- 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 45
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Question 1 |
Which of the following is greater than
$\left( 1-\frac{1}{100} \right)\,\left( 1-\frac{1}{101} \right)\,\left( 1-\frac{1}{102} \right)\,......\left( 1-\frac{1}{200} \right)$ :
0.2 | |
0.3 | |
0.4 | |
0.5 |
Question 1 Explanation:
$\begin{align}
& \left( 1-\frac{1}{100} \right)\,\left( 1-\frac{1}{101} \right)\,\left( 1-\frac{1}{102} \right)\,......\left( 1-\frac{1}{200} \right) \\
& =\frac{99}{100}\times \frac{100}{101}\times \frac{101}{102}\times .....\frac{199}{200}=\frac{99}{200} \\
\end{align}$
Is less than 0.5
Is less than 0.5
Question 2 |
${{\left( \sqrt{3}+\frac{1}{\sqrt{3}} \right)}^{2}}$
is equal to:
$2\frac{1}{3}$ | |
$3\frac{1}{3}$ | |
$4\frac{1}{3}$ | |
$5\frac{1}{3}$ |
Question 2 Explanation:
$\begin{align}
& {{\left( \sqrt{3}+\frac{1}{\sqrt{3}} \right)}^{2}} \\
& =3+\frac{1}{3}+2\times \sqrt{3}\times \frac{1}{\sqrt{3}}=5\frac{1}{3} \\
\end{align}$
Question 3 |
The value of
${{\left( .89 \right)}^{3}}+{{\left( 0.11 \right)}^{3}}+3\times .89\times .11-1$
is:
1.98 | |
1.09 | |
1 | |
0 |
Question 3 Explanation:
Expression
$\begin{align} & {{\left( .89 \right)}^{3}}+{{\left( 0.11 \right)}^{3}}+3\times .89\times .11-1 \\ & ={{\left( .89 \right)}^{3}}+{{\left( 0.11 \right)}^{3}}+3\times .89\times .11\left( 0.89+0.11 \right)-1 \\ & ={{\left( 0.89+0.11 \right)}^{3}}-1=1-1=0 \\ \end{align}$
$\begin{align} & {{\left( .89 \right)}^{3}}+{{\left( 0.11 \right)}^{3}}+3\times .89\times .11-1 \\ & ={{\left( .89 \right)}^{3}}+{{\left( 0.11 \right)}^{3}}+3\times .89\times .11\left( 0.89+0.11 \right)-1 \\ & ={{\left( 0.89+0.11 \right)}^{3}}-1=1-1=0 \\ \end{align}$
Question 4 |
$7.4\overline{2}+0.\overline{8}+0.00\overline{3}$ is equal to
$8.\overline{313}$ | |
$8.3\overline{13}$ | |
$8.31\overline{3}$ | |
$8.3\overline{13}$ |
Question 4 Explanation:
Question 5 |
The value of
$\frac{4}{5}\times \frac{5}{\frac{7}{9}\div \frac{5}{3}\,\,of\,\,1\frac{6}{15}}$
is
2.5 | |
12 | |
10 | |
5 |
Question 5 Explanation:
Expression
\[\begin{align} & =\frac{4}{5}\times \frac{5}{\frac{7}{9}\div \frac{5}{3}\times \frac{21}{15}} \\ & =\frac{4}{5}\times 15=12 \\ \end{align}\]
\[\begin{align} & =\frac{4}{5}\times \frac{5}{\frac{7}{9}\div \frac{5}{3}\times \frac{21}{15}} \\ & =\frac{4}{5}\times 15=12 \\ \end{align}\]
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