Select ALL statements that are FALSE about the region 1 less

Select ALL statements that are FALSE about the region 1 less than or equal to x^2 + y^2 + z^2 less than or equal to 25:

(A) It contains the origin.

(B) It contains only points with positive x, y, and z coordinates.

(C) It is between two concentric spheres of radius 1 and 25, centered at the

origin.

(D) It is between two concentric spheres of radius 1 and 5, centered at the

origin.

Solution

(A) It contains the origin. (B) It contains only points with positive x, y, and z coordinates. (C) It is between two concentric spheres of radius 1 and 25, centered at the origin. because 1<= x^2 + y^2 + z^2 <= 25 contains the region between two concentric spheres of radius 1 and 5, centered at the origin and hence it does not contain (0,0) Also it contains negative x,y and z co-ordinates as they come under the region of spheres and it is not specifically mentioned that x>0,y>0 or z>0.