Question : If $7 a-\frac{7}{a}+4=0$, then find $a^3-\frac{1}{a^3}-1$.

Option 1: $-\frac{995}{343}$

Option 2: $-\frac{875}{248}$

Option 3: $-\frac{694}{315}$

Option 4: $-\frac{765}{262}$

Question : If $x+\frac{1}{x}=6$, then find the value of $\frac{3 x}{2 x^2-5 x+2}$.

Option 1: $1$

Option 2: $\frac{3}{7}$

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

Option 4: $0$

Question : If $\frac{a^2}{b+c}=\frac{b^2}{c+a}=\frac{c^2}{a+b}=1$, then find the value of $\frac{2}{1+a}+\frac{2}{1+b}+\frac{2}{1+c}$.

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 3

Question : If $2 x^2-7 x+5=0$, then what is the value of $x^2+\frac{25}{4 x^2} ?$

Option 1: $5 \frac{1}{2}$

Option 2: $7 \frac{1}{4}$

Option 3: $9 \frac{1}{2}$

Option 4: $9 \frac{3}{4}$

Question : If $8 \cot A = 7$, then find $\sin A$.

Option 1: $\frac{7}{15}$

Option 2: $\frac{8}{\sqrt{113}}$

Option 3: $\frac{7}{8}$

Option 4: $\frac{8}{7}$

Question : If, for a non-zero $x, 5 x^2+7 x+5=0$, then the value of $x^3+\frac{1}{x^3}$ is:

Option 1: $\frac{496}{125}$

Option 2: $\frac{532}{343}$

Option 3: $\frac{125}{532}$

Option 4: $\frac{182}{125}$