51. $$\frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{b - a}}}}$$ is equal to = ?
52. The value of $${\text{3}}\frac{1}{2} - $$ $$\left[ {2\frac{1}{4} \div \left\{ {1\frac{1}{4} - \frac{1}{2}\left( {1\frac{1}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right]$$ = ?
53. The value of $${\text{5}}\frac{1}{3} \div 1\frac{2}{9} \times \frac{1}{4}$$ $$\left( {10 + \frac{3}{{1 - \frac{1}{5}}}} \right)$$ = ?
54. What is $$\frac{{\frac{7}{8} \times \frac{7}{8} + \frac{5}{6} \times \frac{5}{6} + \frac{7}{8} \times \frac{5}{3}}}{{\frac{7}{8} \times \frac{7}{8} - \frac{5}{6} \times \frac{5}{6}}}$$ equal to ?
55. $$\frac{{{{\left( {469 + 174} \right)}^2} - {{\left( {469 - 174} \right)}^2}}}{{469 \times 174}} $$ = ?
56. If a - b = 3 and a2 + b2 = 29, find the value of ab = ?
57. What is the value of $$\frac{{\sqrt {24} + \sqrt {216} }}{{\sqrt {96} }} = ?$$
58. Simplify : $$\sqrt {3 + \frac{{33}}{{64}}} \div $$ $$\sqrt {9 + \frac{1}{7}} \times $$ $$2\sqrt {3\frac{1}{9}} $$ = ?
59. $$\frac{{{{\left( {3\frac{2}{3}} \right)}^2} - {{\left( {2\frac{1}{2}} \right)}^2}}}{{{{\left( {4\frac{3}{4}} \right)}^2} - {{\left( {3\frac{1}{3}} \right)}^2}}}$$ $$ \div $$ $$\frac{{3\frac{2}{3} - 2\frac{1}{2}}}{{4\frac{3}{4} - 3\frac{1}{3}}}$$ = ?
60. The simplified value of $$\frac{{\left( {1 + \frac{1}{{1 + \frac{1}{{100}}}}} \right)\left( {1 + \frac{1}{{1 + \frac{1}{{100}}}}} \right) - \left( {1 - \frac{1}{{1 + \frac{1}{{100}}}}} \right)\left( {1 - \frac{1}{{1 + \frac{1}{{100}}}}} \right)}}{{\left( {1 + \frac{1}{{1 + \frac{1}{{100}}}}} \right) + \left( {1 - \frac{1}{{1 + \frac{1}{{100}}}}} \right)}} = ?$$
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