Answer:
Following are the program in JAVA language  
import java.util.Scanner; // import package
import java.util.Calendar; // import package
public class Main // class main  
{  
public static void main(String[] args) // main function  
{  
Scanner input = new Scanner(System.in); // for user input  
Calendar calendar = Calendar.getInstance(); //get calendar instance for methods  
int nYear , nMonth , date =1 , nDays;
String MonthOfName = "";
 System.out.print(" Enter a month in the year :");
 nMonth = input.nextInt(); //input Month
 System.out.print("Enter a year :");
 nYear = input.nextInt(); //Input Year
  switch (nMonth) //Find month name via 1-12
 {
   case 1:
MonthOfName = "January";
nMonth = Calendar.JANUARY;
break;
case 2:
MonthOfName = "February";
nMonth = Calendar.FEBRUARY;
break;
case 3:
 MonthOfName = "March";
nMonth = Calendar.MARCH;
break;
 case 4:
 MonthOfName = "April";
nMonth = Calendar.APRIL;
 break;
 case 5:
MonthOfName = "May";
nMonth = Calendar.MAY;
break;
case 6:
MonthOfName = "June";
nMonth = Calendar.JUNE;
break;
case 7:
 MonthOfName = "July";
nMonth = Calendar.JULY;
break;
 case 8:
MonthOfName = "August";
nMonth = Calendar.AUGUST;
break;
case 9:
MonthOfName = "September";
nMonth = Calendar.SEPTEMBER;
break;
case 10:
MonthOfName = "October";
nMonth = Calendar.OCTOBER;
break;
case 11:
 MonthOfName = "November";
nMonth = Calendar.NOVEMBER;
break;
case 12:
 MonthOfName = "December";
 nMonth =Calendar. DECEMBER; 
          }        
  calendar.set(nYear, nMonth, date); // set date to calender to get days in month
nDays=calendar.getActualMaximum(Calendar.DAY_OF_MONTH); // get no of days in month
System.out.println(MonthOfName + " " + nYear + " has " + nDays + " days."); //print output
}
}
Output:
Enter a month in the year : : 09
Enter a year : 2019
September 2019 has 30 days.
Explanation:
In this program we have take two user input one for the  month and other for the year Also take two variables which are used for storing the month name and no of days in a month. with the help of switch we match  the cases  and store the month value .After that  set the date to calender with help of calendar.set(nYear, nMonth, date) method and  To get the number of days from a month  we use  calendar.getActualMaximum(Calendar.DAY_OF_MONTH);  method and finally print year and days.