Problem 1

You walk into a restaurant kitchen and observe that after washing all plates are being arranged one on top of the other in a pile. Each time a new plate comes in after wash it is put on top of the last clean plate. And each time a waiter takes the plate he takes a plate from the top of the pile. Then you walk into your office and observe that your secretary is putting the entire paper files one on top of the other for your perusal. Each time she has a new file for inspection she puts it on top of the pile above the latest file kept on the table. And each time you take a file from the pile you take the latest one from the top first.

1. Is the above principle applied in data handling in writing computer programs?
2. What is the principle called?
3. Give a simple example of the above principle using data arrays (keep it very simple)

( Hint : The above principle is called "Stacking" and the special type of stack mentioned above is LIFO, last in first out, which, amongst other applications in finance, is also used in inventory management on a factory floor. Stacking is an important principle of Computer Science which is used in data management . )

Problem 2

You are interested in searching for the value 331 in the following array which is indexed.

Write a simple algorithm (in absolutely plain English ) to search for the value 331 in the array.

( Hint : You need to sort the above data first, i.e. arrange the values either in increasing order or decreasing order and then start from the middle. We use sorting in every day life, without sometimes realizing it. )

Problem 3

Which of the following functions has homogeneity of +3?

1. 
2. 
3. 
4. None of the above

( Hint : Check the power of both x and y in the equations and add them up )

Problem 4

Of all the following geometrical figures which ones will you use to estimate the value of pi numerically ( pi is the mathematical constant, denoted by )?

1. a square
2. a circle and a square
3. a circle and an ellipse
4. a circle and a triangle;
5. a triangle and a square
6. None of the above;

( Hint : You need the areas of the above figures to estimate the value of pi numerically. The correct answer is (b), a circle and a square. )

Problem 5

A financial planner who handles retirement funds of people wants to allocate funds (of each person's retirement portfolio) between stocks (these risky assets, where there could be substantial loss) and government bonds (these are risk free assets where the funds invested can be 100% recovered if investments are held to maturity). The financial planner wants to use only the current age of the retirees (people who will retire from working life in future) and no other parameter in allocating the funds between stocks and bonds. According to him a man who is 30 years of age today should invest:

1. 70% of funds in stocks and 30% in bonds;
2. 30% of funds in bonds and 70% in stocks;
3. 50% of funds in stocks and 50% in bonds;
4. None of the above.

Explain your answer.

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