Question : In a right-angled $\triangle PQR$, PQ = 5 cm, QR = 13 cm and $\angle P=90^{\circ}$. Find the value of $\tan Q-\tan R$.

Option 1: $\frac{5}{14}$

Option 2: $\frac{119}{60}$

Option 3: $\frac{60}{119}$

Option 4: $\frac{14}{5}$

Question : If in a right-angled $\triangle P Q R$, $\tan Q=\frac{5}{12}$, then what is the value of $\cos Q$?

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

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

Option 3: $\frac{12}{13}$

Option 4: $\frac{5}{13}$

Question : $\triangle PQR$ is a right-angled triangle. $\angle Q = 90^\circ$, PQ = 12 cm, and QR = 5 cm. What is the value of $\operatorname{cosec}P+\sec R$?

Option 1: $\frac{26}{5}$

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

Option 3: $\frac{18}{5}$

Option 4: $\frac{14}{5}$

Question : Let ABC be a triangle right-angled at B. If $\tan A = \frac{12}{5}$, then find the values of $\operatorname{cosec A}$ and $\sec A$, respectively.

Option 1: $\frac{13}{10}, \frac{5}{13}$

Option 2: $\frac{13}{12},\frac{13}{5}$

Option 3: $\frac{10}{13}, \frac{5}{13}$

Option 4: $\frac{12}{13}, \frac{5}{13}$

Question : $\triangle PQR$ is right angled at Q. If $m\angle R=60^{\circ}$, what is the length of PR(in cm), If RQ = $4\sqrt3$ cm?

Option 1: $8$

Option 2: $4$

Option 3: $\frac{8}{\sqrt3}$

Option 4: $8\sqrt3$