61). What is the value of \( \Large \frac{725 \times 725 \times 725+371 \times 371 \times 371}{725 \times 725-725 \times 371+371 \times 371}=? \)
A). 9610 |
B). 1960 |
C). 1096 |
D). 1016 |
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62). If \( \Large a^{2}+b^{2}=234\ and\ ab=108 \), value of \( \Large \frac{a+b}{a-b} \)
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63). If \( \Large 0.764 y = 1.236 x \), then what is the value of \( \Large \left(\frac{y-x}{y+x}\right)? \)
A). 0.764 |
B). 0.236 |
C). 2 |
D). 0.472 |
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64). \( \Large \frac{ \left(m-n\right)^{3}+ \left(n-r\right)^{3}+ \left(r-m\right)^{3} }{6 \left(m-n\right) \left(n-r\right) \left(r-m\right) }=? \)
A). \( \Large \frac{1}{2} \) |
B). \( \Large \frac{1}{3} \) |
C). \( \Large \frac{1}{4} \) |
D). \( \Large \frac{1}{6} \) |
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65). If \( \Large a+b+c=14\ and\ a^{2}+b^{2}+c^{2}=96 \), then \( \Large \left(ab+bc+ca\right)=? \)
A). 51 |
B). 55 |
C). 50 |
D). 65 |
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66). \( \Large \left(1-\frac{1}{2}\right) \left(1-\frac{1}{3}\right) \left(1-\frac{1}{4}\right) \left(1-\frac{1}{5}\right)...... \left(1-\frac{1}{m}\right)=? \)
A). \( \Large \frac{1}{m} \) |
B). m |
C). m+1 |
D). \( \Large \frac{1}{ \left(m-1\right) } \) |
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67). If \( \Large a+\frac{1}{a}=\sqrt{3} \), then the value of \( \Large a^{6}-\frac{1}{a^{6}}+2 \) will be
A). \( \Large 3\sqrt{3} \) |
B). 5 |
C). 1 |
D). 2 |
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68). If \( \Large x+\frac{1}{x}=2,\ then\ x- \frac{1}{x} \)is ?
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69). If \( \Large \left(x^{2}+\frac{1}{x^{2}}\right)=\frac{17}{4}\) , then what is \( \Large \left(x^{3}-\frac{1}{x^{3}}\right) \) equal to?
A). \( \Large \frac{75}{16} \) |
B). \( \Large \frac{63}{8} \) |
C). \( \Large \frac{95}{8} \) |
D). None of the above. |
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70). A board 80 inches long is divided into 4 equal parts. What is the length of each part?
A). 20 inches |
B). 25 inches |
C). 15 inches |
D). 18 inches |
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