Question : Solve for $\theta: \cos ^2 \theta-\sin ^2 \theta=\frac{1}{2}, 0<\theta<90^{\circ}$.

Option 1: 45^o

Option 2: 60^o

Option 3: 30^o

Option 4: 40^o

Question : The total surface area of a regular triangular pyramid with each edge of length 1 cm is:

Option 1: $4 \sqrt{3}$ cm²

Option 2: $\frac{4}{3} \sqrt{3}$ cm²

Option 3: $\sqrt{3}$ cm²

Option 4: $4$ cm²

Question : The difference between the semi-perimeter and the sides of ΔPQR are 18 cm, 17 cm, and 25 cm, respectively. Find the area of the triangle.

Option 1: $330\sqrt{510}$ cm²

Option 2: $230\sqrt{510}$ cm²

Option 3: $30\sqrt{510}$ cm²

Option 4: $130\sqrt{510}$ cm²

Question : The sides $P Q$ and $P R$ of $\triangle P Q R$ are produced to points $S$ and $T$, respectively. The bisectors of $\angle S Q R$ and $\angle T R Q$ meet at $\mathrm{U}$. If $\angle \mathrm{QUR}=59^{\circ}$, then the measure of $\angle \mathrm{P}$ is:

Option 1: 31^o

Option 2: 62^o

Option 3: 41^o

Option 4: 49^o

Question : If the angle of elevation of the Sun changes from 30° to 45°, the length of the shadow of a pillar decreases by 20 metres. The height of the pillar is:

Option 1: $20(\sqrt{3}-1)$ m

Option 2: $20(\sqrt{3}+1)$ m

Option 3: $10(\sqrt{3}-1)$ m

Option 4: $10(\sqrt{3}+1)$ m