Question : In $\triangle P Q R, S$ is a point on the side QR such that $\angle Q P S=\frac{1}{2} \angle P S R, \angle Q P R=78^{\circ}$ and $\angle P R S=44^{\circ}$. What is the measure of $\angle PSQ$?

Option 1: 68$^{\circ}$

Option 2: 56$^{\circ}$

Option 3: 58$^{\circ}$

Option 4: 64$^{\circ}$

Question : $\triangle PQR$ is right-angled at $Q$. The length of $PQ$ is 5 cm and $\angle P R Q=30^{\circ}$. Determine the length of the side $QR$.

Option 1: $5 \sqrt{3}~cm$

Option 2: $3 \sqrt{3}~cm$

Option 3: $\frac{1}{\sqrt{3}}~cm$

Option 4: $\frac{5}{\sqrt{3}}~cm$

Question : The angle of elevation of the top of a tower from the top of a building whose height is 680 m is $45^{\circ}$ and the angle of elevation of the top of the same tower from the foot of the same building is $60^{\circ}$. What is the height (in m) of the tower?

Option 1: $340(3 + \sqrt3)$

Option 2: $310(3 - \sqrt3)$

Option 3: $310(3 + \sqrt3)$

Option 4: $340(3 - \sqrt3)$

Question : The angle of elevation of an aeroplane from a point on the ground is 45°. After flying for 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 2500 metres, then the speed of the aeroplane in km/h is:

Option 1: $600$

Option 2: $600(\sqrt{3}+1)$

Option 3: $600\sqrt{3}$

Option 4: $600(\sqrt{3}–1)$

Question : From point P on the level ground, the angle of elevation to the top of the tower is 30°. If the tower is 100 metres high, the distance of point P from the foot of the tower is: (Take $\sqrt{3}$ = 1.73)

Option 1: 149 m

Option 2: 156 m

Option 3: 173 m

Option 4: 188 m