Question : If ${k}+\frac{1}{{k}}=3$, then what is the value of ${k}^2+\frac{1}{{k}^2}$?

Option 1: 9

Option 2: 6

Option 3: 7

Option 4: 5

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 $2 x^2-7 x+5=0$, 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 $\sin\theta=\frac{9}{41}$, $0^{\circ}<\theta<90^{\circ}$. Then, what is the value of $\cot \theta $?

Option 1: $\frac{39}{9}$

Option 2: $\frac{47}{8}$

Option 3: $\frac{35}{8}$

Option 4: $\frac{40}{9}$

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

Option 1: $\frac{11}{13}$

Option 2: $\frac{13}{11}$

Option 3: $\frac{16}{9}$

Option 4: $\frac{9}{16}$