Question : In a $\triangle ABC$, if $2\angle A=3\angle B=6\angle C$, then the value of $\angle B$ is:

Option 1: $60^{\circ}$

Option 2: $30^{\circ}$

Option 3: $45^{\circ}$

Option 4: $90^{\circ}$

Question : If a pole of 12 m height casts a shadow of $4\sqrt{3}$ m long on the ground, then the sun's angle of elevation at that instant is:

Option 1: 30°

Option 2: 60°

Option 3: 45°

Option 4: 90°

Question : Find the value of $\cos 0^{\circ}+\cos 30^{\circ}-\tan 45^{\circ}+\operatorname{cosec} 60^{\circ}+\cot 90^{\circ}$.

Option 1: $\frac{7}{6 \sqrt{3}}$

Option 2: $\frac{\sqrt{3}}{6}$

Option 3: $\frac{7}{6}$

Option 4: $\frac{7}{2 \sqrt{3}}$

Question : If the angle of elevation of the sun changes from 45° and 65°, then the length of the shadow of a pillar decreases by 10 m. The height of the pillar is:

Option 1: $5\left (3-\sqrt{3} \right)$ m

Option 2: $5\left (\sqrt{3}+1 \right)$ m

Option 3: $15\left (\sqrt{3}+1 \right)$ m

Option 4: $5\left (3+\sqrt{3} \right)$ m

Question : If $\cos(A+B)=0$ and $\sin(A-B)=0$, then what is the value of $\angle A$ and $\angle B$ ? ( $0^\circ < A, B \leq 90 ^\circ$)

Option 1: $20^\circ, 70^\circ$

Option 2: $45^\circ, 45^\circ$

Option 3: $60^\circ, 30^\circ$

Option 4: $15^\circ, 75^\circ$