Question : If $a+\frac{1}{a}=7$, then $a^5+\frac{1}{a^5}$ is equal to:

Option 1: 15127

Option 2: 13127

Option 3: 14527

Option 4: 11512

Question : If $5x+\frac{1}{x}=10$, then $x^2+\frac{1}{25x^2}$ is equal to:

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

Option 2: $3\frac{1}{5}$

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

Option 4: $2\frac{3}{5}$

Question : If $\sec \ A + \tan \ A = 3$, then $\cos \ A$ is equal to:

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

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

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

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

Question : If $\frac{10x}{3}+\frac{5}{2}(2-\frac{x}{3})=\frac{7}{2}$, then the value of $x$ is:

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

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

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

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

Question : If $3\sqrt{\frac{1-a}{a}}+9=19-3\sqrt{\frac{a}{1-a}};$ then, what is the value of $a?$

Option 1: $\frac{3}{10}$ and $\frac{7}{10}$

Option 2: $\frac{1}{10}$ and $\frac{9}{10}$

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

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

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