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Basic Maths: Test 60

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Question 1
$\frac{\sqrt{28}+\sqrt{252}}{\sqrt{112}}$ is equal to
A
$\frac{2}{\sqrt{6}}$
B
$2\sqrt{6}$
C
$4\sqrt{6}$
D
2
Question 1 Explanation:
$\begin{align} & \frac{\sqrt{28}+\sqrt{252}}{\sqrt{112}} \\ & =\frac{\sqrt{4\times 7}+\sqrt{36\times 7}}{\sqrt{16\times 7}} \\ & =\frac{\sqrt{7}\left( 2+6 \right)}{4\sqrt{7}} \\ & =\frac{8}{4}=2 \\ \end{align}$
Question 2
$\frac{\left( 100-1 \right)\,\left( 100-2 \right)\,\left( 100-3 \right)\,.....\left( 100-99 \right)}{100\times 99\times 98\times .....\times 3\times 2\times 1}$ is equal to
A
$\frac{100}{99\times 98\times 97\times .....\times 3\times 2\times 1}$
B
0.01
C
0
D
$-\frac{2}{99\times 98\times 97\times ....\times 3\times 2\times 1}$
Question 2 Explanation:
\[\begin{align} & \frac{\left( 100-1 \right)\,\left( 100-2 \right)\,\left( 100-3 \right)\,.....\left( 100-99 \right)}{100\times 99\times 98\times .....\times 3\times 2\times 1} \\ & =\frac{\left( 99 \right)\,\left( 98 \right)\,\left( 97 \right)\,.....\left( 1 \right)}{100\times 99\times 98\times .....\times 3\times 2\times 1} \\ & =\frac{1}{100} \\ & =0.01 \\ \end{align}\]
Question 3
$\left( 7.5\times 7.5-37.5+2.5\times 2.5 \right)$ is equal to
A
20
B
25
C
15
D
30
Question 3 Explanation:
Let 7.5 = a, 2.5 = b
\[\begin{align} & Expression \\ & ={{a}^{2}}-2\times a\times b+{{b}^{2}} \\ & ={{\left( a-b \right)}^{2}} \\ & \left[ a-b=7.5-2.5=5 \right] \\ & ={{5}^{2}} \\ & =25 \\ \end{align}\]
Question 4
$\frac{2.25\times 2.25+2.75\times 2.75-2\times 2.25\times 2.75}{2.25\times 2.25-2.75\times 2.75}$simplified to
A
0.4
B
0.3
C
0.1
D
0.2
Question 4 Explanation:
\[\begin{align} & If\,\,2.75=a\,\,and\,\,\,2.25=b,\,\,then \\ & Expression \\ & =\frac{{{a}^{2}}+{{b}^{2}}-2ab}{{{a}^{2}}-{{b}^{2}}} \\ & =\frac{{{\left( a-b \right)}^{2}}}{\left( a-b \right)\left( a+b \right)}=\frac{\left( a-b \right)}{\left( a+b \right)} \\ & =\frac{0.5}{5} \\ & =0.1 \\ \end{align}\]
Question 5
$\left( \frac{5}{2}+\frac{4}{2} \right)\,\left( \frac{26}{3}-\frac{11}{3}+\frac{7}{3} \right)$ is equal to
A
33
B
19
C
37
D
36
Question 5 Explanation:
$\begin{align} & \left( \frac{5}{2}+\frac{4}{2} \right)\,\left( \frac{26}{3}-\frac{11}{3}+\frac{7}{3} \right) \\ & =\frac{9}{2}\times \frac{22}{3}=33 \\ \end{align}$
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