Problem 1

Which of the following equations/formulas will give an identity that will connect the five fundamental numbers of the universe, , , , 0 and 1.

(a)
(b)
(c)
(d)
(e) None of the above;

Problem 2

In a two species system let and be the number of individuals at time t of deer (prey) and lions (predator). In the absence of the predator the prey grows at a rate, that is proportional to its population size; in the absence of the prey the predator dies out at a rate, that is proportional to its population size. Further, the number of encounters between the two species is proportional to the product of their population sizes. Each encounter increases the growth of the predator by a rate of and inhibits (decreases) the growth of prey by a rate of .

Part A:

The above problem can be modeled as:

a)  a system of linear differential equations;
b)  a system of non-linear differential equations;
c)  a non-linear polynomial;
d)  a feedback-control problem;

Explain your answer clearly;

Part B:

In an economy the solution to the above problem can be applied to model:

a) vulture funds - distressed companies;
b)  banks - corporate customers;
c)  venture capital funds - start up companies;
d)  none of the above;

Problem 3

Calculate the value of (Ninety nine raised to the power of seven) without the help of a calculator or a spreadsheet. Explain your method of calculation.

Problem 4

In how many different ways can a team of 11 be selected from 20 players?

(a) 128765
(b)  167960
(c)  129567
(d)  128450

Problem 5

The sum of the infinite series:

a)  1
b)  2
c)  3
d)  4

Any comments and queries can be sent through our web-based form.

More FEAT>>

back to top