- 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 51

Congratulations - you have completed *Basic Maths: Test 51*.

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Your answers are highlighted below.

Question 1 |

$\frac{{{\left( 6.679 \right)}^{3}}+{{\left( 3.321 \right)}^{3}}}{6.679\times 6.679-\left( 6.679\times 3.321 \right)+3.321\times 3.321}$

10 | |

1.248 | |

20.44 | |

1 |

Question 1 Explanation:

Let 6.679= a

And 3.321= b

Therefore given expression

$\begin{align} & =\frac{{{a}^{3}}+{{b}^{3}}}{{{a}^{2}}-ab+{{b}^{2}}} \\ & =\frac{\left( a+b \right)\left( {{a}^{2}}-ab+{{b}^{2}} \right)}{{{a}^{2}}-ab+{{b}^{2}}} \\ & =a+b=6.679+3.321 \\ & =10 \\ \end{align}$

And 3.321= b

Therefore given expression

$\begin{align} & =\frac{{{a}^{3}}+{{b}^{3}}}{{{a}^{2}}-ab+{{b}^{2}}} \\ & =\frac{\left( a+b \right)\left( {{a}^{2}}-ab+{{b}^{2}} \right)}{{{a}^{2}}-ab+{{b}^{2}}} \\ & =a+b=6.679+3.321 \\ & =10 \\ \end{align}$

Question 2 |

$\frac{127\times 127+127\times 123+123\times 123}{127\times 127\times 127-123\times 123\times 123}$
is equal to

4 | |

270 | |

$\frac{1}{4}$ | |

$\frac{1}{270}$ |

Question 2 Explanation:

Let 127 =a and 123= b

Given expression

$\begin{align} & \frac{a\times a+a\times b+b\times b}{a\times a\times a-b\times b\times b} \\ & =\frac{{{a}^{2}}+ab+{{b}^{2}}}{{{a}^{3}}-{{b}^{3}}} \\ & =\frac{{{a}^{2}}+ab+{{b}^{2}}}{\left( a-b \right)\left( {{a}^{2}}+ab+{{b}^{2}} \right)} \\ & =\frac{1}{a-b}=\frac{1}{127-123}=\frac{1}{4} \\ \end{align}$

Given expression

$\begin{align} & \frac{a\times a+a\times b+b\times b}{a\times a\times a-b\times b\times b} \\ & =\frac{{{a}^{2}}+ab+{{b}^{2}}}{{{a}^{3}}-{{b}^{3}}} \\ & =\frac{{{a}^{2}}+ab+{{b}^{2}}}{\left( a-b \right)\left( {{a}^{2}}+ab+{{b}^{2}} \right)} \\ & =\frac{1}{a-b}=\frac{1}{127-123}=\frac{1}{4} \\ \end{align}$

Question 3 |

The value of
$\frac{0.512+0.343}{0.64-0.56+0.49}$
is

0.2 | |

0.25 | |

0.3 | |

0.8 |

Question 3 Explanation:

$\begin{align}
& \frac{{{\left( 0.8 \right)}^{3}}+{{\left( 0.7 \right)}^{3}}}{{{\left( 0.8 \right)}^{2}}-0.8\times 0.7+{{\left( 0.7 \right)}^{2}}} \\
& Let\,\,0.8=a\,,\,\,\,and\,\,\,0.7=b \\
& Therefore\,\,\,\exp ression \\
& =\frac{{{a}^{3}}+{{b}^{3}}}{{{a}^{2}}-ab+{{b}^{2}}} \\
& =\frac{\left( a+b \right)\left( {{a}^{2}}-ab+{{b}^{2}} \right)}{{{a}^{2}}-ab+{{b}^{2}}} \\
& =a+b=0.8+0.7=1.5 \\
\end{align}$

Question 4 |

$3002\times 66+72716=?\times 128$

2177 | |

2167 | |

2467 | |

2116 |

Question 4 Explanation:

$\begin{align}
& 3002\times 66+72716=?\times 128 \\
& \Rightarrow 198132+72716=?\times 128 \\
& \Rightarrow 270848=?\times 128 \\
& \Rightarrow ?=270848\div 128=2116 \\
\end{align}$

Question 5 |

$\left[ \left( 3\sqrt{11}-\sqrt{11} \right)\times \left( 5\sqrt{11}+2\sqrt{11} \right) \right]-{{\left( 12 \right)}^{2}}=?$

100 | |

$10\sqrt{11}$ | |

10 | |

$\sqrt{11}$ |

Question 5 Explanation:

$\begin{align}
& ?=2\sqrt{11}\times 7\sqrt{11}-{{12}^{2}} \\
& =154-144=10 \\
\end{align}$

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