- 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 13

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*Basic Maths: Test 13*.You scored %%SCORE%% out of %%TOTAL%%.You correct answer percentage: %%PERCENTAGE%% .Your performance has been rated as %%RATING%%
Your answers are highlighted below.

Question 1 |

$ \displaystyle 999\frac{98}{49}\times 49$Â is equal to:

49049 | |

49349 | |

49449 | |

49249 |

Question 1 Explanation:

$ \displaystyle \begin{array}{l}\left( 999+\frac{98}{49} \right)\times 49\\=(999+2)\times 49\\=\left( 1001 \right)49\\=\text{49049}\end{array}$

Question 2 |

The value ofÂ $ \displaystyle 49\frac{95}{49}\times 49$ is

2296 | |

2396 | |

2196 | |

2496 |

Question 2 Explanation:

Expression
$ \displaystyle \begin{array}{l}=\left( 49+\frac{95}{49} \right)\times 49\\=49\times 49+95=\text{2496}\end{array}$

Question 3 |

The value of $ \displaystyle 499\frac{995}{499}\times 499$Â is

249796 | |

249996 | |

249986 | |

249906 |

Question 3 Explanation:

$ \displaystyle \begin{array}{l}=\left( 499+\frac{995}{499} \right)\times 499\\={{\left( 499 \right)}^{2}}+995\\={{\left( 500-1 \right)}^{2}}+995\\=250000+1-1000+995\\=\text{249996}\end{array}$

Question 4 |

$ \displaystyle \frac{{{\left( 998 \right)}^{2}}-{{\left( 997 \right)}^{2}}-240}{{{\left( 98 \right)}^{2}}-{{\left( 97 \right)}^{2}}}$ equals

1995 | |

9 | |

95 | |

10 |

Question 4 Explanation:

$ \displaystyle \begin{array}{l}=\frac{\left[ {{\left( 998 \right)}^{2}}-{{\left( 997 \right)}^{2}} \right]-240}{{{\left( 98 \right)}^{2}}-{{\left( 97 \right)}^{2}}}\\=\frac{\left( 998+997 \right)\,\left( 998-997 \right)-240}{\left( 98+97 \right)\,\left( 98-97 \right)}\\=\frac{1995-240}{195}=\frac{1755}{195}=9\end{array}$

Question 5 |

$ \displaystyle 3+\left( 3+1 \right)\,({{3}^{2}}+1)\,\left( {{3}^{4}}+1 \right)\,\left( {{3}^{8}}+1 \right)\,\left( {{3}^{16}}+1 \right)\,\left( {{3}^{32}}+1 \right)$Â is equal to

$ \displaystyle \frac{{{3}^{64}}-1}{2}$ | |

$ \displaystyle \frac{{{3}^{64}}+5}{2}$ | |

$ \displaystyle {{3}^{64}}-1$ | |

$ \displaystyle {{3}^{64}}+1$ |

Question 5 Explanation:

$ \displaystyle \begin{array}{l}3+\left( 3+1 \right)\,\left( {{3}^{2}}+1 \right)\,\left( {{3}^{4}}+1 \right)\left( {{3}^{8}}+1 \right)\left( {{3}^{16}}+1 \right)\left( {{3}^{32}}+1 \right)\\=3+\frac{\left( 3-1 \right)\,\left( 3+1 \right)}{3-1}\left( {{3}^{2}}+1 \right)\,\left( {{3}^{4}}+1 \right)......\left( {{3}^{32}}+1 \right)\\=3+\frac{\left( {{3}^{2}}-1 \right)\,\left( {{3}^{2}}+1 \right)\,\left( {{3}^{4}}+1 \right).....\left( {{3}^{32}}+1 \right)}{2}\\=3+\frac{\left( {{3}^{4}}-1 \right)\,\left( {{3}^{4}}+1 \right)\,\left( {{3}^{8}}+1 \right).....\left( {{3}^{32}}+1 \right)}{2}\\=3+\frac{\left( {{3}^{8}}-1 \right)\,\left( {{3}^{8}}+1 \right)\,\left( {{3}^{16}}+1 \right).....\left( {{3}^{32}}+1 \right)}{2}\\=3+\frac{\left( {{3}^{16}}-1 \right)\,\left( {{3}^{16}}+1 \right)\,\left( {{3}^{32}}+1 \right)}{2}\\=3+\frac{\left( {{3}^{32}}-1 \right)\,\left( {{3}^{32}}+1 \right)}{2}\\=3+\frac{{{3}^{64}}-1}{2}=\frac{{{3}^{64}}+5}{2}\end{array}$

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