Question : If $\frac{x^{3}+3y^{2}x}{y^{3}+3x^{2}y}=\frac{35}{19}$, what is $\frac{x}{y} =?$

Option 1: $\frac{7}{6}$

Option 2: $\frac{5}{6}$

Option 3: $\frac{5}{1}$

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

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

Option 1: –1

Option 2: 1

Option 3: 2

Option 4: 4

Question : If $\frac{1}{x+2}=\frac{3}{y+3}=\frac{1331}{z+1331}=\frac{1}{3}$, then what is the value of $\frac{x}{x+1}+\frac{y}{y+6}+\frac{z}{z+2662}$?

Option 1: $0$

Option 2: $1$

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

Option 4: $3$

Question : If $x\left(5-\frac{2}{x}\right)=\frac{5}{x}$, then the value of $x^2+\frac{1}{x^2}$ is:

Option 1: $\frac{54}{25}$

Option 2: $\frac{53}{28}$

Option 3: $\frac{53}{27}$

Option 4: $\frac{54}{23}$

Question : The value of $\frac{\left(1 \frac{1}{9} × 1 \frac{1}{20} ÷ \frac{21}{38}-\frac{1}{3}\right) ÷\left(2 \frac{4}{9} ÷ 1 \frac{7}{15} \text { of } \frac{3}{5}\right)}{\frac{1}{5} \text { of } \frac{1}{5} ÷ \frac{1}{125}-\frac{1}{25} ÷ \frac{1}{5} \text { of } \frac{1}{5}}$ lies between ____.

Option 1: 0.1 and 0.15

Option 2: 0.2 and 0.25

Option 3: 0.15 and 0.2

Option 4: 0.25 and 0.3