In the given diagram, O is the center of the circle, and PQ is a tangent at A. If ∠ABC = 50°, then values of x, y and z respectively are :

1. 50°, 100°, 40°

2. 50°, 50°, 65°

3. 40°, 80°, 50°

4. 50°, 25°, 78°

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 right circular cone has the radius of the base equal to the height of the cone. If the volume of the cone is 9702 cu. cm, then the diameter of the base of the cone is :

1. 21 cm

2. 42 cm

3. $21\sqrt{7}$ cm

4. $2\sqrt{7}$ cm

$\Big[\text{Use } \pi = \dfrac{22}{7}\Big]$

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