Diagonal cross section of a cylinder a) circle
cross section parallel to the base of a cone b) triangle
shape created when a semi−circle is rotated about the y−axis c) great circle
diagonal cross section through the widest part of a sphere d) sphere
perpendicular cross section of a cone e) rectangle

1. diagonal cross section of a cylinder - When a cylinder is bisected diagonally is forms a shaped that looks like an eclipse. (this choice is not given though)

2. cross section parallel to the base of a cone - When we cut some figure parallel to its base, it will be same as the base. So, the base of a cone is circle and the answer is circle.

3. shape created when a semi−circle is rotated about the y−axis - When you rotate a semi-circle about its axis it will form a sphere.

4. diagonal cross section through the widest part of a sphere -  If a sphere is cut along its widest part it would form a great circle.

5. perpendicular cross section of a cone - when a cone is cut from the vertex to the center of its base, a triangle is formed.

So, here rectangle is the wrong choice given instead of eclipse.

b