Question : If $\tan A=\frac{5}{12}$, then the value of $\cos A=$______.

Option 1: $\frac{12}{5}$

Option 2: $\frac{13}{5}$

Option 3: $\frac{5}{13}$

Option 4: $\frac{12}{13}$

Question : If $\frac{11-13x}{x}+\frac{11-13y}{y}+\frac{11-13z}{z}=5$, then what is the value of $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$?

Option 1: $1$

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

Option 3: $\frac{13}{5}$

Option 4: $4$

Question : If $\cot A=\frac{12}{5}$, then the value of $\sin A=?$

Option 1: $\frac{5}{13}$

Option 2: $\frac{12}{13}$

Option 3: $\frac{5}{12}$

Option 4: $\frac{13}{12}$

Question : Let $x=\frac{5 \frac{3}{4}-\frac{3}{7} \times 15 \frac{3}{4}+2 \frac{2}{35} \div 1 \frac{11}{25}}{\frac{3}{4} \div 5 \frac{1}{4}+5 \frac{3}{5} \div 3 \frac{4}{15}}$. When $y$ is added to $x$, the result is $\frac{7}{13}$. What is the value of $y$?

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

Option 2: $\frac{9}{13}$

Option 3: $\frac{2}{13}$

Option 4: $\frac{4}{13}$

Question : If $2=x+\frac{1}{1+\frac{1}{5+\frac{1}{2}}}$, then the value of $x$ is equal to:

Option 1: $\frac{14}{13}$

Option 2: 1

Option 3: $\frac{13}{15}$

Option 4: $\frac{15}{13}$