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21). \( \Large \sqrt{289} - \sqrt{625} \div \sqrt{25} \) is equal to
A). 17
B). 15
C). 12
D). \( \Large - \frac{8}{5} \)
22). If \( \Large a^{2} + 1 = a \), then what is the value of \( \Large a^{12} + a^{6} + 1 \) is
A). 2
B). 3
C). -3
D). 1
23). If a, b and c are non-zero, \( \Large a + \frac{1}{b} = 1 \) and \( \Large b + \frac{1}{c} = 1 \), then the value of abc is
A). -3
B). 1
C). -1
D). 3
24). If a + b + c = 0, then the value of \( \Large \left(\frac{a+b}{c} + \frac{b+c}{a} + \frac{c+a}{b}\right) \) \( \Large \left(\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}\right) \)
A). 9
B). 0
C). 8
D). -3
25). If \( \Large a * b = a + b + \frac{a}{b} \), then the value \( \Large 12 * 4 \) is
A). 48
B). 19
C). 20
D). 21


26). If \( \Large x = \frac{\sqrt{2}+1}{\sqrt{2}-1} \) and \( \Large x - y = 4\sqrt{2} \), then the value of \( \Large \left(x^{2} + y^{2}\right) \) is
A). 34
B). 38
C). 30
D). 32
27). If \( \Large x + \frac{a}{x} = 1 \), then the value of \( \Large \frac{x^{2}+x+a}{x^{3}-x^{2}} \) is
A). -2
B). \( \Large - \frac{a}{2} \)
C). \( \Large \frac{2}{a} \)
D). \( \Large - \frac{2}{a} \)
28). If \( \Large \sqrt{28 - 6\sqrt{3}} = \sqrt{3} a + b \), (where a, b are rationale), value of \( \Large \left(a + b\right) \) is
A). -2
B). 2
C). 1
D). -1
29). If \( \Large x + y = 1 \), then the value of \( \Large x^{3} + y^{3} + 3xy\) is
A). -2
B). 1
C). 2
D). 3
30). If \( \Large a = \left(\sqrt{2}-1\right)^{\frac{1}{3}} \), then the value of \( \Large \left(a - a^{-1}\right)^{3} + 3 \left(a - a^{-1}\right) \) is
A). -2
B). 2
C). \( \Large 2\sqrt{2} \)
D). \( \Large \sqrt{2} \)
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