Basic Maths: Test 52

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Basic Maths: Test 52

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Question 1

The simplified value of

$\left( 1-\frac{1}{5} \right)\,\left( 1-\frac{1}{6} \right)\,\left( 1-\frac{1}{7} \right)\,......\left( 1-\frac{1}{49} \right)\,\left( 1-\frac{1}{50} \right)$ <br> is

A	$\frac{2}{25}$
B	$\frac{1}{25}$
C	$\frac{1}{50}$
D	$\frac{1}{100}$

Question 1 Explanation:

$\begin{align} & =\left( 1-\frac{1}{5} \right)\,\left( 1-\frac{1}{6} \right)\,\left( 1-\frac{1}{7} \right)\,......\left( 1-\frac{1}{49} \right)\,\left( 1-\frac{1}{50} \right) \\ & =\left( \frac{5-1}{5} \right)\,\left( \frac{6-1}{6} \right)\,\left( \frac{7-1}{7} \right)\,......\left( \frac{49-1}{49} \right)\,\left( \frac{50-1}{50} \right) \\ & =\frac{4}{5}\times \frac{5}{6}\times \frac{6}{7}\times ......\times \frac{48}{49}\times \frac{49}{50} \\ & =\frac{4}{50} \\ & =\frac{2}{25} \\ \end{align}$

Question 2

$\frac{125{{\left( 1.3 \right)}^{3}}+1}{{{\left( 6.5 \right)}^{2}}-5.5}$ is equal to

A	2.75
B	9/5
C	4.75
D	7.5

Question 2 Explanation:

$\begin{align} & =\frac{125{{\left( 1.3 \right)}^{3}}+1}{{{\left( 6.5 \right)}^{2}}-5.5} \\ & =\frac{{{\left( 5\times 1.3 \right)}^{3}}+1}{{{\left( 6.5 \right)}^{2}}-6.5\times 1+{{1}^{2}}} \\ & =\frac{{{\left( 6.5 \right)}^{3}}+1}{{{\left( 6.5 \right)}^{2}}-6.5\times 1+{{1}^{2}}} \\ & \left[ {{a}^{3}}+{{b}^{3}}=\left( a+b \right)\left( {{a}^{2}}-ab+{{b}^{2}} \right) \right] \\ & =6.5+1 \\ & =7.5 \\ \end{align}$

Question 3

The value of

$\frac{{{\left( 1.987-4.523 \right)}^{2}}+{{\left( 1.987+4.523 \right)}^{2}}}{1.987\times 1.987+4.523\times 4.523}$ is

A	4
B	2
C	2.199
D	3.195

Question 3 Explanation:

Let 1.987=a and 4.523=b
Therefore expression

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

Question 4

$\left( 5555\div 110 \right)+\left( 925\div 75 \right)+\left( 5168\div 51 \right)=?$

A	164.16
B	174.26
C	184.16
D	194.26

Question 4 Explanation:

$\begin{align} & ?=\frac{5555}{110}+\frac{925}{75}+\frac{5168}{51} \\ & =50.5+12.33+101.33 \\ & =164.16 \\ \end{align}$

Question 5

$\sqrt{32041}\times \sqrt{1681}-{{\left( 71 \right)}^{2}}={{\left( ? \right)}^{2}}+{{\left( 23 \right)}^{2}}$ (? Is approximately equal to)

A	47
B	42
C	44
D	48

Question 5 Explanation:

$\begin{align} & \sqrt{32041}\times \sqrt{1681}-{{\left( 71 \right)}^{2}}={{\left( ? \right)}^{2}}+{{\left( 23 \right)}^{2}} \\ & \Rightarrow 179\times 41-5041={{?}^{2}}+529 \\ & \Rightarrow 2298={{?}^{2}}+529 \\ & \Rightarrow {{?}^{2}}=2298-529=1769 \\ & \Rightarrow ?=\sqrt{1769}=42.06 \\ \end{align}$
Approximately equals to 42

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