Simplify : \(\frac{{\frac{5}{3} \times \frac{7}{{51}}{ \text{ of }}\frac{17}{5} - \frac{1}{3}}}{{\frac{2}{9} \times \frac{5}{7}{ \text{ of }}\frac{{28}}{5} - \frac{2}{3}}}{\kern 1pt} {\kern 1pt} = ?\)
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\(\frac{{38 \times 38 \times 38 + 34 \times 34 \times 34 + 28 \times 28 \times 28 - 38 \times 34 \times 84}}{{38 \times 38 + 34 \times 34 + 28 \times 28 - 38 \times 34 - 34 \times 28 - 38 \times 28}}\) is equal to = ?
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2
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The value of \(\frac{{{{\left( {x - y} \right)}^3} + {{\left( {y - z} \right)}^3} + {{\left( {z - x} \right)}^3}}}{{{{\left( {{x^2} - {y^2}} \right)}^3} + {{\left( {{y^2} - {z^2}} \right)}^3} + {{\left( {{z^2} - {x^2}} \right)}^3}}}\) is = ?
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3
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If \(\left( {x + \frac{1}{x}} \right) = 3,\) then \(\left( {{x^2} + \frac{1}{{{x^2}}}} \right)\) is = ?
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4
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\(1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{7} + \frac{1}{{14}} + \frac{1}{{28}}\) is equal to = ?
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5
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Simplify : \(\frac{{ - \frac{1}{2} - \frac{2}{3} + \frac{4}{5} - \frac{1}{3} + \frac{1}{5} + \frac{3}{4}}}{{\frac{1}{2} + \frac{2}{3} - \frac{4}{3} + \frac{1}{3} - \frac{1}{5} - \frac{4}{5}}}\)
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6
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\(\left( {\frac{{785 \times 785 \times 785 + 435 \times 435 \times 435}}{{785 \times 785 + 435 \times 435 - 785 \times 435}}} \right)\) simplifies to = ?
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7
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If \(\frac{{x + 1}}{{x - 1}}{ \text{ = }}\frac{a}{b} \) and \(\frac{{1 - y}}{{1 + y}}{ \text{ = }}\frac{b}{a}{ \text{,}} \) then the value of \(\frac{{x - y}}{{1 + xy}}\) = ?
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8
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One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
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9
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The number of pairs of natural numbers the difference of whose squares is 45 will be ?
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10
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If 45 - [28 - {37 - (15 - *)}] then * equal to?
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