41. If $$\frac{{\sqrt 7 - 2}}{{\sqrt 7 + 2}} = a\sqrt 7 + b{\text{,}}$$ then the value of a is?
42. If $$a + \frac{1}{b} = 1$$ and $$b + \frac{1}{c} = 1$$ then $$c + \frac{1}{a}$$ is equal to?
43. If x + y = 7, then the value of x3 + y3 + 21xy is?
44. If ⊗ is an operation such that a ⊗ b = 2a when a > b, a + b when a < b, a2 when a = b, then $$\left[ {\frac{{\left( {5 \otimes 7} \right) + \left( {4 \otimes 4} \right)}}{{3\left( {5 \otimes 5} \right) - \left( {15 \otimes 11} \right) - 3}}} \right]$$ is equal to?
45. If (125)x = 3125, then the value of x is?
46. If $$n + \frac{2}{3}n + \frac{1}{2}n + \frac{1}{7}n = 97{\text{,}}$$ then the value of n is?
47. If $$x - \frac{1}{x} = 4{\text{,}}$$ then $$\left( {x + \frac{1}{x}} \right)$$ is equal to?
48. If $$4{b^2} + \frac{1}{{{b^2}}} = 2,$$ then the value of $$8{b^3} + \frac{1}{{{b^3}}}{\text{ is?}}$$
49. $${\text{If }}{\left( {\frac{3}{5}} \right)^3} \times {\left( {\frac{3}{5}} \right)^{ - 6}} = $$ $${\left( {\frac{3}{5}} \right)^{2x - 1}}{\text{,}}$$ then x is equal to?
50. $$\frac{{\sqrt {3 + x} + \sqrt {3 - x} }}{{\sqrt {3 + x} - \sqrt {3 - x} }} = 2{\text{,}}$$ then x is equal to?
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