31. If 999x + 888y = 1332 and 888x + 999y = 555, then the value of x + y is?
32. If a2 + b2 + c2 = ab + bc + ca, then the value of $$\frac{{a + c}}{b}$$ is?
33. If a + b = 1, find the value of a3 + b3 - ab - (a2 - b2)2 = ?
34. If $$a - \frac{1}{{a - 3}} = 5{\text{,}}$$ then the value of $${\left( {a - 3} \right)^3}$$ - $$\frac{1}{{{{\left( {a - 3} \right)}^3}}} = ?$$
35. (3x - 2y) : (2x + 3y) = 5 : 6, then one of the value of $${\left( {\frac{{\root 3 \of x + \root 3 \of y }}{{\root 3 \of x - \root 3 \of y }}} \right)^2}$$ is?
36. If $${\text{ }}x - \sqrt 3 - \sqrt 2 = 0$$ and $$y - \sqrt 3 + \sqrt 2 {\text{,}}$$ then the value of $$\left( {{x^3} - 20\sqrt 2 } \right) - $$ $$\left( {{y^3} + 2\sqrt 2 } \right)?$$
37. 3(a2 + b2 + c2) = (a + b + c)2 then the relation between a, b and c is ?
38. If $$m = \sqrt {5 + \sqrt {5 + \sqrt {5.....} } } $$ and $$n = \sqrt {5 - \sqrt {5 - \sqrt {5.....} } } $$ then among the following the relation between m & n holds is?
39. If 2s = a + b + c, then the value of s(s - c) + (s - a) (s - b) is?
40. When xm is multiplied by xn, product is 1. The relation between m and n is?
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