- 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 45

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Question 1 |

Which of the following is greater than
$\left( 1-\frac{1}{100} \right)\,\left( 1-\frac{1}{101} \right)\,\left( 1-\frac{1}{102} \right)\,......\left( 1-\frac{1}{200} \right)$ :

0.2 | |

0.3
| |

0.4 | |

0.5 |

Question 1 Explanation:

$\begin{align}
& \left( 1-\frac{1}{100} \right)\,\left( 1-\frac{1}{101} \right)\,\left( 1-\frac{1}{102} \right)\,......\left( 1-\frac{1}{200} \right) \\
& =\frac{99}{100}\times \frac{100}{101}\times \frac{101}{102}\times .....\frac{199}{200}=\frac{99}{200} \\
\end{align}$

Is less than 0.5

Is less than 0.5

Question 2 |

${{\left( \sqrt{3}+\frac{1}{\sqrt{3}} \right)}^{2}}$
is equal to:

$2\frac{1}{3}$
| |

$3\frac{1}{3}$ | |

$4\frac{1}{3}$ | |

$5\frac{1}{3}$ |

Question 2 Explanation:

$\begin{align}
& {{\left( \sqrt{3}+\frac{1}{\sqrt{3}} \right)}^{2}} \\
& =3+\frac{1}{3}+2\times \sqrt{3}\times \frac{1}{\sqrt{3}}=5\frac{1}{3} \\
\end{align}$

Question 3 |

The value of
${{\left( .89 \right)}^{3}}+{{\left( 0.11 \right)}^{3}}+3\times .89\times .11-1$
is:

1.98
| |

1.09 | |

1 | |

0 |

Question 3 Explanation:

Expression

$\begin{align} & {{\left( .89 \right)}^{3}}+{{\left( 0.11 \right)}^{3}}+3\times .89\times .11-1 \\ & ={{\left( .89 \right)}^{3}}+{{\left( 0.11 \right)}^{3}}+3\times .89\times .11\left( 0.89+0.11 \right)-1 \\ & ={{\left( 0.89+0.11 \right)}^{3}}-1=1-1=0 \\ \end{align}$

$\begin{align} & {{\left( .89 \right)}^{3}}+{{\left( 0.11 \right)}^{3}}+3\times .89\times .11-1 \\ & ={{\left( .89 \right)}^{3}}+{{\left( 0.11 \right)}^{3}}+3\times .89\times .11\left( 0.89+0.11 \right)-1 \\ & ={{\left( 0.89+0.11 \right)}^{3}}-1=1-1=0 \\ \end{align}$

Question 4 |

$7.4\overline{2}+0.\overline{8}+0.00\overline{3}$ is equal to

$8.\overline{313}$
| |

$8.3\overline{13}$ | |

$8.31\overline{3}$ | |

$8.3\overline{13}$ |

Question 4 Explanation:

Question 5 |

The value of
$\frac{4}{5}\times \frac{5}{\frac{7}{9}\div \frac{5}{3}\,\,of\,\,1\frac{6}{15}}$
is

2.5 | |

12
| |

10 | |

5 |

Question 5 Explanation:

Expression

\[\begin{align} & =\frac{4}{5}\times \frac{5}{\frac{7}{9}\div \frac{5}{3}\times \frac{21}{15}} \\ & =\frac{4}{5}\times 15=12 \\ \end{align}\]

\[\begin{align} & =\frac{4}{5}\times \frac{5}{\frac{7}{9}\div \frac{5}{3}\times \frac{21}{15}} \\ & =\frac{4}{5}\times 15=12 \\ \end{align}\]

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