 This is an assessment test.
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Basic Maths: Test 37
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Question 1 
The value of $\left( 1\frac{1}{2} \right)\,\left( 1\frac{1}{3} \right)\,\left( 1\frac{1}{4} \right)\,.......\left( 1\frac{1}{120} \right)$is
1/120  
120  
119/120  
1

Question 1 Explanation:
$\begin{align}
& \left( \frac{21}{2} \right)\,\left( \frac{31}{3} \right)\,\left( \frac{41}{4} \right)\,.......\left( \frac{1201}{120} \right) \\
& =\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times ......\times \frac{119}{120} \\
& =\frac{1}{120} \\
\end{align}$
Question 2 
The least on among the following
is
is
$13\frac{1}{2}%\,\,of\,\,100$
 
$13.\overline{55}$  
${{\left( \frac{18.5}{5} \right)}^{2}}$  
$\sqrt{187}$ 
Question 2 Explanation:
$\begin{align}
& 13\frac{1}{2}%\,\,of\,\,100=\frac{27}{2}=13.5 \\
& \\
& 13.\overline{55}=13\frac{55}{99}\simeq 13.555555556(approx) \\
& {{\left( \frac{18.5}{5} \right)}^{2}}={{\left( 3.7 \right)}^{2}}=13.69 \\
& =\sqrt{187}=13.675 \\
\end{align}$
Question 3 
Which of the following is the largest?
1000^{10000}  
2^{100000}  
100000^{1000}  
3^{200} 
Question 3 Explanation:
\[\begin{align}
& {{\left( 1000 \right)}^{10000}}={{\left( {{10}^{3}} \right)}^{10000}}={{\left( 10 \right)}^{30000}} \\
& {{\left( 100000 \right)}^{1000}}={{\left( {{10}^{5}} \right)}^{1000}}={{10}^{5000}} \\
& {{2}^{100000}}={{\left( {{2}^{10}} \right)}^{10000}}={{\left( 1024 \right)}^{10000}} \\
& {{\left( 1024 \right)}^{10000}}>{{\left( 1000 \right)}^{10000}} \\
& {{3}^{200}}={{\left( {{3}^{2}} \right)}^{100}}={{\left( 9 \right)}^{100}} \\
& {{\left( 9 \right)}^{100}}\le {{\left( 10 \right)}^{100}} \\
\end{align}\]
Question 4 
A sum of three nonzero numbers is five times the first number, four times the second number and k times the third number. The value of k is
11/20
 
20/13  
20/11  
11/24 
Question 4 Explanation:
$\begin{align}
& If\,\,the\,\,\,sum\,\,\,\,of\,\,\,three\,\,\,nonzero\,\,\,\operatorname{int}egers\,\,\,be\,\,\,S,\,\,then \\
& First\,\,\,number=\frac{S}{5} \\
& \operatorname{Sec}ond\,\,\,number=\frac{S}{4} \\
& Third\,\,\,number\,=\frac{S}{k} \\
& Therefore\,\,\,\frac{1}{5}+\frac{1}{4}+\frac{1}{k}=1 \\
& \Rightarrow \frac{1}{k}=1\frac{1}{5}\frac{1}{4}=\frac{2045}{20} \\
& \Rightarrow \frac{1}{k}=\frac{11}{20} \\
& \Rightarrow k=\frac{20}{11} \\
\end{align}$
Question 5 
Unit’s digit of $\left( {{3}^{\left( {{3}^{3}} \right)}}+{{333}^{333}} \right)$ is
0  
4
 
1  
7 
Question 5 Explanation:
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