In the adjoining figure, AC is a diameter of the circle, AP = 3 cm and PB = 4 cm and QP ⊥ AB. If the area of △ APQ is 18 cm², then the area of shaded portion QPBC is :

1. 32 cm²

2. 49 cm²

3. 80 cm²

4. 98 cm²

In the adjoining diagram, O is the center of the circle and PT is a tangent. The value of x is :

1. 20°

2. 40°

3. 55°

4. 70°

A solid sphere is cut into identical hemispheres.

Statement 1 : The total volume of two hemispheres is equal to the volume of the original sphere.

Statement 2 : The total surface area of two hemispheres together is equal to the surface area of the original sphere.

Which of the following is valid ?

1. Both the statements are true

2. Both the statements are false

3. Statement 1 is true, and statement 2 is false

4. Statement 1 is false, and statement 2 is true

Given that the sum of the squares of the first seven natural numbers is 140, then their mean is :

1. 20

2. 70

3. 280

4. 980