Problem 1

A safe builder has written the blueprints of a safe that can never be opened or broken with any known codes. He is however afraid that someone might get hold of this blue print and actually build the safe. How should be protect the blueprints of the safe?

Problem 2

The probability that a particle described by the function is between two points and is given by:

a) the differential of with respect to at the point multiplied by the     differential of at the point
b) the integral of between and
c) the limit of as tends to multiplied by the limit of as tends to
d) None of the above

Problem 3

A 3 x 3 correlation matrix is given by:

Which of the following row vectors (1 x 3 matrix) is a factor of the above matrix?

a) 
b) 
c) 
d)  None of the Above;

Problem 4

The price of a stock, that you are analyzing, depends on 10 company specific variables, 25 industry specific variables and 10 macro-economic variables. Each company specific variable in turn depends on the 25 industry specific variables and each industry specific variable in turn depends on the 10 macro economic variables.

You have the historical data for all the above variables and access to the fastest computer in your organization. Your approach to analysis will be:

(a)  developing multiple linear regression analysis between the variables;
(b)  developing multiple non-linear regression analysis between the variables;
(c)  developing discriminant analysis based on factor analysis;
(d)  developing "rules based" analysis based on fuzzy associations;
(e)  Your own home grown model;

Explain your answer in not more than 100 words.

Problem 5

A complex number, is defined by the equation: , where and are real numbers (from minus infinity to plus infinity on a number line) and is given by . A modulus is defined as the absolute value of any complex number and can be expressed as: . Thus, the only complex number with modulus zero will be:

(a) 0
(b) 1
(c) 2
(d) -1

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