41). If \( \Large a=\frac{\sqrt{5}+1}{\sqrt{5}-1}\ and\ b=\frac{\sqrt{5}-1}{\sqrt{5}+1} \), then the value of \( \Large \frac{a^{2}+ab+b^{2}}{a^{2}-ab+b^{2}} \)
| A). \( \Large \frac{3}{4} \) |
| B). \( \Large \frac{4}{3} \) |
| C). \( \Large \frac{3}{5} \) |
| D). \( \Large \frac{5}{3} \) |
|
42). If a=4.36, b=2.39 and c=1.97, then the value of \( \Large a^{3}-b^{3}-c^{3}-3abc \) is
| A). 3.94 |
| B). 2.39 |
| C). 0 |
| D). 1 |
|
43). If \( \Large \frac{3a+5b}{3a-5b}=5 \), then a:b is equal to:
| A). 2:1 |
| B). 2:3 |
| C). 1:3 |
| D). 5:2 |
|
44). If p:q=r:s=t:u=2:3, then \( \Large \left(mp+nr+ot\right): \left(mq+ns+ou\right) \) equals
| A). 3:2 |
| B). 2:3 |
| C). 1:3 |
| D). 1:2 |
|
45). If x:y=3:4, then \( \Large \left(7x+3y\right): \left(7x-3y\right) \) is equal to:
| A). 5:2 |
| B). 4:3 |
| C). 11:3 |
| D). 37:19 |
|
46). For what value(s) of a is \( \Large x+\frac{1}{4}\sqrt{x}+a^{2} \) a perfect square?
| A). \( \Large \pm \frac{1}{18} \) |
| B). \( \Large \frac{1}{8} \) |
| C). \( \Large -\frac{1}{5} \) |
| D). \( \Large \frac{1}{4} \) |
|
47). If \( \Large a\ne b \), then which of the following statements is true?
| A). \( \Large \frac{a+b}{2}=\sqrt{ab} \) |
| B). \( \Large \frac{a+b}{2}<\sqrt{ab} \) |
| C). \( \Large \frac{a+b}{2}>\sqrt{ab} \) |
| D). All of the above |
|
48). If x, y are two positive real number and , then which of the following relations is true?
| A). \( \Large x^{3}=y^{4} \) |
| B). \( \Large x^{3}=y \) |
| C). \( \Large x=y^{4} \) |
| D). \( \Large x^{20}=y^{15} \) |
|
49). If \( \Large x=\frac{\sqrt{3}}{2} \), then \( \Large \frac{\sqrt{1+x}}{1+\sqrt{1+x}}+\frac{\sqrt{1-x}}{1-\sqrt{1-x}} \) is equal to:
| A). 1 |
| B). \( \Large 2/\sqrt{3} \) |
| C). \( \Large 2-\sqrt{3} \) |
| D). 2 |
|
50). If for non-zero, \( \Large x, x^{2}-4x-1=0 \), the value of \( \Large x^{2}+\frac{1}{x^{2}} \) is:
| A). 4 |
| B). 10 |
| C). 12 |
| D). 18 |
|
