1. (a) A boatsman must ferry across a river with a wolf, a sheep and a bundle of fodder. His boat is too small to carry more than himself and one of the passengers at a time. He cannot leave the wolf alone with sheep, or the sheep alone with the fodder. Show how he can cross without any detriment to either sheep or fodder. [20 marks] (b) What is Internet ? how does it work ? [5 marks] (c) What is a Search engine ? What are the different type of search engines ? [ 5 marks] (d) Define Macros of Excel. Explain the differnt options available to run macro. [5 marks] (e) Define a function in Excel. Explain any three of the Excel functions with the help of examples. [5 marks] 2. (a) What is chart in Excel ? How many types of charts are available in Excel ? Give examples of any two charts. [6 marks] (b) What is aprotocol ? Explain any two commonly used Internet Protocols. [4 marks] 3. (a) What is a decision Tree ? Solve the following problem using decision Tree : "You have been given 12 (twelve) coins, one of which is differnt from the rest in wieght, how will you pick it in three weighings ? Also draw the decision tree for the given problem. [6 marks] (b) What is a URL ? Explain the parts of URL. [4 marks] 4. (a) What is a Pivot Table ? What is the use of Pivot table ? How do you create it ? [5 marks] (b) Prove that Sn = (1/2n(n + 1))2 for sum of first n cubes by method of induction. [5 marks] 5. (a) Write short notes on any five of the following : [10 marks] (a) FTP (B) E-mail (c) CELING() (d) Template (e) NCSA Mosaic (f) Netscape Navigator (g) FLOOR() 6. (a) Given 13 cricket balls, one of them heavier than the rest, how can you determine it, in not more than 3 weighing, using decision tree ? [7 marks] (b) Explain the concept of filtering a database in MS-Excel using Autofilters and using Advanced filters. [7 marks] (c) What is the difference between 'Internet' and 'Network' ? What is the role of TCP/IP in Internet ? Also, list the hardware components usied in the Internet. [6 marks] (d) What is Chart Wizard in MS-Excel ? Write the step-by-step method to create charts using Chart Wizard. What are the components of Chart Wizard ? [7 marks] (e) What is a template ? Explain with an example. [3 marks] 7. (a) Prove that for any prime p >= 5, p2 + 2 is composite. [5 marks] (b) What is a Function Wizard in Excel ? What are its uses ? [2 marks] (c) What is the use of GOAL SEEK ? Explain with an exmple. [3 marks] 8. (a) Prove that for every integer n > 2, (n!)2 > nn. [7 marks] (b) What is meant by URL ? What are its components ? [3 marks] 9. (a) Compare the different types of Internet connectivity mechanisms. [6 marks] (b) Explain how the access of workbook in Excel can be restricted from other users. [4 marks] 10. (a) Write short notes on any two of the following: • HTTP • Telnet • FTP • Domain Name System [4 marks] (b) Explain the following functions giving example for each : • EXACT() • IF() • MOD() [6 marks]