- 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 60

Congratulations - you have completed *Basic Maths: Test 60*.

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Question 1 |

$\frac{\sqrt{28}+\sqrt{252}}{\sqrt{112}}$ is equal to

$\frac{2}{\sqrt{6}}$ | |

$2\sqrt{6}$ | |

$4\sqrt{6}$ | |

2 |

Question 1 Explanation:

$\begin{align}
& \frac{\sqrt{28}+\sqrt{252}}{\sqrt{112}} \\
& =\frac{\sqrt{4\times 7}+\sqrt{36\times 7}}{\sqrt{16\times 7}} \\
& =\frac{\sqrt{7}\left( 2+6 \right)}{4\sqrt{7}} \\
& =\frac{8}{4}=2 \\
\end{align}$

Question 2 |

$\frac{\left( 100-1 \right)\,\left( 100-2 \right)\,\left( 100-3 \right)\,.....\left( 100-99 \right)}{100\times 99\times 98\times .....\times 3\times 2\times 1}$ is equal to

$\frac{100}{99\times 98\times 97\times .....\times 3\times 2\times 1}$ | |

0.01 | |

0 | |

$-\frac{2}{99\times 98\times 97\times ....\times 3\times 2\times 1}$ |

Question 2 Explanation:

\[\begin{align}
& \frac{\left( 100-1 \right)\,\left( 100-2 \right)\,\left( 100-3 \right)\,.....\left( 100-99 \right)}{100\times 99\times 98\times .....\times 3\times 2\times 1} \\
& =\frac{\left( 99 \right)\,\left( 98 \right)\,\left( 97 \right)\,.....\left( 1 \right)}{100\times 99\times 98\times .....\times 3\times 2\times 1} \\
& =\frac{1}{100} \\
& =0.01 \\
\end{align}\]

Question 3 |

$\left( 7.5\times 7.5-37.5+2.5\times 2.5 \right)$ is equal to

20 | |

25 | |

15 | |

30 |

Question 3 Explanation:

Let 7.5 = a, 2.5 = b

\[\begin{align} & Expression \\ & ={{a}^{2}}-2\times a\times b+{{b}^{2}} \\ & ={{\left( a-b \right)}^{2}} \\ & \left[ a-b=7.5-2.5=5 \right] \\ & ={{5}^{2}} \\ & =25 \\ \end{align}\]

\[\begin{align} & Expression \\ & ={{a}^{2}}-2\times a\times b+{{b}^{2}} \\ & ={{\left( a-b \right)}^{2}} \\ & \left[ a-b=7.5-2.5=5 \right] \\ & ={{5}^{2}} \\ & =25 \\ \end{align}\]

Question 4 |

$\frac{2.25\times 2.25+2.75\times 2.75-2\times 2.25\times 2.75}{2.25\times 2.25-2.75\times 2.75}$simplified to

0.4 | |

0.3 | |

0.1 | |

0.2 |

Question 4 Explanation:

\[\begin{align}
& If\,\,2.75=a\,\,and\,\,\,2.25=b,\,\,then \\
& Expression \\
& =\frac{{{a}^{2}}+{{b}^{2}}-2ab}{{{a}^{2}}-{{b}^{2}}} \\
& =\frac{{{\left( a-b \right)}^{2}}}{\left( a-b \right)\left( a+b \right)}=\frac{\left( a-b \right)}{\left( a+b \right)} \\
& =\frac{0.5}{5} \\
& =0.1 \\
\end{align}\]

Question 5 |

$\left( \frac{5}{2}+\frac{4}{2} \right)\,\left( \frac{26}{3}-\frac{11}{3}+\frac{7}{3} \right)$ is equal to

33 | |

19 | |

37 | |

36 |

Question 5 Explanation:

$\begin{align}
& \left( \frac{5}{2}+\frac{4}{2} \right)\,\left( \frac{26}{3}-\frac{11}{3}+\frac{7}{3} \right) \\
& =\frac{9}{2}\times \frac{22}{3}=33 \\
\end{align}$

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