- 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 35

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Question 1 |

$ \displaystyle \frac{2\frac{1}{3}-\frac{5}{7}\,of\,\frac{7}{10}}{3\frac{1}{2}\div \frac{7}{6}\left( \frac{9}{14}+11\frac{1}{7} \right)}-\left[ \left( 2\frac{3}{4}\,of\,2\frac{2}{11} \right)\div 135 \right]$

is equal to

is equal to

1 | |

1/135 | |

135 | |

$15\frac{1}{2}$ |

Question 1 Explanation:

Question 2 |

The value of $\frac{0.5\times 0.5\times 0.5+0.7\times 0.7\times 0.7+0.9\times 0.9\times 0.9-3\times 0.5\times 0.7\times 0.9}{0.5\times 0.5+0.7\times 0.7+0.9\times 0.9-0.5\times 0.7-0.7\times 0.9-0.9\times 0.5}$ is

0.21 | |

0.02 | |

1 | |

2.1
â€ƒ |

Question 2 Explanation:

\[\begin{align}
& Let\,\,\,0.5\,\,=a,\,\,0.7=b\,\,and\,\,0.9=c \\
& Then,\,\,we\,\,have, \\
& \frac{a\times a\times a+b\times b\times b+c\times c\times c-3abc}{a\times a+b\times b+c\times c-ab-bc-ac} \\
& =\frac{{{a}^{3}}+b{}^{3}+{{c}^{3}}-3abc}{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ac} \\
& =\frac{\left( a+b+c \right)\left( {{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ac \right)}{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ac} \\
& =a+b+c \\
& =0.5+0.7+0.9=2.1 \\
\end{align}\]

Question 3 |

The value of
$\frac{4.096\times 5241\times 2.167}{49.986\times 1362.114}$is closest to

0.062 | |

0.62 | |

6.2 | |

62 |

Question 3 Explanation:

Taking approximate values, we have
$\frac{4\times 5241\times 2}{50\times 1362}=0.61568=0.62$

Question 4 |

$\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}=?$

$12$ | |

$\frac{1}{9}$ | |

$\frac{5}{27}$ | |

$\frac{1}{12}$ |

Question 4 Explanation:

$\begin{align}
& \frac{1}{6\times 7}+\frac{1}{7\times 8}+\frac{1}{8\times 9}+\frac{1}{9\times 10}+\frac{1}{10\times 11}+\frac{1}{11\times 12} \\
& =\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12} \\
& =\frac{1}{6}-\frac{1}{12}=\frac{2-1}{12}=\frac{1}{12} \\
\end{align}$

Question 5 |

Simplify
$\sqrt{\,\left[ \,{{\left( 10.1 \right)}^{2}}-{{\left( 6.1 \right)}^{2}} \right]/\left[ \,{{\left( 0.25 \right)}^{2}}+\left( 0.25 \right)\,\left( 15.95 \right)\, \right]}$

1 | |

2 | |

3 | |

4 |

Question 5 Explanation:

$\begin{align}
& \sqrt{\frac{16.2\times 4}{0.25\times 16.2}}=\sqrt{\frac{4}{0.25}} \\
& =\sqrt{\frac{400}{25}}=\sqrt{16}=4 \\
\end{align}$

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