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Simplify : $\sqrt{3 + \frac{33}{64}} \div \sqrt{9 + \frac{1}{7}} \times 2 \sqrt{3 \frac{1}{9}} = ?$ $\sqrt {3 + \frac{{33}}{{64}}} \div \sqrt {9 + \frac{1}{7}} \times 2\sqrt {3\frac{1}{9}} = ?$

1 $\frac{45}{256}$ $\frac{{45}}{{256}}$
2 $1 \frac{17}{28}$ $1\frac{{17}}{{28}}$
3 $4 \frac{3}{8}$ $4\frac{3}{8}$
4 $2 \frac{3}{16}$ $2\frac{3}{{16}}$

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} According to question \\ \sqrt{3 + \frac{33}{64}} \div \sqrt{9 + \frac{1}{7}} \times 2 \sqrt{3 \frac{1}{9}} \\ = \sqrt{\frac{225}{64}} \div \sqrt{\frac{64}{7}} \times 2 \sqrt{\frac{28}{9}} \\ = \sqrt{\frac{225}{64} \times \frac{7}{64} \times \frac{28}{9}} \times 2 \\ = \frac{5 \times 7}{8 \times 4} \times 2 \\ = \frac{35}{16} \\ = 2 \frac{3}{16} \end{aligned}

$\eqalign{ & {\text{According to question}} \cr & \sqrt {3 + \frac{{33}}{{64}}} \div \sqrt {9 + \frac{1}{7}} \times 2\sqrt {3\frac{1}{9}} \cr & = \sqrt {\frac{{225}}{{64}}} \div \sqrt {\frac{{64}}{7}} \times 2\sqrt {\frac{{28}}{9}} \cr & = \sqrt {\frac{{225}}{{64}} \times \frac{7}{{64}} \times \frac{{28}}{9}} \times 2 \cr & = \frac{{5 \times 7}}{{8 \times 4}} \times 2 \cr & = \frac{{35}}{{16}} \cr & = 2\frac{3}{{16}} \cr}$

What is the value of $\frac{\sqrt{24} + \sqrt{216}}{\sqrt{96}} = ?$ $\frac{{\sqrt {24} + \sqrt {216} }}{{\sqrt {96} }} = ?$

12√6
24√6
32
44

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} According to question \\ \frac{\sqrt{24} + \sqrt{216}}{\sqrt{96}} \\ = \frac{\sqrt{2 \times 2 \times 6} + \sqrt{6 \times 6 \times 6}}{\sqrt{4 \times 4 \times 6}} \\ = \frac{2 \sqrt{6} + 6 \sqrt{6}}{4 \sqrt{6}} \\ = \frac{8}{4} \\ = 2 \end{aligned}

$\eqalign{ & {\text{According to question}} \cr & \,\,\frac{{\sqrt {24} + \sqrt {216} }}{{\sqrt {96} }} \cr & = \frac{{\sqrt {2 \times 2 \times 6} + \sqrt {6 \times 6 \times 6} }}{{\sqrt {4 \times 4 \times 6} }} \cr & = \frac{{2\sqrt 6 + 6\sqrt 6 }}{{4\sqrt 6 }} \cr & = \frac{8}{4} \cr & = 2 \cr}$

03. If a - b = 3 and a² + b² = 29, find the value of ab = ?

110
212
315
418

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} 2 a b \\ = (a^{2} + b^{2}) - {(a - b)}^{2} \\ = 29 - 9 = 20 \\ ∴ a b = 10 \end{aligned}

$\eqalign{ & 2ab \cr & = \left( {{a^2} + {b^2}} \right) - {\left( {a - b} \right)^2} \cr & = 29 - 9 = 20 \cr & \therefore ab = 10 \cr}$

$\frac{{(469 + 174)}^{2} - {(469 + 174)}^{2}}{469 \times 174} = ?$ $\frac{{{{\left( {469 + 174} \right)}^2} - {{\left( {469 + 174} \right)}^2}}}{{469 \times 174}} = ?$

12
24
3295
41023

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} Given expression, \\ \frac{{(a + b)}^{2} - {(a - b)}^{2}}{a \times b} \\ = \frac{4 a b}{a b} \\ {where a = 469, b = 174} \\ = 4 \end{aligned}

$\eqalign{ & {\text{Given expression,}} \cr & \frac{{{{\left( {a + b} \right)}^2} - {{\left( {a - b} \right)}^2}}}{{a \times b}} \cr & = \frac{{4ab}}{{ab}} \cr & \left\{ {{\text{where }}a = 469,b = 174} \right\} \cr & = 4 \cr}$

The value of $5 \frac{1}{3} \div 1 \frac{2}{9} \times \frac{1}{4} (10 + \frac{3}{1 - \frac{1}{5}}) = ?$ ${\text{5}}\frac{1}{3} \div 1\frac{2}{9} \times \frac{1}{4}\left( {10 + \frac{3}{{1 - \frac{1}{5}}}} \right) = ?$

115
2 $\frac{67}{25}$ $\frac{{67}}{{25}}$
3 $\frac{128}{11}$ $\frac{{128}}{{11}}$
4 $\frac{128}{99}$ $\frac{{128}}{{99}}$

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} According to question \\ 5 \frac{1}{3} \div 1 \frac{2}{9} \times \frac{1}{4} (10 + \frac{3}{1 - \frac{1}{5}}) \\ = \frac{16}{3} \div \frac{11}{9} \times \frac{1}{4} (10 + \frac{3}{\frac{4}{5}}) \\ = \frac{16}{3} \div \frac{11}{9} \times \frac{1}{4} (10 + \frac{15}{4}) \\ = \frac{16}{3} \times \frac{9}{11} \times \frac{1}{4} \times \frac{55}{4} \\ = \frac{48}{11} \times \frac{1}{4} \times \frac{55}{4} \\ = 15 \end{aligned}

$\eqalign{ & {\text{According to question}} \cr & {\text{5}}\frac{1}{3} \div 1\frac{2}{9} \times \frac{1}{4}\left( {10 + \frac{3}{{1 - \frac{1}{5}}}} \right) \cr & = \frac{{16}}{3} \div \frac{{11}}{9} \times \frac{1}{4}\left( {10 + \frac{3}{{\frac{4}{5}}}} \right) \cr & = \frac{{16}}{3} \div \frac{{11}}{9} \times \frac{1}{4}\left( {10 + \frac{{15}}{4}} \right) \cr & = \frac{{16}}{3} \times \frac{9}{{11}} \times \frac{1}{4} \times \frac{{55}}{4} \cr & = \frac{{48}}{{11}} \times \frac{1}{4} \times \frac{{55}}{4} \cr & = 15 \cr}$

The value of $3 \frac{1}{2} - [2 \frac{1}{4} \div {1 \frac{1}{4} - \frac{1}{2} (1 \frac{1}{2} - \frac{1}{3} - \frac{1}{6})}] = ?$ ${\text{3}}\frac{1}{2} - \left[ {2\frac{1}{4} \div \left\{ {1\frac{1}{4} - \frac{1}{2}\left( {1\frac{1}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right] = ?$

1 $\frac{1}{2}$ $\frac{1}{2}$
2 $2 \frac{1}{2}$ $2\frac{1}{2}$
3 $3 \frac{1}{2}$ $3\frac{1}{2}$
4 $9 \frac{1}{2}$ $9\frac{1}{2}$

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} According to question \\ 3 \frac{1}{2} - [2 \frac{1}{4} \div {1 \frac{1}{4} - \frac{1}{2} (1 \frac{1}{2} - \frac{1}{3} - \frac{1}{6})}] \\ = \frac{7}{2} - [\frac{9}{4} \div {\frac{5}{4} - \frac{1}{2} (\frac{3}{2} - \frac{1}{3} - \frac{1}{6})}] \\ = \frac{7}{2} - [\frac{9}{4} \div {\frac{5}{4} - \frac{1}{2} \times 1}] \\ = \frac{7}{2} - [\frac{9}{4} \div \frac{3}{4}] \\ = \frac{7}{2} - [\frac{9}{4} \times \frac{4}{3}] \\ = \frac{7}{2} - 3 \\ = \frac{7 - 6}{2} \\ = \frac{1}{2} \end{aligned}

$\eqalign{ & {\text{According to question}} \cr & {\text{3}}\frac{1}{2} - \left[ {2\frac{1}{4} \div \left\{ {1\frac{1}{4} - \frac{1}{2}\left( {1\frac{1}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right] \cr & = \frac{7}{2} - \left[ {\frac{9}{4} \div \left\{ {\frac{5}{4} - \frac{1}{2}\left( {\frac{3}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right] \cr & = \frac{7}{2} - \left[ {\frac{9}{4} \div \left\{ {\frac{5}{4} - \frac{1}{2} \times 1} \right\}} \right] \cr & = \frac{7}{2} - \left[ {\frac{9}{4} \div \frac{3}{4}} \right] \cr & = \frac{7}{2} - \left[ {\frac{9}{4} \times \frac{4}{3}} \right] \cr & = \frac{7}{2} - 3 \cr & = \frac{{7 - 6}}{2} \cr & = \frac{1}{2} \cr}$

$\frac{1}{1 + 2^{a - b}} + \frac{1}{1 + 2^{b - a}}$ $\frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{b - a}}}}$ is equal to = ?

1a - b
2b - a
31
40

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} \frac{1}{1 + 2^{a - b}} + \frac{1}{1 + 2^{b - a}} \\ = \frac{1}{1 + 2^{a - b}} + \frac{1}{1 + 2^{- (a - b)}} \\ = \frac{1}{1 + 2^{a - b}} + \frac{2^{a - b}}{2^{a - b} + 1} \\ = \frac{1 + 2^{a - b}}{1 + 2^{a - b}} \\ = 1 \end{aligned}

$\eqalign{ & \frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{b - a}}}} \cr & = \frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{ - \left( {a - b} \right)}}}} \cr & = \frac{1}{{1 + {2^{a - b}}}} + \frac{{{2^{a - b}}}}{{{2^{a - b}} + 1}} \cr & = \frac{{1 + {2^{a - b}}}}{{1 + {2^{a - b}}}} \cr & = 1 \cr}$

The simplification of $(\frac{75983 \times 75983 - 45983 \times 45983}{30000})$ $\left( {\frac{{75983 \times 75983 - 45983 \times 45983}}{{30000}}} \right)$ yields the result = ?

1121796
2121866
3121956
4121966

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} Given expression, \\ \frac{{(75983)}^{2} - {(45983)}^{2}}{75983 - 45983} \\ = \frac{(75983 - 45983) (75983 + 45983)}{(75983 - 45983)} \\ = 75983 + 45983 \\ = 121966 \end{aligned}

$\eqalign{ & {\text{Given expression,}} \cr & \,\,\,\,\,\frac{{{{\left( {75983} \right)}^2} - {{\left( {45983} \right)}^2}}}{{75983 - 45983}} \cr & = \frac{{\left( {75983 - 45983} \right)\left( {75983 + 45983} \right)}}{{(75983 - 45983)}} \cr & = \,75983 + 45983 \cr & = 121966 \cr}$

$\sqrt{\frac{4 \frac{1}{7} - 2 \frac{1}{4}}{3 \frac{1}{2} + 1 \frac{1}{7}} \div \frac{1}{2 + \frac{1}{2 + \frac{1}{5 - \frac{1}{5}}}}}$ $\sqrt {\frac{{4\frac{1}{7} - 2\frac{1}{4}}}{{3\frac{1}{2} + 1\frac{1}{7}}} \div \frac{1}{{2 + \frac{1}{{2 + \frac{1}{{5 - \frac{1}{5}}}}}}}}$ is equal to = ?

11
24
33
42

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} Take first part \\ \frac{4 \frac{1}{7} - 2 \frac{1}{4}}{3 \frac{1}{2} + 1 \frac{1}{7}} \\ = \frac{\frac{29}{7} - \frac{9}{4}}{\frac{7}{2} + \frac{8}{7}} \\ = \frac{\frac{116 - 63}{28}}{\frac{49 + 16}{14}} \\ = \frac{53}{28} \times \frac{14}{65} \\ = \frac{53}{130} \\ The second part \\ \frac{1}{2 + \frac{1}{2 + \frac{1}{5 - \frac{1}{5}}}} \\ = \frac{1}{2 + \frac{1}{2 + \frac{1}{\frac{25 - 1}{5}}}} \\ = \frac{1}{2 + \frac{1}{2 + \frac{5}{24}}} \\ = \frac{1}{2 + \frac{1}{\frac{53}{24}}} \\ = \frac{1}{2 + \frac{24}{53}} \\ = \frac{1}{\frac{106 + 24}{53}} \\ = \frac{53}{130} \\ According to question \\ \sqrt{\frac{53}{130} \div \frac{53}{130}} \\ = \sqrt{\frac{53}{130} \times \frac{130}{63}} \\ = \sqrt{1} \\ = 1 \end{aligned}

$\eqalign{ & {\text{Take first part }} \cr & \frac{{4\frac{1}{7} - 2\frac{1}{4}}}{{3\frac{1}{2} + 1\frac{1}{7}}} \cr & = \frac{{\frac{{29}}{7} - \frac{9}{4}}}{{\frac{7}{2} + \frac{8}{7}}} \cr & = \frac{{\frac{{116 - 63}}{{28}}}}{{\frac{{49 + 16}}{{14}}}} \cr & = \frac{{53}}{{28}} \times \frac{{14}}{{65}} \cr & = \frac{{53}}{{130}} \cr & {\text{The second part}} \cr & \frac{1}{{2 + \frac{1}{{2 + \frac{1}{{5 - \frac{1}{5}}}}}}} \cr & = \frac{1}{{2 + \frac{1}{{2 + \frac{1}{{\frac{{25 - 1}}{5}}}}}}} \cr & = \frac{1}{{2 + \frac{1}{{2 + \frac{5}{{24}}}}}} \cr & = \frac{1}{{2 + \frac{1}{{\frac{{53}}{{24}}}}}} \cr & = \frac{1}{{2 + \frac{{24}}{{53}}}} \cr & = \frac{1}{{\frac{{106 + 24}}{{53}}}} \cr & = \frac{{53}}{{130}} \cr & {\text{According to question}} \cr & \,\,\,\,\,\,\sqrt {\frac{{53}}{{130}} \div \frac{{53}}{{130}}} \cr & = \sqrt {\frac{{53}}{{130}} \times \frac{{130}}{{63}}} \cr & = \sqrt 1 \cr & = 1 \cr}$

$If [4 - \frac{5}{1 + \frac{1}{3 + \frac{1}{2 + \frac{1}{4}}}}]$ ${\text{If }}\left[ {4 - \frac{5}{{1 + \frac{1}{{3 + \frac{1}{{2 + \frac{1}{4}}}}}}}} \right]$ part of a journey takes ten minutes, then to complete $\frac{3}{5}$ $\frac{3}{5}$ th of that journey, it will take = ?

140 minutes
245 minutes
348 minutes
436 minutes

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} According to question \\ [4 - \frac{5}{1 + \frac{1}{3 + \frac{1}{2 + \frac{1}{4}}}}] \\ = 4 - \frac{5}{1 + \frac{1}{3 + \frac{1}{\frac{9}{4}}}} \\ = 4 - \frac{5}{1 + \frac{1}{3 + \frac{4}{9}}} \\ = 4 - \frac{5}{1 + \frac{1}{\frac{31}{9}}} \\ = 4 - \frac{5}{1 + \frac{9}{31}} \\ = 4 - \frac{5}{\frac{40}{31}} \\ = 4 - \frac{5 \times 30}{40} \\ = 4 - \frac{31}{8} \\ = \frac{1}{8} \\ According to question \\ \frac{1}{8} part  =  10 minutes \\ 1 part  =  10 minutes \\ \frac{3}{5} part  =  80 \times \frac{3}{5} \\ =  48 minutes \end{aligned}

$\eqalign{ & {\text{According to question}} \cr & \,\,\,\left[ {4 - \frac{5}{{1 + \frac{1}{{3 + \frac{1}{{2 + \frac{1}{4}}}}}}}} \right] \cr & = 4 - \frac{5}{{1 + \frac{1}{{3 + \frac{1}{{\frac{9}{4}}}}}}} \cr & = 4 - \frac{5}{{1 + \frac{1}{{3 + \frac{4}{9}}}}} \cr & = 4 - \frac{5}{{1 + \frac{1}{{\frac{{31}}{9}}}}} \cr & = 4 - \frac{5}{{1 + \frac{9}{{31}}}} \cr & = 4 - \frac{5}{{\frac{{40}}{{31}}}} \cr & = 4 - \frac{{5 \times 30}}{{40}} \cr & = 4 - \frac{{31}}{8} \cr & = \frac{1}{8} \cr & {\text{According to question}} \cr & \frac{1}{8}{\text{part = 10 minutes}} \cr & {\text{1 part = 10 minutes}} \cr & \frac{3}{5}{\text{ part = 80}} \times \frac{3}{5} \cr & {\text{ = 48 minutes}} \cr}$

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Simplification - 03

Simplify : $\sqrt{3 + \frac{33}{64}} \div \sqrt{9 + \frac{1}{7}} \times 2 \sqrt{3 \frac{1}{9}} = ?$ $\sqrt {3 + \frac{{33}}{{64}}} \div \sqrt {9 + \frac{1}{7}} \times 2\sqrt {3\frac{1}{9}} = ?$

What is the value of $\frac{\sqrt{24} + \sqrt{216}}{\sqrt{96}} = ?$ $\frac{{\sqrt {24} + \sqrt {216} }}{{\sqrt {96} }} = ?$

03. If a - b = 3 and a² + b² = 29, find the value of ab = ?

$\frac{{(469 + 174)}^{2} - {(469 + 174)}^{2}}{469 \times 174} = ?$ $\frac{{{{\left( {469 + 174} \right)}^2} - {{\left( {469 + 174} \right)}^2}}}{{469 \times 174}} = ?$

The value of $5 \frac{1}{3} \div 1 \frac{2}{9} \times \frac{1}{4} (10 + \frac{3}{1 - \frac{1}{5}}) = ?$ ${\text{5}}\frac{1}{3} \div 1\frac{2}{9} \times \frac{1}{4}\left( {10 + \frac{3}{{1 - \frac{1}{5}}}} \right) = ?$

The value of $3 \frac{1}{2} - [2 \frac{1}{4} \div {1 \frac{1}{4} - \frac{1}{2} (1 \frac{1}{2} - \frac{1}{3} - \frac{1}{6})}] = ?$ ${\text{3}}\frac{1}{2} - \left[ {2\frac{1}{4} \div \left\{ {1\frac{1}{4} - \frac{1}{2}\left( {1\frac{1}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right] = ?$

$\frac{1}{1 + 2^{a - b}} + \frac{1}{1 + 2^{b - a}}$ $\frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{b - a}}}}$ is equal to = ?

The simplification of $(\frac{75983 \times 75983 - 45983 \times 45983}{30000})$ $\left( {\frac{{75983 \times 75983 - 45983 \times 45983}}{{30000}}} \right)$ yields the result = ?

$\sqrt{\frac{4 \frac{1}{7} - 2 \frac{1}{4}}{3 \frac{1}{2} + 1 \frac{1}{7}} \div \frac{1}{2 + \frac{1}{2 + \frac{1}{5 - \frac{1}{5}}}}}$ $\sqrt {\frac{{4\frac{1}{7} - 2\frac{1}{4}}}{{3\frac{1}{2} + 1\frac{1}{7}}} \div \frac{1}{{2 + \frac{1}{{2 + \frac{1}{{5 - \frac{1}{5}}}}}}}}$ is equal to = ?

$If [4 - \frac{5}{1 + \frac{1}{3 + \frac{1}{2 + \frac{1}{4}}}}]$ ${\text{If }}\left[ {4 - \frac{5}{{1 + \frac{1}{{3 + \frac{1}{{2 + \frac{1}{4}}}}}}}} \right]$ part of a journey takes ten minutes, then to complete $\frac{3}{5}$ $\frac{3}{5}$ th of that journey, it will take = ?

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Simplification - 03

01. Simplify : 3+3364−−−−−−√÷9+17−−−−−√×2319−−−√=?3+3364÷9+17×2319=?\sqrt {3 + \frac{{33}}{{64}}} \div \sqrt {9 + \frac{1}{7}} \times 2\sqrt {3\frac{1}{9}} = ?

02. What is the value of 24−−√+216−−−√96−−√=?24+21696=?\frac{{\sqrt {24} + \sqrt {216} }}{{\sqrt {96} }} = ?

03. If a - b = 3 and a2 + b2 = 29, find the value of ab = ?

04. (469+174)2−(469+174)2469×174=?(469+174)2−(469+174)2469×174=?\frac{{{{\left( {469 + 174} \right)}^2} - {{\left( {469 + 174} \right)}^2}}}{{469 \times 174}} = ?

05. The value of 513÷129×14(10+31−15)=?513÷129×14(10+31−15)=?{\text{5}}\frac{1}{3} \div 1\frac{2}{9} \times \frac{1}{4}\left( {10 + \frac{3}{{1 - \frac{1}{5}}}} \right) = ?

06. The value of 312−[214÷{114−12(112−13−16)}]=?312−[214÷{114−12(112−13−16)}]=?{\text{3}}\frac{1}{2} - \left[ {2\frac{1}{4} \div \left\{ {1\frac{1}{4} - \frac{1}{2}\left( {1\frac{1}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right] = ?

07. 11+2a−b+11+2b−a11+2a−b+11+2b−a\frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{b - a}}}} is equal to = ?

08. The simplification of (75983×75983−45983×4598330000)(75983×75983−45983×4598330000)\left( {\frac{{75983 \times 75983 - 45983 \times 45983}}{{30000}}} \right) yields the result = ?

09. 417−214312+117÷12+12+15−15−−−−−−−−−−−−−−−−−−−⎷417−214312+117÷12+12+15−15\sqrt {\frac{{4\frac{1}{7} - 2\frac{1}{4}}}{{3\frac{1}{2} + 1\frac{1}{7}}} \div \frac{1}{{2 + \frac{1}{{2 + \frac{1}{{5 - \frac{1}{5}}}}}}}} is equal to = ?

10. If ⎡⎣⎢⎢⎢4−51+13+12+14⎤⎦⎥⎥⎥If [4−51+13+12+14]{\text{If }}\left[ {4 - \frac{5}{{1 + \frac{1}{{3 + \frac{1}{{2 + \frac{1}{4}}}}}}}} \right] part of a journey takes ten minutes, then to complete 3535\frac{3}{5}th of that journey, it will take = ?

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Simplify : $\sqrt{3 + \frac{33}{64}} \div \sqrt{9 + \frac{1}{7}} \times 2 \sqrt{3 \frac{1}{9}} = ?$ $\sqrt {3 + \frac{{33}}{{64}}} \div \sqrt {9 + \frac{1}{7}} \times 2\sqrt {3\frac{1}{9}} = ?$

What is the value of $\frac{\sqrt{24} + \sqrt{216}}{\sqrt{96}} = ?$ $\frac{{\sqrt {24} + \sqrt {216} }}{{\sqrt {96} }} = ?$

03. If a - b = 3 and a² + b² = 29, find the value of ab = ?

$\frac{{(469 + 174)}^{2} - {(469 + 174)}^{2}}{469 \times 174} = ?$ $\frac{{{{\left( {469 + 174} \right)}^2} - {{\left( {469 + 174} \right)}^2}}}{{469 \times 174}} = ?$

The value of $5 \frac{1}{3} \div 1 \frac{2}{9} \times \frac{1}{4} (10 + \frac{3}{1 - \frac{1}{5}}) = ?$ ${\text{5}}\frac{1}{3} \div 1\frac{2}{9} \times \frac{1}{4}\left( {10 + \frac{3}{{1 - \frac{1}{5}}}} \right) = ?$

The value of $3 \frac{1}{2} - [2 \frac{1}{4} \div {1 \frac{1}{4} - \frac{1}{2} (1 \frac{1}{2} - \frac{1}{3} - \frac{1}{6})}] = ?$ ${\text{3}}\frac{1}{2} - \left[ {2\frac{1}{4} \div \left\{ {1\frac{1}{4} - \frac{1}{2}\left( {1\frac{1}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right] = ?$

$\frac{1}{1 + 2^{a - b}} + \frac{1}{1 + 2^{b - a}}$ $\frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{b - a}}}}$ is equal to = ?

The simplification of $(\frac{75983 \times 75983 - 45983 \times 45983}{30000})$ $\left( {\frac{{75983 \times 75983 - 45983 \times 45983}}{{30000}}} \right)$ yields the result = ?

$\sqrt{\frac{4 \frac{1}{7} - 2 \frac{1}{4}}{3 \frac{1}{2} + 1 \frac{1}{7}} \div \frac{1}{2 + \frac{1}{2 + \frac{1}{5 - \frac{1}{5}}}}}$ $\sqrt {\frac{{4\frac{1}{7} - 2\frac{1}{4}}}{{3\frac{1}{2} + 1\frac{1}{7}}} \div \frac{1}{{2 + \frac{1}{{2 + \frac{1}{{5 - \frac{1}{5}}}}}}}}$ is equal to = ?

$If [4 - \frac{5}{1 + \frac{1}{3 + \frac{1}{2 + \frac{1}{4}}}}]$ ${\text{If }}\left[ {4 - \frac{5}{{1 + \frac{1}{{3 + \frac{1}{{2 + \frac{1}{4}}}}}}}} \right]$ part of a journey takes ten minutes, then to complete $\frac{3}{5}$ $\frac{3}{5}$ th of that journey, it will take = ?

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