- 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 37

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Question 1 |

The value of $\left( 1-\frac{1}{2} \right)\,\left( 1-\frac{1}{3} \right)\,\left( 1-\frac{1}{4} \right)\,.......\left( 1-\frac{1}{120} \right)$is

1/120 | |

120 | |

119/120 | |

1 |

Question 1 Explanation:

$\begin{align}
& \left( \frac{2-1}{2} \right)\,\left( \frac{3-1}{3} \right)\,\left( \frac{4-1}{4} \right)\,.......\left( \frac{120-1}{120} \right) \\
& =\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times ......\times \frac{119}{120} \\
& =\frac{1}{120} \\
\end{align}$

Question 2 |

The least on among the following

is

is

$13\frac{1}{2}%\,\,of\,\,100$ | |

$13.\overline{55}$ | |

${{\left( \frac{18.5}{5} \right)}^{2}}$ | |

$\sqrt{187}$ |

Question 2 Explanation:

$\begin{align}
& 13\frac{1}{2}%\,\,of\,\,100=\frac{27}{2}=13.5 \\
& \\
& 13.\overline{55}=13\frac{55}{99}\simeq 13.555555556(approx) \\
& {{\left( \frac{18.5}{5} \right)}^{2}}={{\left( 3.7 \right)}^{2}}=13.69 \\
& =\sqrt{187}=13.675 \\
\end{align}$

Question 3 |

Which of the following is the largest?

1000 ^{10000} | |

2 ^{100000} | |

100000 ^{1000} | |

3 ^{200} |

Question 3 Explanation:

\[\begin{align}
& {{\left( 1000 \right)}^{10000}}={{\left( {{10}^{3}} \right)}^{10000}}={{\left( 10 \right)}^{30000}} \\
& {{\left( 100000 \right)}^{1000}}={{\left( {{10}^{5}} \right)}^{1000}}={{10}^{5000}} \\
& {{2}^{100000}}={{\left( {{2}^{10}} \right)}^{10000}}={{\left( 1024 \right)}^{10000}} \\
& {{\left( 1024 \right)}^{10000}}>{{\left( 1000 \right)}^{10000}} \\
& {{3}^{200}}={{\left( {{3}^{2}} \right)}^{100}}={{\left( 9 \right)}^{100}} \\
& {{\left( 9 \right)}^{100}}\le {{\left( 10 \right)}^{100}} \\
\end{align}\]

Question 4 |

A sum of three non-zero numbers is five times the first number, four times the second number and k times the third number. The value of k is

11/20 | |

20/13 | |

20/11 | |

11/24 |

Question 4 Explanation:

$\begin{align}
& If\,\,the\,\,\,sum\,\,\,\,of\,\,\,three\,\,\,non-zero\,\,\,\operatorname{int}egers\,\,\,be\,\,\,S,\,\,then \\
& First\,\,\,number=\frac{S}{5} \\
& \operatorname{Sec}ond\,\,\,number=\frac{S}{4} \\
& Third\,\,\,number\,=\frac{S}{k} \\
& Therefore\,\,\,\frac{1}{5}+\frac{1}{4}+\frac{1}{k}=1 \\
& \Rightarrow \frac{1}{k}=1-\frac{1}{5}-\frac{1}{4}=\frac{20-4-5}{20} \\
& \Rightarrow \frac{1}{k}=\frac{11}{20} \\
& \Rightarrow k=\frac{20}{11} \\
\end{align}$

Question 5 |

Unit’s digit of $\left( {{3}^{\left( {{3}^{3}} \right)}}+{{333}^{333}} \right)$ is

0 | |

4 | |

1 | |

7 |

Question 5 Explanation:

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