61). If \( \Large n+\frac{2}{3}n+\frac{1}{2}n+\frac{1}{7}n=97 \), then the value of n is
A). 40 |
B). 42 |
C). 44 |
D). 46 |
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62). If \( \Large x=3+\sqrt{8} \), then \( \Large x^{2}+\frac{1}{x^{2}} \) is equal to
A). 38 |
B). 36 |
C). 34 |
D). 30 |
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63). If \( \Large x-\frac{1}{x}=4 \), then \( \Large \left(x+\frac{1}{x}\right) \) is equal to
A). \( \Large 5\sqrt{2} \) |
B). \( \Large 2\sqrt{5} \) |
C). \( \Large 4\sqrt{2} \) |
D). \( \Large 4\sqrt{5} \) |
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64). If \( \Large 4b^{2}+\frac{1}{b^{2}}=2 \), then the value of \( \Large 8b^{3}+\frac{1}{b^{3}} \) is
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65). If \( \Large 2^{2x-y}=16\ and\ 2^{x+y}=32 \), the value of xy is
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66). If \( \Large \left(\frac{3}{5}\right)^{3} \left(\frac{3}{5}\right)^{-6}= \left(\frac{3}{5}\right)^{2x-1} \), then x is equal to
A). -2 |
B). 2 |
C). -1 |
D). 1 |
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67). If a and b be positive integers such that \( \Large a^{2}-b^{2}=19 \), then the value of a is
A). 19 |
B). 20 |
C). 9 |
D). 10 |
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68). \( \Large \frac{\sqrt{3+x}+\sqrt{3-x}}{\sqrt{3+x}-\sqrt{3-x}} \), then x is equal to
A). \( \Large \frac{5}{12} \) |
B). \( \Large \frac{12}{5} \) |
C). \( \Large \frac{5}{7} \) |
D). \( \Large \frac{7}{5} \) |
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69). If \( \Large x=\frac{\sqrt{3}}{2} \), then the value of \( \Large \left(\frac{\sqrt{1+x}+\sqrt{1-}}{\sqrt{1+x}-\sqrt{1-x}}\right) \) is
A). \( \Large -\sqrt{3} \) |
B). -1 |
C). 1 |
D). \( \Large \sqrt{3} \) |
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70). If \( \Large 4^{4x+1}=\frac{1}{64} \), then the value of x is
A). \( \Large \frac{1}{2} \) |
B). -1 |
C). \( \Large -\frac{1}{2} \) |
D). \( \Large \frac{1}{6} \) |
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