- 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 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
$\frac{2}{25}$ | |
$\frac{1}{25}$ | |
$\frac{1}{50}$ | |
$\frac{1}{100}$ |
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
2.75 | |
9/5 | |
4.75 | |
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
4 | |
2 | |
2.199 | |
3.195 |
Question 3 Explanation:
Let 1.987=a and 4.523=b
Therefore expression
$\begin{align} & =\frac{{{\left( a-b \right)}^{2}}+{{\left( a+b \right)}^{2}}}{{{a}^{2}}+{{b}^{2}}} \\ & =\frac{2\left( {{a}^{2}}+{{b}^{2}} \right)}{{{a}^{2}}+{{b}^{2}}}=2 \\ \end{align}$
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 |
$\left( 5555\div 110 \right)+\left( 925\div 75 \right)+\left( 5168\div 51 \right)=?$
164.16 | |
174.26 | |
184.16 | |
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)
47 | |
42 | |
44 | |
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
Approximately equals to 42
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