A circle with center at $(x, y)=(0.5,0)$ and radius $=0.5$ intersects with another circle with center at $(x, \mathrm{y})=(1,1)$ and radius $=1$ at two points. One of the points of intersection $(x, \mathrm{y})$ is:

Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder.

The length of the container is equal to the length of the chalk-sticks. The ratio of the occupied space to the empty space of the container is

The plot below shows the relationship between the mortality risk of cardiovascular disease and the number of steps a person walks per day. Based on the data, which one of the following options is true?

Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. The magnitude of the minimum angle of rotation is