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

Option 1: $\left(1-a^4\right)^\frac{1}{4}$

Option 2: $a$

Option 3: $\left(a^4-1\right)^\frac{1}{4}$

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

Question : If $\frac{x}{2}-\frac{\left [4\left (\frac{15}{2}-\frac{x}{3} \right ) \right ]}{3} = –\frac{x}{18}$ then what is the value of $x$?

Option 1: –$10$

Option 2: $\frac{9}{8}$

Option 3: $10$

Option 4: $–\frac{9}{8}$

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: $2$

Question : If $\tan ^2 \alpha=3+Q^2$, then $\sec \alpha+\tan ^3 \alpha \operatorname{cosec} \alpha=?$

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

Option 2: $\left(7+Q^2\right)^{\frac{3}{2}}$

Option 3: $\left(5-Q^2\right)^{\frac{3}{2}}$

Option 4: $\left(4+Q^2\right)^{\frac{3}{2}}$