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ICSE Notes 2018 : Computer Applications (Lawrence High School, HSR Layout, Bangalore)

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Chapter 7: Repetitive Structures Practice Questions187 A. Answer the following questions: 1. Explain the term loop with an example. [ICSE 2005] Ans. Loop is a repetitive structure that allows a group of statements to be executed repeatedly. The loop structure executes as long as the given test-expression is executed. For example, the following for loop will execute 10 times displaying the first 10 natural numbers. int i; for( i =1 ; i<=10 ; i++) { System.out.print(i+" "); } The loop starts with the initial value of 1 for i' and iterates every time increasing the value of i' by 1 as long as the value of i is less than or equal to 10. The loop body in the mean while displays each value of i , thus giving the output as: 1 2 3 4 5 6 7 8 9 10 2. Discuss "Elements That Control a Loop". Ans. Elements that control the loop are: 1. Initialization Expression(s): Before entering a loop, the variable that controls the execution of it is called initialization. The initialization of a variable may be inside a loop or outside it. Whatever it may be it is executed only once before the iteration starts. 2. Test Expression. The test-expression is a condition, which decides whether the loop body will be executed or not. Till the test-expression evaluates to true, the loop body gets executed otherwise the loop is terminated. 3. Update Expression(s). The update expression(s) change the value(s) of the control variable(s). The update expression(s) is usually made to be executed; before the next iteration. 4. The Body of the Loop. The statements that are executed repeatedly (as long as the, test-expression is true) form the body of the loop. 3. What are the three types of looping statements available in Java? Ans. The three types of looping statements in Java are: a) for b) while c) do-while 4. Classify loops depending upon the priority in which a test expression is evaluated. Ans. Depending upon the priority of a test-expression loops may be categorized as: a) Entry-controlled loop b) Exit-controlled loop 5. Give the general syntax of a for loop and discuss each of its components. Ans. The general syntax of for loop is: for (initialization expression(s) ; test-expression ; update expression(s)) { //body of the loop; } o Initialization Expression(s): Before entering a loop, the variable that controls the execution of it is called initialization. o Test Expression. The test-expression is a condition, which decides whether the loop body will be executed or not. o Update Expression(s). The update expression(s) change the value(s) of the control variable(s). The update expression(s) is usually made to be executed; before the next iteration. o The Body of the Loop. The statements that are executed repeatedly (as long as the, test-expression is true) form the body of the loop. 6. Give an example to show how multiple initialization and updation are performed in a for loop. Ans. For multiple initialization and multiple updation in a for loop they are separated by comma (,). The following example shows how multiple initialization and updation is performed in a for loop. for(i=1, j=10 ; i<=10 ; j-- , i++) { System.out.println("i=" +i+" "+"j="+j); } 7. What is an empty for loop. Give an example. Ans. If the loop doesn t contain a body, it is called an empty loop. For example, for(i=1;i<=100;i++); Notice the semicolon at the end of the parenthesis, indicating that the for loop does not have body and therefore no statement is repeatedly executed again and again. 8. State one similarity and one difference between while and do-while loops. [ICSE 2005] Ans. Similarity: The similarity between while and do-while loop is that, both the loops executes as long as the given test-expression is satisfied. Difference: The difference between while and do-while loop is that, while is an entry-controlled loop and do-while loop is an exit-controlled loop. 9. State one similarity and one difference between while and for loops. [ICSE 2009] Ans. Similarity: The similarity between while and for loop is that, both the loops are entry-controlled loops.. Difference: The difference between while and for loop is that, initialization in while loop is outside the loop structure, whereas initialization of for loop is within the loop structure. 10. What is meant by an infinite loop? Give one example. [ICSE 2008] Ans. Infinite loop is a loop which executes indefinitely i.e. the given test-expression is forever evaluated to true. For example, for(i=1;i>0;i++) { System.out.println(i); } The loop executes infinitely because the value of i' is always greater than 0. 11. Give the general syntax of a while loop. How do you create infinite loops using a while loop structure? Ans. The general syntax of while loop is: while (condition or test-expression) { //body of the loop; } The easiest way of creating an infinite loop using while loop is: while(true) { //body of the loop } 12. Give the general syntax of a do-while loop. How do you create infinite loops using do-while loop structure? Ans. The general syntax of do-while loop is: do { //body of the loop; } while (condition or test-expression) The easiest way of creating an infinite loop using while loop is: do { //body of the loop } while(true); 13. Compare loops according to its usage. Ans. The for loop is appropriate when you know in advance how many times the loop will be executed i.e. the first and the last limit is already known. The other two loops while and do-while loops are more suitable in situations when it is not known in advance when the loop will terminate. The while should be preferred when you may not want to execute the body-of-the-loop even once (in case the test-expression is false), and the dowhile loop should be preferred when you re sure you want to execute the body-of-theloop at least once. 14. What are nested loops? Give an example of a nested for loop to show its functionality. Ans. A loop within a loop is called a nested loop. The following example shows how nested for loop works: for(i=1;i<=5;i++) { for(j=1;j<=i;j++) { System.out.print(j); } System.out.println( ); } The output received for the above program fragment is: 1 12 123 1234 12345 15. Name two jump statements and their use. [ICSE 2010] Ans. The two jump statements in Java are break and continue. Whereas break statement is used to exit from the loop or switch block, the continue statement is used to skip the remaining statements in a loop and force the next iteration. 16. Explain the meaning of break and continue statements. [ICSE 2005, 2008] Ans. The break statement is used to exit from the loop or switch block, the continue statement is used to skip the remaining statements in a loop and force the next iteration. 17. Explain how break statement works in a nested loop. Also give an example to show how continue statement works in a nested loop. Ans. The break statement is used to exit from the nested loop in a nested loop of which it is a content. Example of continue statement: for(x=1;x<=2;x++) { for(y=1; y<=4 ; y++) { if(y==3) continue; System.out.println(x+" \t "+y); } System.out.println("x="+x); } The output for the above code fragment would be, 1 1 1 2 1 4 x=1 2 1 2 2 2 4 x=2 As you can see whenever the value of y reaches 3 it skips the statements only within the inner loop but the execution of the outer loop continues remaining same thus System.out.println("x="+x); do get executed as it is actually present only within the outer loop. 18. With the help of an example, determine the working of i) labelled break and ii) labelled continue. Ans. i) The following example shows the working of labeled break statement: int i,j; outer: //label for the outer block for(i=1;i<=3;i++) { inner: //label for the inner block for(j=1;j<=5;j++) { if (j>3) break outer; System.out.println(i+"\t"+j); } //End of the inner block System.out.println(j); } The output would be 1 1 1 2 1 3 Here you can see that there are two blocks labeled (outer and inner). Notice that when the value of j>3 it exits from the block labeled outer, which makes it ultimately come out of both the loops. ii)The following example shows the working of labeled break statement: int i,j; outer: for (i=0;i<10;i++) { for(j=0;j<10;j++) { if (j>i) { System.out.println( ); continue outer; } System.out.print(" " + (i*j)); } } The output will be 0 01 024 0369 0 4 8 12 16 0 5 10 15 20 25 0 6 12 18 24 30 36 0 7 14 21 28 35 42 49 0 8 16 24 32 40 48 56 64 0 9 18 27 36 45 54 63 72 81 The continue statement in this example terminates the loop counting j and continues with the next iteration of the loop counting i. 19. How does the return statement works as a jump statement? Ans. The return statement is used to force an exit from the method or function. The following program shows the working of return statement: class ReturnDemo { static void exit() //called method { System.out.println("Before the return"); if (true) return; System.out.println("This won t execute"); } static void test( ) //calling method { exit( ); } } If the test( ) method is executed it gives the following output. Before the return As you can see that, the final System.out.println( ) statement is not executed. As soon as return is executed, control passes back to the caller function i.e. test( ). B. Do as directed in the following questions: 1. Convert the following segment into an equivalent do loop. int x,c; for(x=10,c=20;c>10;c=c-2) x++; Ans. int x, c; [ICSE 2009] x=10; c=20; while(c>10) { x++; c=c-2; } 2. Analyze the following program segment and determine how many times the body of loop will be executed (show the working). [ICSE 2009] x=5; y=50; while(x<=y) { y=y/x; System.out.println(y); } Ans. Working: x y x<=y 5 50 true 5 10 true 5 2 false The loop will iterate for 2 times. y=y/x 10 2 --- System.out.println(y) 10 2 --- 3. Convert the following segment into equivalence for loop. int i=0; while(i<=20) { System.out.print(i+" "); i++; } Ans. int i; for(i=0;i<=20;i++) { System.out.print(i+" "); [ICSE 2007] } 4. What will be the output of the following code? int m=2; int n=15; for(int i = 1; i<5; i++); m++; n; System.out.println("m=" +m); System.out.println("n="+n); Ans. m=3 n=14 5. Give the output of the following program: class Output1 { static void find( ) { int n=1234, d ,s=0; while(n!=0) { d=n%10; s=s*10+d; n=n/10; } System.out.println(s); } } Ans. 4321 6. a) Give the output of the following program: class Output2 { static void find( ) { int n=1234, d ,s=0,c=0; while(n!=0) { d=n%10; s=s+d*(int)Math.pow(10,c++); n=n/10; } System.out.println(s); } [ICSE 2010] } b) Write programs to display the following series: i) 1, 3, 5, 7, 9, ... 29 ii) 2, 4, 6, 8, 10, ... 30 iii) 100, 90, 80, 70, 60, ... 0 iv) 1, 2, 4, 7, 11, 16, 22, 29, ... nth term. (Take n as input). v) 2, 4, 8, 14, 22, 32, ... nth terms. (Taken n as input). Ans. a)1234 b) import java.util.*; public class Question6b { static void i() { int i; for(i=1;i<=29;i+=2) { System.out.print(i+" "); } } static void ii() { int i; for(i=2;i<=30;i+=2) { System.out.print(i+" "); } } static void iii() { int i; for(i=100;i>=0;i-=10) { System.out.print(i+" "); } } static void iv() { Scanner sc=new Scanner(System.in); int i,n,p=1; System.out.println("Enter the value of n:"); n=sc.nextInt(); for(i=1;i<=n;i++) { System.out.print(p+" "); p=p+i; } } static void v() { Scanner sc=new Scanner(System.in); int i,n,p=2,c=2; System.out.println("Enter the value of n:"); n=sc.nextInt(); for(i=1;i<=n;i++) { System.out.print(p+" "); p=p+c; c=c+2; } } } 7. Write a program to find the sum of first 10 odd natural numbers. Ans. public class Question7 { static void main() { int i,s=0; for(i=1;i<=19;i+=2) { s=s+i; } System.out.println("Sum of first 10 odd numbers="+s); } } 8. Write a program to find the sum of first 10 even natural numbers. Ans. public class Question8 { static void main() { int i,s=0; for(i=2;i<=20;i+=2) { s=s+i; } System.out.println("Sum of first 10 even numbers="+s); } } 9. Write a program to find the sum of all 3-digit even natural numbers. Ans. public class Question9 { static void main() { int i,s=0; for(i=100;i<=998;i+=2) { s=s+i; } System.out.println("Sum of all 3-digit even natural numbers="+s); } } 10. Write a program to find the sum of all 3 digit odd natural numbers, which are multiples of 5. Ans. public class Question10 { static void main() { int i,s=0; for(i=101;i<=999;i+=2) { if(i%5==0) s=s+i; } System.out.println("Sum="+s); } } 11. Write a program to input an integer and find its factorial. Factorial of a number is the product of b) Write programs to display the following series: Ans. import java.util.*; public class Question11 { static void main() { Scanner sc=new Scanner(System.in); int i,n; long f=1; System.out.print("Enter an integer:"); n=sc.nextInt(); for(i=1;i<=n;i++) { f=f*i; } System.out.println("Factorial ="+f); } } 12. Write a program to input an integer and print its factors. For Example, INPUT: INPUT: Enter an integer: 12 Enter an integer:10 OUTPUT: OUTPUT: Factors: 1 2 3 4 6 12 Factors: 1 2 5 10 Ans. import java.util.*; public class Question12 { static void main() { Scanner sc=new Scanner(System.in); int i,n; System.out.print("Enter an integer:"); n=sc.nextInt(); for(i=1;i<=n;i++) { if(n%i==0) System.out.print(i+" "); } } } 13. Write a program to input an integer and count the number of factors. Ans. import java.util.*; public class Question13 { static void main() { Scanner sc=new Scanner(System.in); int i,n,c=0; System.out.print("Enter an integer:"); n=sc.nextInt(); for(i=1;i<=n;i++) { if(n%i==0) c++; } System.out.print("Number of Factors="+c); } } 14. Write a program to input an integer and check whether it is a prime number or not. (Remember, prime number has 2 factors). Ans. import java.util.*; public class Question14 { static void main() { Scanner sc=new Scanner(System.in); int i,n,c=0; System.out.print("Enter an integer:"); n=sc.nextInt(); for(i=1;i<=n;i++) { if(n%i==0) c++; } if(c==2) System.out.print("Prime Number"); else System.out.print("Not a Prime Number"); } } 15. Write a program to input 10 integers and find their sum. Ans. import java.util.*; public class Question15 { static void main() { Scanner sc=new Scanner(System.in); int i,n,s=0; System.out.println("Enter 10 integers:"); for(i=1;i<=10;i++) { n=sc.nextInt(); s=s+n; } System.out.print("Sum="+s); } } 16. Write a program to input 10 integers and find the sum of even numbers only. Ans. import java.util.*; public class Question16 { static void main() { Scanner sc=new Scanner(System.in); int i,n,s=0; System.out.println("Enter 10 integers:"); for(i=1;i<=10;i++) { n=sc.nextInt(); if(n%2==0) s=s+n; } System.out.print("Sum of even numbers="+s); } } 17. Write a program to input 10 integers and find the sum of two-digit as well as three-digit numbers separately. Ans. import java.util.*; public class Question17 { static void main() { Scanner sc=new Scanner(System.in); int i,n,s1=0,s2=0; System.out.println("Enter 10 integers:"); for(i=1;i<=10;i++) { n=sc.nextInt(); if(n>=10 && n<=99) s1=s1+n; else if(n>=100 && n<=999) s2=s2+n; } System.out.println("Sum of 2-digit numbers="+s1); System.out.println("Sum of 3-digit numbers="+s2); } } 18. Write a program to input 10 integers and display the largest integer. Ans. import java.util.*; public class Question18 { static void main() { Scanner sc=new Scanner(System.in); int i,n,l=0; System.out.println("Enter 10 integers:"); for(i=1;i<=10;i++) { n=sc.nextInt(); if(i==1) l=n; else if(n>l) l=n; } System.out.println("Largest Number="+l); } } 19. Write a program to input 10 integers and display the largest as well as the smallest integer. Ans. import java.util.*; public class Question19 { static void main() { Scanner sc=new Scanner(System.in); int i,n,l=0,s=0; System.out.println("Enter 10 integers:"); for(i=1;i<=10;i++) { n=sc.nextInt(); if(i==1) s=l=n; if(n>l) l=n; if(n<s) s=n; } System.out.println("Largest Number="+l); System.out.println("Smallest Number="+s); } } 20. Write a program to input 10 integers and display the largest even integer. In case there is no even integer, it should print "No even integer found". Ans. import java.util.*; public class Question20 { static void main() { Scanner sc=new Scanner(System.in); int i,n,l=0,f=0; System.out.println("Enter 10 integers:"); for(i=1;i<=10;i++) { n=sc.nextInt(); if(n%2==0) { if(f==0) l=n; f=1; if(n>l) l=n; } } if(f==1) System.out.println("Largest Even Number="+l); else System.out.println("No even integer found"); } } 21. Write a program to input 10 integers and display the largest even and smallest odd integer. Ans. import java.util.*; public class Question21 { static void main() { Scanner sc=new Scanner(System.in); int i,n,l=0,f1=0,f2=0,s=0; System.out.println("Enter 10 integers:"); for(i=1;i<=10;i++) { n=sc.nextInt(); if(n%2==0) { if(f1==0) { l=n; f1=1; } if(n>l) l=n; } else { if(f2==0) { s=n; f2=1; } if(n<s) s=n; } } if(f1==1) System.out.println("Largest Even Number="+l); else if(f1==0) System.out.println("No even integer found"); if(f2==1) System.out.println("Smallest Odd Number="+s); else if(f2==0) System.out.println("No odd integer found"); } } 22. Write a program to input 10 integers and check whether all the entered numbers are even numbers or not. Ans. import java.util.*; public class Question22 { static void main() { Scanner sc=new Scanner(System.in); int i,n,f=0; System.out.println("Enter 10 integers:"); for(i=1;i<=10;i++) { n=sc.nextInt(); if(n%2!=0) f=1; } if(f==0) System.out.println("All are Even Numbers"); else System.out.println("All are not Even Numbers"); } } 23. Write a program to input 10 integers and check whether all the entered numbers are odd numbers or not. Ans. import java.util.*; public class Question23 { static void main() { Scanner sc=new Scanner(System.in); int i,n,f=0; System.out.println("Enter 10 integers:"); for(i=1;i<=10;i++) { n=sc.nextInt(); if(n%2==0) f=1; } if(f==0) System.out.println("All are Odd Numbers"); else System.out.println("All are not Odd Numbers"); } } 24. Write a program to input 10 integers and check whether all the entered numbers are same or not. For Example, INPUT: Enter 10 numbers: 10 12 13 234 45 34 67 78 76 12 OUTPUT: All numbers are not same. INPUT: Enter 10 numbers: 12 12 12 12 12 12 12 12 12 12 OUTPUT: All numbers are same. Ans. import java.util.*; public class Question24 { static void main() { Scanner sc=new Scanner(System.in); int i,n,f=0,l=0; System.out.println("Enter 10 numbers:"); for(i=1;i<=10;i++) { n=sc.nextInt(); if(i==1) l=n; if(n!=l) f=1; } if(f==0) System.out.println("All numbers are same"); else System.out.println("All numbers are not same"); } } 25. Write a program to input 10 integers and check whether the entered numbers are in ascending order or not. For Example, INPUT: Enter 10 numbers: 10 12 13 25 45 55 67 78 106 122 OUTPUT: The numbers are in ascending order. INPUT: Enter 10 numbers: 25 34 56 67 12 32 43 21 23 111 OUTPUT: The numbers are not in ascending order. Ans. import java.util.*; public class Question25 { static void main() { Scanner sc=new Scanner(System.in); int i,n,f=0,l=0; System.out.println("Enter 10 numbers:"); for(i=1;i<=10;i++) { n=sc.nextInt(); if(i==1) l=n; else { if(n<l) f=1; l=n; } } if(f==0) System.out.println("All numbers are in ascending order"); else System.out.println("All numbers are not in ascending order"); } } 26. Write a program to calculate and print the sum of odd numbers and the sum of even numbers for the first n natural numbers. The integer n is to be entered by the user. [ICSE-2006] Ans. import java.util.*; public class Question26 { static void main() { Scanner sc=new Scanner(System.in); int i,n,s1=0,s2=0; System.out.println("Enter a number:"); n=sc.nextInt(); for(i=1;i<=n;i++) { if(i%2==0) s1=s1+i; else s2=s2+i; } System.out.println("Sum of even numbers="+s1); System.out.println("Sum of odd numbers="+s2); } } 27. Write programs to find the sum of each of the following series: i) s=1*2+2*3+3*4+ +9*10 ii) s=1*2+3*4+5*6+ +9*10 iii) s=1*3+2*4+3*5+ +9*11 iv) s=1 2+3 4+5 6+ +19 20 v) s= 1+1/2+1/3+1/4+1/5+ +1/10 vi) s= 1/2+2/3+3/4+4/5+ +9/10 vii) s= 1-1/2+1/3-1/4+1/5- -1/10 Ans. public class Question27 { static void i() { int i,s=0; for(i=1;i<=9;i++) { s=s+i*(i+1); } System.out.println("Sum ="+s); } static void ii() { int i,s=0; for(i=1;i<=9;i+=2) { s=s+i*(i+1); } System.out.println("Sum ="+s); } static void iii() { int i,s=0; for(i=1;i<=9;i++) { s=s+i*(i+2); } System.out.println("Sum ="+s); } static void iv() { int i,s=0; for(i=1;i<=19;i+=2) { s=s+i-(i+1); } System.out.println("Sum ="+s); } static void v() { int i; float s=0; for(i=1;i<=10;i++) { s=s+(float)1/i; } System.out.println("Sum ="+s); } static void vi() { int i; float s=0; for(i=1;i<=9;i++) { s=s+(float)i/(i+1); } System.out.println("Sum ="+s); } static void vii() { int i; float s=0; for(i=1;i<=9;i++) { if(i%2==0) s=s-(float)i/(i+1); else s=s+(float)i/(i+1); } System.out.println("Sum ="+s); } } 28. Write a program to find the sum of 1st 10 numbers of Fibonacci series, i.e. 1,1,2,3,5, 8,13 . Lucas series is such a series which starting from 1 and 1, and subsequent numbers are the sum of the previous two numbers. Ans. public class Question28 { static void main() { int i,a=1,b=0,c; System.out.println("Fibonacci series ="); for(i=1;i<=10;i++) { c=a+b; System.out.print(c+" "); a=b; b=c; } } } 29. Write a program to print the first 15 numbers of the Pell series. Pell series is such a series which starts from 1 and 2, and subsequent numbers are the sum of twice the previous number and the number previous to the previous number. Pell series: 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, Ans. public class Question29 { static void main() { int i,a=1,b=0,c; System.out.println("Pell series ="); for(i=1;i<=15;i++) { c=a+2*b; System.out.print(c+" "); a=b; b=c; } } } 30. Write a program to find the sum of 1st 10 numbers of Lucas series, i.e. 2,1,3,4,7,11, 18, Lucas series is such a series which starting from 2 and 1, and subsequent numbers are the sum of the previous two numbers. Ans. public class Question30 { static void main() { int i,a=2,b=1,c; System.out.println("Pell series ="); System.out.print(a+" "+b+" "); for(i=1;i<=8;i++) { c=a+b; System.out.print(c+" "); a=b; b=c; } } } 31. Write a program to input an integer and check whether it is perfect, abundant or deficient number. If the sum of the factors excluding itself is equal to that number it is perfect, if greater than that number it is abundant and if less than that number it is deficient number. Ans. import java.util.*; public class Question31 { static void main() { Scanner sc=new Scanner(System.in); int i,n,s=0; System.out.println("Enter an integer:"); n=sc.nextInt(); for(i=1;i<n;i++) { if(n%i==0) s+=i; } if(s==n) System.out.println("Perfect Number"); else if(s<n) System.out.println("Deficient Number"); else System.out.println("Abundant Number"); } } 32. Write a program to input two integers and check whether it forms an amicable pair or not. An amicable pair is such that the sum of the factors excluding itself of one number is the other number and sum of the factors excluding itself of the other number is this number. Example, (220, 284). Since sum of factors excluding itself of: 220= 1+2+4+5+10+11+20+22+ 44+55+110=284 284= 1+ 2+4+71+142=220.1 Ans. import java.util.*; public class Question32 { static void main() { Scanner sc=new Scanner(System.in); int i,a,b,s1=0,s2=0; System.out.println("Enter 2 integers:"); a=sc.nextInt(); b=sc.nextInt(); for(i=1;i<a;i++) { if(a%i==0) s1+=i; } for(i=1;i<b;i++) { if(b%i==0) s2+=i; } if(s1==b && s2==a) System.out.println("Amicable Pair"); else System.out.println("Not an amicable pair"); } } ass 33. Write a program to pass an integer as argument and find the sum of its digits. Ans. public class Question33 { static void main(int n) { int d,s=0; while(n!=0) { d=n%10; s=s+d; n=n/10; } System.out.println("Sum of the digits="+s); } } 34. Write a program to pass an integer as argument and find the sum of odd digits and even digits separately. Ans. public class Question34 { static void main(int n) { int d,se=0,so=0; while(n!=0) { d=n%10; if(d%2==0) se=se+d; else so=so+d; n=n/10; } System.out.println("Sum of the even digits="+se); System.out.println("Sum of the odd digits="+so); } } 35. Write a program to pass an integer as argument and find the average of its digits. Ans. public class Question35 { static void main(int n) { int d,s=0,c=0; float av; while(n!=0) { d=n%10; s=s+d; c++; n=n/10; } av=(float)s/c; System.out.println("Average of its digits="+av); } } 36. Write a program to pass an integer as argument and print the largest as well as smallest digit. Ans. public class Question36 { static void main(int n) { int d,s=0,l=0,f=0; while(n!=0) { d=n%10; if(f==0) { l=s=d; f=1; } if (d>l) l=d; if(d<s) s=d; n=n/10; } System.out.println("Largest digit="+l); System.out.println("Smallest digit="+s); } } 37. Write a program to pass an integer as argument and print the second largest digit. Ans. public class Question37 { static void main(int n) { int d,s=0,l=0,f=0,sl=0,t=n; while(n!=0) { d=n%10; if(f==0) { l=d; f=1; } if (d>l) l=d; n=n/10; } f=0; while(t!=0) { d=t%10; if(d!=l) { if(f==0) { sl=d; f=1; } if(d>sl) sl=d; } t=t/10; } System.out.println("Second Largest digit="+sl); } } 38. Write a program to input an integer and remove all the even digits from it. Ans. import java.util.*; public class Question38 { static void main() { Scanner sc=new Scanner(System.in); int i,n,d,c=0,s=0; System.out.println("Enter an integer:"); n=sc.nextInt(); while(n!=0) { d=n%10; if(d%2!=0) s=s+d*(int)Math.pow(10,c++); n=n/10; } System.out.println("New Number="+s); } } 39. Write a program to input an integer and remove all the even digits from it. For Example, INPUT: Enter an integer: 1234 OUPUT: 13 Ans. Same as question38. 40. Write a program to pass an integer as argument and form a new number by having the digits arranged in ascending order. Ans. public class Question40 { static void main(int n) { int d,s=0,c=0,i,t; for(i=9;i>=0;i--) { t=n; while(t!=0) { d=t%10; if(d==i) s=s+d*(int)Math.pow(10,c++); t=t/10; } } System.out.println("Digits in ascending order="+s); } } 41. Write a program to input an integer and check whether all digits in it are same or not. Ans. import java.util.*; public class Question41 { static void main() { Scanner sc=new Scanner(System.in); int d,n,last,f=0; System.out.println("Enter an integer:"); n=sc.nextInt(); last=n%10; while(n!=0) { d=n%10; if(d!=last) f=1; n=n/10; } if(f==0) System.out.println("All digits are same"); else System.out.println("All digits are not same"); } } 42. Write a program to input an integer and check whether all digits in it are even digits or not. Ans. import java.util.*; public class Question42 { static void main() { Scanner sc=new Scanner(System.in); int d,n,f=0; System.out.println("Enter an integer:"); n=sc.nextInt(); while(n!=0) { d=n%10; if(d%2!=0) f=1; n=n/10; } if(f==0) System.out.println("All digits are even"); else System.out.println("All digits are not even"); } } 43. Write a program to input an integer and check whether all digits are unique or not. Ans. import java.util.*; public class Question43 { static void main() { Scanner sc=new Scanner(System.in); int d1,d2,n,t,f=0; System.out.println("Enter an integer:"); n=sc.nextInt(); while(n!=0) { d1=n%10; t=n/10; while(t!=0) { d2=t%10; if(d1==d2) f=1; t=t/10; } n=n/10; } if(f==0) System.out.println("All digits are unique"); else System.out.println("All digits are not unique"); } } 44. Write a program to input an integer and check whether all are prime digits or not. Ans. import java.util.*; public class Question44 { static void main() { Scanner sc=new Scanner(System.in); int d,n,f=0; System.out.println("Enter an integer:"); n=sc.nextInt(); while(n!=0) { d=n%10; if(d!=2 && d!=3 && d!=5 && d!=7) f=1; n=n/10; } if(f==0) System.out.println("All digits are prime"); else System.out.println("All digits are not prime"); } } 45. Write a program to input an integer and check whether al digits are in ascending order or not. Ans. import java.util.*; public class Question45 { static void main() { Scanner sc=new Scanner(System.in); int d1,d2,n,f=0; System.out.println("Enter an integer:"); n=sc.nextInt(); while(n>9) { d2=n%10; d1=(n/10)%10; if(d1>d2) f=1; n=n/10; } if(f==0) System.out.println("All digits are in ascending order"); else System.out.println("All digits are not in ascending order"); } } 46. Write a program to input an integer and check whether all digits are in desending order or not. Ans. import java.util.*; public class Question46 { static void main() { Scanner sc=new Scanner(System.in); int d1,d2,n,f=0; System.out.println("Enter an integer:"); n=sc.nextInt(); while(n>9) { d2=n%10; d1=(n/10)%10; if(d1<d2) f=1; n=n/10; } if(f==0) System.out.println("All digits are in descending order"); else System.out.println("All digits are not in descending order"); } } 47. Write a program to pass an integer as argument and check whether it is armstrong number or not. Numbers whose sum of the cube of its digit is equal to the number itself is called Armstrong numbers. Example 153=13+53 +32. Ans. import java.util.*; public class Question47 { static void main() { Scanner sc=new Scanner(System.in); int t,d,s=0,n,f=0; System.out.println("Enter an integer:"); n=sc.nextInt(); t=n; while(t!=0) { d=t%10; s=s+d*d*d; t=t/10; } if(s==n) System.out.println("Armstrong Number"); else System.out.println("Not an Armstrong Number"); } } 48. Write a program to input an integer and check whether it is an automorphic, trimorphic or tri-automorphic number or not. A number n is said to be automorphic if its square ends in n. For instance 5 is automorphic, because 52= 25, which ends in 5, 25 is automorphic, because 252=625, which ends in 25. A number n is called trimorphic if n3 ends in n. For example, 493, = 117649, is trimorphic. A number n is called tri-automorphic if 3n2 ends in n; for example, 667 is triautomorphic because 3 6672, = 1334667, ends in 667. Ans. import java.util.*; public class Question48 { static void main() { Scanner sc=new Scanner(System.in); int c=0,s,t,n,f=0; System.out.println("Enter an integer:"); n=sc.nextInt(); t=n; while(t!=0) { c++; t=t/10; } if((n*n)%(int)Math.pow(10,c)==n) System.out.println("Automorphic Number"); else if((n*n*n)%(int)Math.pow(10,c)==n) System.out.println("Trimorphic Number"); else if((3*n*n)%(int)Math.pow(10,c)==n) System.out.println("Tri-automorphic Number"); } } 49. Write a program to input an integer and check whether it is a happy number or not. If you iterate the process of summing the squares of the digits of a number and if this process terminates in 1, then the original number is called a happy number. For example 7=> (72) =49=> (42+92) =97=>(92+72)=130 =>(12 +32+02)=10 =>(12+02)=1. Ans. import java.util.*; public class Question49 { static void main() { Scanner sc=new Scanner(System.in); int d,s,n; System.out.println("Enter an integer:"); n=sc.nextInt(); do { s=0; while(n!=0) { d=n%10; s=s+d*d; n=n/10; } n=s; }while(n>9); if(n==1) System.out.println("Happy Number"); else System.out.println("Not a Happy Number"); } } 50. Write a program to input an integer and check whether it is a magic number or not. If you iterate the process of summing the squares of the digits of a number and if this process terminates in 1, then the original number is called a magic number. For example 55=> (5+5)=10=>(1+0)=1. Ans. import java.util.*; public class Question50 { static void main() { Scanner sc=new Scanner(System.in); int d,s,n; System.out.println("Enter an integer:"); n=sc.nextInt(); do { s=0; while(n!=0) { d=n%10; s=s+d; n=n/10; } n=s; }while(n>9); if(n==1) System.out.println("Magic Number"); else System.out.println("Not a Magic Number"); } } 51. Write a program to input an integer and check whether it is Harshad or Niven number or not. A number is said to be Harshad if it is divisible by the sum of the digits of that number, example 126 and 1729. Ans. import java.util.*; public class Question51 { static void main() { Scanner sc=new Scanner(System.in); int d,s=0,n,t; System.out.println("Enter an integer:"); n=sc.nextInt(); t=n; while(t!=0) { d=t%10; s=s+d; t=t/10; } if(n%s==0) System.out.println("Harshad Number"); else System.out.println("Not a Harshad Number"); } } 52. Write a program to input a number and check whether it is a Kaprekar number or not. Take a positive whole number n that has d number of digits. Take the square n and separate the result into two pieces: a right-hand piece that has d digits and a left-hand piece that has either d or d 1 digits. Add these two pieces together. If the result is n, then n is a Kaprekar number. Examples are: 9 (92 = 81, 8 + 1 = 9), 45 (452 = 2025, 20 + 25 = 45) and 297 (2972 = 88209, 88 + 209 = 297). Ans. import java.util.*; public class Question52 { static void main() { Scanner sc=new Scanner(System.in); int c=0,n,t,first,last; System.out.println("Enter an integer:"); n=sc.nextInt(); t=n; while(t!=0) { c++; t=t/10; } first=(n*n)/(int)Math.pow(10,c); last=(n*n)%(int)Math.pow(10,c); if(first+last==n) System.out.println("Kaprekar Number"); else System.out.println("Not a Kaprekar Number"); } } 53. Write a program to input two integers and find their Least Common Multiple (LCM). For Example, INPUT: Enter 2 integers: 12 8 OUTPUT: LCM = 24 Ans. import java.util.*; public class Question53 { static void main() { Scanner sc=new Scanner(System.in); int i,a,b; System.out.println("Enter 2 integers:"); a=sc.nextInt(); b=sc.nextInt(); for(i=a;i<=a*b;i++) { if(i%a==0 && i%b==0) break; } System.out.println("L.C.M.="+i); } } 54. Write a program to input two integers and find their Highest Common Factor(HCF). For Example, INPUT: Enter 2 integers: 12 8 OUTPUT: HCF = 4 Ans. import java.util.*; public class Question54 { static void main() { Scanner sc=new Scanner(System.in); int i,a,b; System.out.println("Enter 2 integers:"); a=sc.nextInt(); b=sc.nextInt(); for(i=a;i>=1;i--) { if(a%i==0 && b%i==0) break; } System.out.println("H.C.F.="+i); } } 55. An interesting method of multiplication of integers (not very large numbers) is illustrated by the following example. If the numbers 17 and 19 are to be multiplied, they are put at the top of two columns as shown below: 17 19 The numbers at the left-hand side is successively divided by 2 (integer division) while the other is successively multiplied by 2. The results are written one below the other in their respective columns. The process is repeated till the column containing the division results reached 1. At this stage all the numbers in the right-hand column are struck off where numbers corresponding to them on the left-hand column are even. 17 19 8 (even) 38 4 (even) 76 2 (even) 152 1 304 Now the remaining numbers on the right-hand side are added: 19+304=323 which is equal to the product of 17 and 19. Write a program to input 2 integers and using the above method, find their product. Ans. import java.util.*; public class Question55 { static void main() { Scanner sc=new Scanner(System.in); int a,b,s=0; System.out.println("Enter 2 integers:"); a=sc.nextInt(); b=sc.nextInt(); while(a>=1) { if(a%2!=0) s=s+b; a=a/2; b=b*2; } System.out.println("Product="+s); } } 56. Write a program to calculate and print the sum of odd numbers and the sum of even numbers for the first n natural numbers. The integer n is to be entered by the user. [ICSE 2006] Ans. import java.util.*; public class Question56 { static void main() { Scanner sc=new Scanner(System.in); int i,n,s1=0,s2=0; System.out.println("Enter a number:"); n=sc.nextInt(); for(i=1;i<=n;i++) { if(i%2==0) s1=s1+i; else s2=s2+i; } System.out.println("Sum of even numbers="+s1); System.out.println("Sum of odd numbers="+s2); } } 57. Write a menu-driven class to accept a number from the user and check whether it is a palindrome or a perfect number. [ICSE 2008] i) Palindrome number (a number is palindrome which when read in reverse order is same as read in the right order). Example: 11, 101, 151, etc. ii) Perfect number (a number is called Perfect if it is equal to the sum of its factors other than the number itself). Example: 6=1+2+3 [ICSE 2009] Ans. import java.util.*; public class Question57 { static void main() { Scanner sc=new Scanner(System.in); int d,n,ch,t,s=0,i; System.out.println("Enter a number:"); n=sc.nextInt(); System.out.println("MENU"); System.out.println("1. to check whether it is a Palindrome Number"); System.out.println("2. to check whether it is a Perfect Number"); System.out.println("Enter your choice:"); ch=sc.nextInt(); switch(ch) { case 1: t=n; while(t!=0) { d=t%10; s=s*10+d; t=t/10; } if(s==n) System.out.println("Palindrome Number"); else System.out.println("Not a Palindrome Number"); break; case 2: for(i=1;i<n;i++) { if(n%i==0) s+=i; } if(s==n) System.out.println("Perfect Number"); else System.out.println("Not a Perfect Number"); break; default: System.out.println("Invalid Choice!"); } } } 193 58. Write a menu-driven program to accept a number from the user and check whether it is BUZZ number or to accept any two numbers and print the GCD of them. [ICSE 2009] i) A BUZZ number is the number which either ends with 7 or divisible by 7. ii) GCD (Greatest Common Divisor) of two integers is calculated by continued division method. Divide the larger number by the smaller; the remainder then divides the previous divisor. The process is repeated till the remainder is zero. The divisor then results the GCD. Ans. import java.util.*; public class Question58 { static void main() { Scanner sc=new Scanner(System.in); int d,n,ch,r; System.out.println("MENU"); System.out.println("1. to check for BUZZ Number"); System.out.println("2. to find the GCD of two numbers"); System.out.println("Enter your choice:"); ch=sc.nextInt(); switch(ch) { case 1: System.out.println("Enter a number:"); n=sc.nextInt(); if(n%10==7 || n%7==0) System.out.println("BUZZ Number"); else System.out.println("Not a BUZZ Number"); break; case 2: System.out.println("Enter 2 numbers:"); n=sc.nextInt(); d=sc.nextInt(); do { r=n%d; if(r!=0) { n=d; d=r; } }while(r!=0); System.out.println("GCD="+d); break; default: System.out.println("Invalid Choice!"); } } } 59. Write a menu-driven program to accept a number and check and display whether it is a prime number or not OR an automorphic number or not (Use switch-case statement). i) Prime number: A number is said to be a prime number if it is divisible only by 1 and itself and not by any other number. Example: 3,5,7,11,13, etc. ii) Automorphic number: An automorphic number is the number which is contained in the last digit(s) of its square. Example: 25 is an automorphic number as its square is 625 and 25 is present as the last two digits. Ans. import java.util.*; public class Question59 { static void main() { Scanner sc=new Scanner(System.in); int i,t,c=0,n,ch,r; System.out.println("MENU"); System.out.println("1. to check for Prime Number"); System.out.println("2. to check for Automorphic Number"); System.out.println("Enter your choice:"); ch=sc.nextInt(); switch(ch) { case 1: System.out.println("Enter a number:"); n=sc.nextInt(); for(i=1;i<=n;i++) { if(n%i==0) c++; } if(c==2) System.out.println("Prime Number"); else System.out.println("Not a Prime Number"); break; case 2: System.out.println("Enter a number:"); n=sc.nextInt(); t=n; while(t!=0) { c++; t=t/10; } if((n*n)%(int)Math.pow(10,c)==n) System.out.println("Automorphic Number"); else System.out.println("Not an Automorphic Number"); break; default: System.out.println("Invalid Choice!"); } } } 60. Write a program to input 10 integers and print the second largest number. Assume that there is at least one second largest number in the given set of integers. For example, INPUT: Enter 10 integers: 12 35 46 22 34 56 78 89 23 21 OUTPUT: Second Largest Integer: 78 Ans. import java.util.*; public class Question60 { static void main() { Scanner sc=new Scanner(System.in); int i,n,l=0,sl=0; System.out.println("Enter 10 numbers:"); for(i=1;i<=10;i++) { n=sc.nextInt(); if(i==1) l=n; else { if(n>l) { sl=l; l=n; } else if(sl==0) sl=n; else if(n>sl) sl=n; } } System.out.println("Second Largest Number="+sl); } } 61. Write a program to find the sum of the following series: S=1+(1+2) + (1+2+3) + (1+2+3+4) + (1+2+3+4+5) + +(1+2+3+4+ +10) [ICSE 2003] Ans. public class Question61 { static void main() { int i,p=0,s=0; for(i=1;i<=10;i++) { p=p+i; s=s+p; } System.out.println("Sum="+s); } } 62. Write a program to calculate and print the sum of each of the following series: i) Sum (S) = 2 4 + 6 8 + . 20 ii) Sum (S) =x/2+x/5+x/8+x/11+ +x/20 where x is to be taken as input. Ans. import java.util.*; public class Question62 { static void sumi() { int i,s=0; for(i=2;i<=20;i+=2) { if(i%4==0) s=s-i; else s=s+i; } System.out.println("Sum="+s); } static void sumii() { int i,x; float s=0; Scanner sc=new Scanner(System.in); System.out.println("Enter the value of x:"); x=sc.nextInt(); for(i=2;i<=20;i+=3) { s=s+(float)x/i; } System.out.println("Sum="+s); } } 63. Write a program to find the sum of series, taking the value of a and n from the user. s= a/2+a/3+a/4+ +a/n Ans. import java.util.*; public class Question63 { static void main() { int i,n,a; float s=0; Scanner sc=new Scanner(System.in); System.out.println("Enter the value of a and n:"); a=sc.nextInt(); n=sc.nextInt(); for(i=2;i<=n;i++) { s=s+(float)a/i; } System.out.println("Sum="+s); } } 64. Write a program to find the sum of series, taking the value of a and n from the user. s= a + 1/2+a + 3/4+a + 5/6+a + 7/8+... up to n terms Ans. import java.util.*; public class Question64 { static void main() { int i,n,a,p=1; float s=0; Scanner sc=new Scanner(System.in); System.out.println("Enter the value of a and n:"); a=sc.nextInt(); n=sc.nextInt(); for(i=1;i<=n;i++) { s=s+(float)(a+p)/(p+1); p=p+2; } System.out.println("Sum="+s); } } 65. Write a program to find the sum of series, taking the value of n from the user. s= 1 + 2/2 * 3+2 + 3/3 * 4+3 + 4/4 * 5+4 + 5/5 * 6+... up to n terms Ans. import java.util.*; public class Question65 { static void main() { int i,n; float s=0; Scanner sc=new Scanner(System.in); System.out.println("Enter the value of n:"); n=sc.nextInt(); for(i=1;i<=n;i++) { s=s+(float)(i+(i+1))/((i+1)*(i+2)); } System.out.println("Sum="+s); } } 66. Write a program to compute and display the sum of the following series: [ICSE 2007] s= 1 + 2/1 * 2+1 + 2 + 3/1 * 2 * 3+1 + 2 + 3 + 4/1 * 2 * 3 * 4+1 + 2 + 3 + 4 + 5/1 * 2 * 3 * 4 * 5+... up to n terms where n is to be taken as input from the user. Ans. import java.util.*; public class Question66 { static void main () { int i,n,p=1,q=1; float s=0; Scanner sc=new Scanner(System.in); System.out.println("Enter the value of n:"); n=sc.nextInt(); for(i=1;i<=n;i++) { p=p+(i+1); q=q*(i+1); s=s+(float)p/q; } System.out.println("Sum="+s); } } 67. Write a program to print the sum of negative numbers, sum of positive even numbers and sum of positive odd numbers from a list of numbers (N) entered by the user. The list terminates when the user enters a zero. [ICSE 2005] Ans. import java.util.*; public class Question67 { static void main() { int N,sn=0,spe=0,spo=0; Scanner sc=new Scanner(System.in); do { System.out.println("Enter the value of N:"); N=sc.nextInt(); if(N<0) sn+=N; else if(N>0) { if(N%2==0) spe+=N; else spo+=N; } }while(N!=0); System.out.println("Sum of negative numbers="+sn); System.out.println("Sum of positive even numbers="+spe); System.out.println("Sum of positive odd numbers="+spo); } } 68. Shasha Travels Pvt. Ltd. gives the following discount to its customers: [ICSE 2010] Write a program to input the name and ticket amount for the customer and calculate the discount amount and net amount to be paid. Display the output in the following format for each customer: SL. NO. Name Ticket mount (Assume that there are 15 customers, first customer is given the serial no (SL. No. 1), next customer 2 and so on. Ans. import java.util.*; public class Question68 { static void main() { int ta,i; float disc,net; String n; Scanner sc=new Scanner(System.in); for(i=1;i<=15;i++) { System.out.println("Enter the name of the customer:"); n=sc.nextLine(); System.out.println("Enter the ticket amount:"); ta=sc.nextInt(); sc.nextLine();//dummy input if(ta>70000) disc=18/100f*ta; else if(ta>=55001) disc=16/100f*ta; else if(ta>=35001) disc=12/100f*ta; else if(ta>=25001) disc=16/100f*ta; else disc=2/100f*ta; net=ta-disc; System.out.println("Serial Number="+i); System.out.println("Customer Name="+n); System.out.println("Ticket Amount="+ta); System.out.println("Discount="+disc); System.out.println("Net Amount="+net); } } } 69. Using nested loops try producing the following patterns on the screen: Ans. class Question69 { static void pattern_i() { int i,j; for(i=1;i<=5;i++) { for(j=1;j<=i;j++) { System.out.print(j); } System.out.println(); } } static void pattern_ii() { int i,j; for(i=5;i>=1;i--) { for(j=5;j>=i;j--) { System.out.print(j); } System.out.println(); } } static void pattern_iii() { int i,j; for(i=1;i<=5;i++) { for(j=i;j>=1;j--) { System.out.print(j); } System.out.println(); } } static void pattern_iv() { int i,j; for(i=1;i<=5;i++) { for(j=5;j>=i;j--) { System.out.print(j); } System.out.println(); } } static void pattern_v() { int i,j; for(i=5;i>=1;i--) { for(j=i;j>=1;j--) { System.out.print(j); } System.out.println(); } } static void pattern_vi() { int i,j; for(i=1;i<=5;i++) { for(j=1;j<=i;j++) { System.out.print(i); } System.out.println(); } } static void pattern_vii() { int i,j; for(i=5;i>=1;i--) { for(j=1;j<=i;j++) { System.out.print(i); } System.out.println(); } } static void pattern_viii() { int i,j; for(i=1;i<=5;i++) { for(j=5;j>=i;j--) { System.out.print(i); } System.out.println(); } } static void pattern_ix() { int i,j; for(i=5;i>=1;i--) { for(j=5;j>=i;j--) { System.out.print(i); } System.out.println(); } } static void pattern_x() { int i,j; for(i=1;i<=5;i++) { for(j=1;j<=i;j++) { System.out.print("*"); } System.out.println(); } } static void pattern_xi() { int i,j; for(i=5;i>=1;i--) { for(j=1;j<=i;j++) { System.out.print("*"); } System.out.println(); } } static void pattern_xii() { int i,j; for(i=1;i<=5;i++) { for(j=1;j<=5;j++) { if(i==j || i+j==6) System.out.print("*"); else System.out.print(" "); } System.out.println(); } } static void pattern_xiii() { int i,j; for(i=1;i<=5;i++) { for(j=1;j<=i;j++) { if((i+j)%2!=0) System.out.print(0); else System.out.print(1); } System.out.println(); } } static void pattern_xiv() { int i,j; for(i=1;i<=5;i++) { for(j=i;j<=5;j++) { System.out.print(j); } System.out.println(); } } static void pattern_xv() { int i,j; for(i=1;i<=5;i++) { for(j=1;j<=5;j++) { if(i+j>=6) System.out.print(j); else System.out.print(" "); } System.out.println(); } } static void pattern_xvi() { int i,j; for(i=1;i<=6;i++) { for(j=i;j>=1;j--) { System.out.print(j); } System.out.println(); } } static void pattern_xvii() { int i,j; for(i=1;i<=6;i++) { for(j=1;j<=i;j++) { if(i==j || j==1) System.out.print(1); else System.out.print(0); } System.out.println(); } } static void pattern_xviii() { int i,j,a,b,c; for(i=1;i<=6;i++) { a=1;b=0; for(j=1;j<=i;j++) { c=a+b; System.out.print(c); a=b; b=c; } System.out.println(); } } static void pattern_xix() { int i,j; for(i=1;i<=6;i++) { for(j=i;j<=5;j++) { System.out.print(" "); } for(j=1;j<=i;j++) { System.out.print(j); } for(j=i-1;j>=1;j--) { System.out.print(j); } System.out.println(); } } static void pattern_xx() { int i,j; for(i=6;i>=1;i--) { for(j=i;j<6;j++) { System.out.print(" "); } for(j=i;j>=1;j--) { System.out.print(j); } for(j=2;j<=i;j++) { System.out.print(j); } System.out.println(); } } static void pattern_xxi() { int i,j; for(i=1;i<=5;i++) { for(j=1;j<=5;j++) { if(j>=i) System.out.print(j); else System.out.print(" "); } System.out.println(); } } static void pattern_xxii() { int i,j; for(i=1;i<=5;i++) { for(j=1;j<=5;j++) { if((j+i)%2==0) System.out.print(1); else System.out.print(0); } System.out.println(); } } static void pattern_xxiii() { int i,j; for(i=1;i<=9;i+=2) { for(j=1;j<=9;j+=2) { if(j>=i) System.out.print(10-i); else System.out.print(" "); } System.out.println(); } } static void pattern_xxiv() { int i,j; for(i=1;i<=9;i+=2) { for(j=1;j<=9;j+=2) { if(j+i>=10) System.out.print(i); else System.out.print(" "); } System.out.println(); } } static void pattern_xxv() { /* 12345 23451 34512 45123 51234 */ int i,j; for(i=1;i<=5;i++) { for(j=i;j<=5;j++) { System.out.print(j); } for(j=1;j<=i-1;j++) { System.out.print(j); } System.out.println(); } } static void pattern_xxvi() { /* 54321 43215 32154 21543 15432 */ int i,j; for(i=5;i>=1;i--) { for(j=i;j>=1;j--) { System.out.print(j); } for(j=5;j>=i+1;j--) { System.out.print(j); } System.out.println(); } } static void pattern_xxvii() { /* 12345 51234 45123 34512 23451 */ int i,j; for(i=5;i>=1;i--) { for(j=i+1;j<=5;j++) { System.out.print(j); } for(j=1;j<=i;j++) { System.out.print(j); } System.out.println(); } } } 70. Write a program to input a number and print all its prime factors using prime factorization method. For Example, INPUT: Enter an integer: 24 OUTPUT: Prime factors using prime factorisation are: 2 2 2 3 Ans. import java.util.*; public class Question70 { static void main() { int n,p=2; Scanner sc=new Scanner(System.in); System.out.println("Enter an integer:"); n=sc.nextInt(); System.out.println("Prime factors using prime factorisation are:"); while(n>1) { if(n%p==0) { System.out.println(p); n=n/p; } else p++; } } } 71. Write a program to input a number and check whether it is a Smith number or not. Smith number is such a number the sum of whose digits equals the sum of the digits of its prime factors. Smith number is a composite number in which the sum of its digits is equal to the sum of the digits of all its prime factors. For example, 378 is a Smith number as the sum of the digits of 378 are: 3+7+8 = 18. The prime factors of 378 are: 2, 3, 3, 3, 7 (sum = 2+3+3+3+7 = 18). Similarly, 22 is a Smith number as the sum of the digits are: 2+2=4. The prime factors of 22 are: 2 and 11 (sum = 2+(1+1) = 4 Other examples include 27, 58, 85, 94, 121, 166, 202, 265, etc. Ans. import java.util.*; public class Question71 { static void main() { int n,d,s1=0,t,t1,s2=0,p=2; Scanner sc=new Scanner(System.in); System.out.println("Enter an integer:"); n=sc.nextInt(); t=n; while(t!=0) { d=t%10; s1=s1+d; t=t/10; } t=n; while(t>1) { if(t%p==0) { t1=p;; while(t1!=0) { d=t1%10; s2=s2+d; t1=t1/10; } t=t/p; } else p++; } if(s1==s2) System.out.println("Smith Number"); else System.out.println("Not Smith Number"); } }

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