should all the methods in an abstract class be implemented code example

Example 1: is it necessary for abstract class to have abstract method

No, abstract class can have zero abstract methods.

Example 2: write a program in which an abstract class is being defined containg an abstract method omputer(int a, int b) and a non abstract method as well

abstract class Sum{
   
   public abstract int compute(int a, int b);
   public void disp(){
	System.out.println("Method of class Sum");
   }
}
class Demo extends Sum{

   public int compute(int a, int b){
	return a+b;
   }
   public static void main(String args[]){
	Sum obj = new Demo();
	System.out.println(obj.compute(3, 7));
	obj.disp();
   }
}