# Simplification Questions and answers

Topics

31). If $$\Large x = \frac{\sqrt{3}+1}{\sqrt{3}-1}$$ and $$\Large y = \frac{\sqrt{3}-1}{\sqrt{3}+1}$$ then the value of $$\Large \frac{x^{2}}{y} + \frac{y^{2}}{x}$$
 A). 52 B). 76 C). 4 D). 64
32). If p + q= 10 and pq = 5, then the numerical value of $$\Large \frac{p}{q}+\frac{q}{p}$$will be
 A). 22 B). 18 C). 16 D). 20
33). If x+ y=18 and xy= 72, what is the value of $$\Large x^{2} + y^{2}$$
 A). 120 B). 90 C). 180 D). Cannot be determined
34). $$\Large \frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 10} + \frac{1}{10 \times 13} + \frac{1}{13 \times 16} = ?$$
 A). $$\Large \frac{5}{16}$$ B). $$\Large \frac{3}{16}$$ C). $$\Large \frac{7}{16}$$ D). $$\Large \frac{11}{16}$$
35). $$\Large \left(2 -\frac{1}{3}\right) \left(2 - \frac{3}{5}\right) \left(2 - \frac{5}{7}\right) \left(2 - \frac{997}{999}\right)$$ is equal to
 A). $$\Large \frac{1001}{999}$$ B). $$\Large \frac{999}{1001}$$ C). $$\Large \frac{1001}{3}$$ D). $$\Large \frac{5}{1001}$$

36). The value of $$\Large \left(1 +\frac{1}{2}\right) \left(1 + \frac{1}{3}\right) \left(1 + \frac{1}{4}\right)$$ ... $$\Large \left(1 + \frac{1}{150}\right)$$ is
 A). 65.5 B). 50.5 C). 105 D). 75.5
37). If $$\Large x = \frac{\sqrt{3}}{2}$$, then the value of $$\Large \frac{1+x}{1+\sqrt{1+x}} + \frac{1-x}{1-\sqrt{1-x }}$$
 A). 0 B). 1 C). $$\Large \frac{\sqrt{3}}{2}$$ D). $$\Large \sqrt{3}$$
38). If $$\Large x + \frac{1}{x} = 2$$, then $$\Large \frac{2x^{2} + 2}{3x^{2} + 5x + 3}$$ = ?
 A). $$\Large \frac{4}{11}$$ B). $$\Large \frac{1}{2}$$ C). $$\Large 1\frac{3}{4}$$ D). $$\Large 2\frac{1}{3}$$
39). If $$\Large a + \frac{1}{b} = 1 \ and \ b + \frac{1}{c} = 1$$, then the value of $$\Large c + \frac{1}{a} = ?$$
 A). 4 B). 24 C). 3 D). 1
40). If $$\Large x + \frac{a}{x} = b$$, then the value of $$\Large \frac{x^{2} + bx + a }{bx^{2} - x^{3}}$$
 A). a + b B). $$\Large \frac{2b}{a}$$ C). $$\Large \frac{b}{a}$$ D). ab
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