In the given figure, PT and QT are tangents to a circle such that ∠TPS = 45° and ∠TQS = 30°. Then, the value of x is :

1. 30°

2. 45°

3. 75°

4. 105°

A cylindrical metallic wire is stretched to double its length. Which of the following will NOT change for the wire after stretching?

1. Its curved surface area

2. Its total surface area

3. Its volume

4. Its radius

A solid sphere with a radius of 4 cm is cut into 4 identical pieces by two mutually perpendicular planes passing through its center. Find the total surface area of one-quarter piece.

1. 24π

2. 32π

3. 48π

4. 64π

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