Question : If ${P}+\frac{1}{{P}}=5$, then what is the value of ${P}^3+\frac{1}{{P}^3}$?

Option 1: 110

Option 2: 95

Option 3: 125

Option 4: 120

Question : If $x+\left [\frac{1}{(4x)} \right]=\frac{5}{2}$; then, what is the value of $\frac{64x^{6}+1}{8x^{3}} \;?$

Option 1: 110

Option 2: 115

Option 3: 125

Option 4: 140

Question : If 3 cot A = 4 and A is an acute angle, then find the value of sec A.

Option 1: $\frac{3}{4}$

Option 2: $\frac{5}{4}$

Option 3: $\frac{4}{5}$

Option 4: $\frac{5}{3}$

Question : If $x+\frac{1}{x}=3$, then the value of $\frac{3x^{2}-4x+3}{x^{2}-x+1}$ is:

Option 1: $\frac{4}{3}$

Option 2: $\frac{3}{2}$

Option 3: $\frac{5}{2}$

Option 4: $\frac{5}{3}$

Question : In $\triangle$ABC, $\angle$A = $90^{\circ}$, BP and CQ are two medians. Then the value of $\frac{BP^2 + CQ^2}{BC^2}$ is:

Option 1: $\frac{4}{5}$

Option 2: $\frac{5}{4}$

Option 3: $\frac{3}{4}$

Option 4: $\frac{3}{5}$