21). \( \Large \sqrt{289} - \sqrt{625} \div \sqrt{25} \) is equal to
A). 17 |
B). 15 |
C). 12 |
D). \( \Large - \frac{8}{5} \) |
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22). If \( \Large a^{2} + 1 = a \), then what is the value of \( \Large a^{12} + a^{6} + 1 \) is
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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 |
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24). If a + b + c = 0, then the value of \( \Large \left(\frac{a+b}{c} + \frac{b+c}{a} + \frac{c+a}{b}\right) \) \( \Large \left(\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}\right) \)
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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 |
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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 |
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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). \( \Large - \frac{2}{a} \) |
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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 |
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29). If \( \Large x + y = 1 \), then the value of \( \Large x^{3} + y^{3} + 3xy\) is
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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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