Question : If $\frac{2 p}{p^2-5 p+1}=\frac{1}{10}, p \neq 0$, then the value of $\left(p+\frac{1}{p}\right)$ is:

Option 1: 10

Option 2: 25

Option 3: 1

Option 4: 15

Question : If $\sec \theta+\tan \theta=5, (\theta \neq 0)$, then $\sec \theta$ is equal to:

Option 1: $\left(5+\frac{1}{5}\right)$

Option 2: $\frac{1}{2}\left(3+\frac{1}{3}\right)$

Option 3: $\frac{1}{2}\left(5+\frac{1}{5}\right)$

Option 4: $\left(3+\frac{1}{3}\right)$

Question : The value of $15 \div 8-\frac{5}{4}$ of $\left(\frac{8}{3} \times \frac{9}{16}\right)+\left(\frac{9}{8} \times \frac{3}{4}\right)-\left(\frac{5}{32} \div \frac{5}{7}\right)+\frac{3}{8}$ is:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 3

Question : If $\left (4x+\frac{1}{x} \right)=5,x\neq 0,$ then the value of $\frac{5x}{4x^{2}+10x+1}$ is:

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

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

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

Option 4: $3$

Question : The value of
$51 \div\left\{25+(25\right.$ of $12 \div 30)-\left(5^4 \div 5\right.$ of 125$\left.)\right\}$ is:

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

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

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

Option 4: $-\frac{3}{2}$

Question : If $x^{2} -3x +1=0$, then the value of $\frac{\left(x^4+\frac{1}{x^2}\right)}{\left(x^2+5 x+1\right)}$ is:

Option 1: $\frac{9}{4}$

Option 2: $\frac{27}{8}$

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

Option 4: $2$