Simplify : \({{{5 \over 3} \times {7 \over {51}}{ \text{ of }}{{17} \over 5} - {1 \over 3}} \over {{2 \over 9} \times {5 \over 7}{ \text{ of }}{{28} \over 5} - {2 \over 3}}}\)
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If \(\frac{p}{a} + \frac{q}{b} + \frac{r}{c} = 1\) and \(\frac{a}{p} + \frac{b}{q} + \frac{c}{r} = 0\) where a, b, c, p, q, r are non-zero real numbers, then \(\frac{{{p^2}}}{{{a^2}}} + \frac{{{q^2}}}{{{b^2}}} + \frac{{{r^2}}}{{{c^2}}}\) is equal to = ?
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2
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Simplify : \(\left[ {\left( {1 + \frac{1}{{10 + \frac{1}{{10}}}}} \right) \times \left( {1 + \frac{1}{{10 + \frac{1}{{10}}}}} \right) - \left( {1 - \frac{1}{{10 + \frac{1}{{10}}}}} \right) \times \left( {1 - \frac{1}{{10 + \frac{1}{{10}}}}} \right)} \right] \div \left[ {\left( {1 + \frac{1}{{10 + \frac{1}{{10}}}}} \right) + \left( {1 - \frac{1}{{10 + \frac{1}{{10}}}}} \right)} \right] = ?\)
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3
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98643 – 21748 = 51212 + ?
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4
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24.962 ÷ (34.11 ÷ 20.05) + 67.96 - 89.11 = ?
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5
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If \(\root 3 \of {{3^n}} { \text{ = 27,}}\) then the value of n is = ?
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6
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If x = a + m, y = b + m, z = c + m, then the value of \(\frac{{{x^2} + {y^2} + {z^2} - yz - zx - xy}}{{{a^2} + {b^2} + {c^2} - ab - bc - ca}}\) is = ?
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7
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The value of \(\frac{{25 - 5\left[ {2 + 3\left\{ {2 - 2\left( {5 - 3} \right) + 5} \right\} - 10} \right]}}{4} = ?\)
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8
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Simplify : \(1 + {1 \over {1 + {2 \over {2 + {3 \over {1 + {4 \over 5}}}}}}}\)
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9
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52 + 132 – 112 = (?)3 – 52
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10
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The Value of (\(\sqrt {6} + \sqrt {10} - \sqrt {21} - \sqrt {35}) × (\sqrt {6} - \sqrt {10} + \sqrt {21} - \sqrt {35}\)) = ?
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