Two identical solid hemispheres are kept in contact to form a sphere. The ratio of the total surface areas of two hemispheres to the surface area of the sphere formed is :

1. 1 : 1

2. 3 : 2

3. 2 : 3

4. 2 : 1

cosec² θ + sec² θ is equal to :

1. tan² θ + cot² θ

2. cot θ + tan θ

3. (cot θ + tan θ)²

4. 1

At a certain time of day, the ratio of the height of the pole to the length of its shadow is 1 : $\sqrt{3}$, then the angle of elevation of the sun at that time of the day is :

1. 30°

2. 45°

3. 60°

4. 90°

A man standing on a ship approaching the port towards the lighthouse is observing the top of the lighthouse. In 10 minutes, the angle of elevation of the top of the lighthouse changes from α to β. Then :

1. α > β

2. α < β

3. α = β

4. α ≤ β