- This is an assessment test.
- These tests focus on the basics of Maths and are meant to indicate your preparation level for the subject.
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## Basic Maths: Test 21

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Question 1 |

Find the value of

$ \displaystyle \frac{1}{1+\frac{1}{1-\frac{1}{2}}}\times \frac{1}{\frac{5}{6}\,\,of\,\frac{3}{2}\div \,1\frac{1}{4}\,}$

$ \displaystyle \frac{1}{1+\frac{1}{1-\frac{1}{2}}}\times \frac{1}{\frac{5}{6}\,\,of\,\frac{3}{2}\div \,1\frac{1}{4}\,}$

1/2 | |

1/7 | |

1/6 | |

1/3 |

Question 1 Explanation:

The equation can be simplified as

$ \displaystyle \begin{array}{l}\frac{1}{1+\frac{1}{\frac{1}{2}}}\times \frac{1}{\left( \frac{5}{6}\,\times \frac{3}{2} \right)\div \,\frac{5}{4}\,}\\=\frac{1}{1+2}\times \frac{1}{\frac{5}{4}\div \frac{5}{4}}\\=\frac{1}{3}\times \frac{1}{\frac{5}{4}\times \frac{4}{5}}\\=\frac{1}{3}\end{array}$

So the answer for the question is d

$ \displaystyle \begin{array}{l}\frac{1}{1+\frac{1}{\frac{1}{2}}}\times \frac{1}{\left( \frac{5}{6}\,\times \frac{3}{2} \right)\div \,\frac{5}{4}\,}\\=\frac{1}{1+2}\times \frac{1}{\frac{5}{4}\div \frac{5}{4}}\\=\frac{1}{3}\times \frac{1}{\frac{5}{4}\times \frac{4}{5}}\\=\frac{1}{3}\end{array}$

So the answer for the question is d

Question 2 |

$ \displaystyle \frac{1}{2+\frac{2}{3+\frac{2}{3+\frac{2}{3}}}\times 0.78}$
is simplified to

7/3 | |

100/11 | |

111/100 | |

None of these |

Question 2 Explanation:

$ \displaystyle \begin{array}{l}\frac{1}{2+\frac{2}{3+\frac{2}{\frac{11}{3}}}\times 0.78}\\=\frac{1}{2+\frac{2}{3+\frac{6}{11}}\times 0.78}\\=\frac{1}{2+\frac{2}{\frac{33+6}{11}}\times 0.78}\\=\frac{1}{\begin{array}{l}2+\frac{11\times 2}{39}\times 0.78\\=\frac{1}{2+\frac{11\times 2}{39}\times \frac{78}{100}}\end{array}}\\=\frac{1}{2+\frac{11}{25}}\\=25/61\end{array}$

Question 3 |

$ \displaystyle 3+\frac{1}{1+\frac{1}{2}}$

is equal to

is equal to

3/5 | |

3/2 | |

11/3 | |

7/3 |

Question 3 Explanation:

The Expression can be solved like as

$ \displaystyle 3+\frac{1}{1+\frac{1}{2}}$

$ \displaystyle \begin{array}{l}=3+\frac{1}{\frac{2+1}{2}}\\=3+\frac{2}{3}\\=\frac{9+2}{3}\\=\frac{11}{3}\end{array}$

$ \displaystyle 3+\frac{1}{1+\frac{1}{2}}$

$ \displaystyle \begin{array}{l}=3+\frac{1}{\frac{2+1}{2}}\\=3+\frac{2}{3}\\=\frac{9+2}{3}\\=\frac{11}{3}\end{array}$

Question 4 |

The value of

$ \displaystyle 5+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{2}{3}}}}}$ is

$ \displaystyle 5+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{2}{3}}}}}$ is

134/21 | |

132/23 | |

143/21 | |

118/21 |

Question 4 Explanation:

$ \displaystyle \begin{array}{l}5+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{\frac{3+2}{3}}}}}\\\end{array}$

$ \displaystyle \begin{array}{l}=5+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{3}{5}}}}\\=5+\frac{1}{1+\frac{1}{1+\frac{1}{\frac{5+3}{5}}}}\\=5+\frac{1}{1+\frac{1}{1+\frac{5}{8}}}\\=5+\frac{1}{1+\frac{1}{\frac{8+5}{8}}}\\=5+\frac{1}{1+\frac{8}{13}}=5+\frac{1}{\frac{13+8}{13}}\\=5+\frac{13}{21}=\frac{105+13}{21}=\frac{118}{21}\end{array}$

$ \displaystyle \begin{array}{l}=5+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{3}{5}}}}\\=5+\frac{1}{1+\frac{1}{1+\frac{1}{\frac{5+3}{5}}}}\\=5+\frac{1}{1+\frac{1}{1+\frac{5}{8}}}\\=5+\frac{1}{1+\frac{1}{\frac{8+5}{8}}}\\=5+\frac{1}{1+\frac{8}{13}}=5+\frac{1}{\frac{13+8}{13}}\\=5+\frac{13}{21}=\frac{105+13}{21}=\frac{118}{21}\end{array}$

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