence,\,\,\,the\,\,\,greatest\,\,\,\,number \\
& =1.4-\frac{1.2}{24} \\
\end{align}$

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