Problem #1

The shortest distance between two points on a plane is:

(a) a straight line;
(b) can be zero depending upon the curvature of the plane:
(c) a curved line;
(d) all the above;

If you answer (b), (c) or (d) then please explain your answer;

Problem #2

You are given an equation involving the number 135:

What is the value of x in the above equation? Can you think of any other number which follows the above equation?

Problem #3

A rich banker a relatively poor academic are betting their life's savings on a game of "coin tossing". The banker has $10,000,000 with him and the academic has $200,000 with him. The banker gains a dollar if the outcome is "heads" and loses a dollar if it is "tails". The game must go on until one of these guys have gone bankrupt (assuming that the game can go on for a very long time). The probability that the academic will go bankrupt first is:

(a) 98%;
(b) 90%;
(c) 11%;
(d) 50%

Explain your answer.

Problem #4

The mean value of temperature of your town over a certain period is 10 degrees. The weatherman on the TV tells you that over the next period there is 50% chance that the temperature will rise to 15 degrees or fall to 5 degrees. The standard deviation of the temperature in degrees is:

(a) 2.5
(b) 3.5
(c) 5.0
(d) 7.5

Problem #5

Company A has an abundance of copper in its warehouse but it needs iron for its manufacturing process and it does not have any iron in its inventory. Company B has an abundance of iron in its warehouse but needs copper for its manufacturing. Iron and copper have different market prices (on a per tonne basis). However, the market price of both these metals is going up, though unevenly. What would each company do?

(a)Each company would exchange the requisite amount of the metal it needs with
     each other immediately at the current market price (i.e. company A will give
     copper to company B and company B will give Iron to company A) and settle
     the difference in cash;
(b)Each company will sell the respective amounts of metal in the market and using
      the cash that it receives will buy the required metal from the market. This way
      they have a chance of making a profit on the overall transaction.
(c)Each company will contract with the other company to exchange small amounts of
      the respective metals in stages (as per the requirement of the production process)
      but at a predetermined prices and any settlement of the difference between the
      prices will be made in cash;

Explain your answer.

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