The region between an arc and two radii , joining the center to the end points of the arc is called
a. Sector
b. Segment
c. Semicircle
d. None of the above

Hint : A sector is the region which lies between an arc and two radii joining the extremities of the arc and the center .

Complete step-by-step answer:
Given , in a circle , there are two radii and an arc , which joins the center of the circle to the end points of the arc . By definition , the above region is called a sector
Option b) Segment is a portion of the circumference of a circle which is cut by a chord of the circle , so it cannot be the required answer for the given question.
Option c) Semicircle is a half circle which is formed by cutting a whole circle along the diameter line , thus it cannot be the required answer for the above question since the arc , as mentioned in the question , could be a half circle or a small portion of the circle as well . But by definition , a sector is a portion of a circle enclosed by two radii and an arc , where the smaller area is known as a minor sector , and the larger part is called the major sector .
 Hence , option d) cannot be the required answer
Hence , the required option is a) sector

Note : A student needs to keep in mind the definition of Sector, Segment and Semicircle to solve the question.