Basic Maths: Test 51

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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 51

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Question 1

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

A	10
B	1.248
C	20.44
D	1

Question 1 Explanation:

Let 6.679= a
And 3.321= b
Therefore given expression

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

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

A	4
B	270
C	$\frac{1}{4}$
D	$\frac{1}{270}$

Question 2 Explanation:

Let 127 =a and 123= b
Given expression

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

Question 3

The value of

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

A	0.2
B	0.25
C	0.3
D	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

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

A	2177
B	2167
C	2467
D	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