Student Name: Akash Chaubey Course: B.ComRegistration No.1205023997 Subject Code: BCC204Subject Name: Business Math LC Code:00918

Q:-1 Describe the various methods available to the declarer in situation of uncertainty.

Ans:-1 In decision making the decision maker is concerned of choosing from among the available alternative courses action that yield the best result. If the consequences of choise are known with certainty the decision maker easily more known with certainty the decision maker easily more decision. But in most of the real life for the decision maker has to deal with situations where certainty of the outcome prevails.

Thus decision making problems can be classified us the following heads on the basis of their environment.

1. Decision making under certainity2. Decision making under uncertainity3. Decision making under risk4. Decision making under conflict

1.Decision making under certainity: in this environment these exist only one outcome for a decision as the are certainty about the future.

2. decision making under uncertainty: here more than one status of nature exist but the decision maker lacks sufficient knowledge to assign probilities to the various status of nature suitiation like launching a new product fall under this category.

3. Decision making under risk: if the availability of information for a decision invironment is partial then a decision under such environment is called decision under risk.

4.Decision making under conflict: conflict arises when two or more persons desire a particular thing and they complete with each other to get an upeer hand.

If the consequences of choise are known with certainty the decision maker easily more known with certainty the decision maker easily more decision. But in most of the real life for the decision maker has to deal with situations where certainty of the outcome prevails.

Q:-2 Discuss the various application of set theory?

Ans:-2 Set theory has application in different branch mathemathics. This is so because set theory is various general rather ensured in nature in analysis mathemathical function

understanding of limit person and concept of continuity are based on set theory Boolen algebra can be viewed as algebraic threat of set operations. Intersections union and difference correrspondence to logical operation are switching operation in which entire logic circuits are based.

To understand how media affects large structural changes in human outlook, McLuhan classified media as either hot or cool. Hot media refers to a high-definition communication that demands little involvement from audience, whereas, Cool media describes media that demands active involvement from audience. McLuhan with his son Eric McLuhan expanded the theory in 1988 by developing a way to look further into the effects of technology on society. They offer the tetrad as an organized concept that allows people to know the laws of media, the past, present and current effects of media.

Media ecology is a contested term within media studies for it has different meanings in European and North American contexts. The North American definition refers to an interdisciplinary field of media theory and media design involving the study of media environments. The European version of media ecology is a materialist investigation of media systems as complex dynamic systems.

Level 1 of the framework describes what drives individuals to carry out actions in online communities such as posting messages and adding content. Level 2 looks at the cognitions they use to determine whether or not to take such actions. Level 3 looks at the means by which they go about carrying out the action in the environment. The framework can be applied to the problem of encouraging members to participate in media environments taking into account how people can be persuaded to participate by changing the way they interpret their desires and their environment as part of their socially constructed media ecology.

Q:-3 state the various properties of matrix addition.

Ans:-3 Basic operation of addition substraction and multiplication can be performed on matrix. For addition and substraction order of both the matrix should be the same.

Addition of matrix: If A and B are two matrix of some order than adding of A and B is defined to the matrix obtained by adding the corresponding elements of A and B.

For example if

A= (1, 2, 3, 4, 5, 6) and B= (2, 3, 4, 5, 6, 7) than

A+B= (1+2, 4+5, 2+3, 3+4, 5+6, 6+7)

(3, 5, 7, 9, 11, 13)

Properties of Matrix Addition

1. Matrix addition is cumulative i.e. A+B=B+A

For (I, j) the element of A+B is(a1+ b1) and of B+A is and they are same as a, s and b are real number.

2. Matrix addition is associativei.e. A+(B+C)= (A+B)+Cfor (I,j) the element of A+(B+C) is a +(b+c) and of (A+B)+C is(a+b)+c which are same

3. If o denotes null matrix of the same order as that of A then A+O=A=O+Afor (I,j) the element of A+O is a+o =a which is same as (I, j) the element of A

4. The each matrix A, there correspond of matrix B such that A+B=O=B+A

now let (I,j) the element of B be – a then (I, j) the element of A+B is a-a =o thus the set of mxn matrixs forms an abelion group under the composition of matrix addition.

Q:-4 The sum of three number in GP is 35 and their product is 1000. Find the number.

Ans:-4 let the number be a/r, d, dr

The product of a/αx αx αx α=1000

α 3=1000

α=10

so the number are 10/ α, 10, 10 α

the sum of these numbers =35

= 10/ α + 10+10r= 35

= 2/ α+ 2r = 5

=2 α2 -5r+ 2=0

=(2r-1)(r-2)=0

R=2 or ½

R=2 gives the number as 5, 10, 20

R=1/2 gives the number as 20, 10, 5 the same as the first set

Hence the required number are 5, 10 and 20

Q:-5 Prove binomial theorem

Ans:-5 If n is a positive integer then

(x+y)n = xn+ nc1xn-1y+n-2y2+…………+ncnyn.

Proof= clearly for n=1, LHS = X+Y

And RHS = X+1 c1y= x+y

So that result is true for n =1

Let n+1> 1 and the result be true for n

i.e, (x+Y)n+1= (x+y)n (x+y)

consider (x+y) n+1= (x+y)n (x+y)

According to the theorem, it is possible to expand any power of x + y into a sum of the form

where each   is a specific positive integer known as binomial coefficient. This formula is also referred to as the Binomial Formula or the Binomial Identity. Using summation notation, it can be written as

The final expression follows from the previous one by the symmetry of x and y in the first expression, and by comparison it follows that the sequence of binomial coefficients in the formula is symmetrical.

A variant of the binomial formula is obtained by substituting 1 for y, so that it involves only a single variable. In this form, the formula reads

or equivalently

Q:-6 Solve the system of equations,

2x- 5y+7z = 6

x-3y+ 4z = 3

#x-8y+11z = 11, if constant

Ans:-6 A linear equation in the n variables x1, x2, …, xn is an equation of the form

a1x1 + a2x2 + … + anxn = bwhere the symbols  a1, a2, … , an  and  b  represent constants (real numbers).In a linear equation, all of the n variables appear to the first power, there are no products and no roots of variables, and the variables do not appear as arguments of functions such as rational functions, trigonometric functions, exponential functions, logarithmic functions, etc. The following are examples of linear equations:a)   3x + 4 = 0                                       b)   5x – 3y = 2c)   2x – 8y + 7z = 6                              d)   4x + 2y – 3z + 5w = 9e)   6x + 4y – 4z + 8w – 2t = 5               f)    7x1 + 5x2 – x3 + 2x4 – 9x5 + 3x6 + 4x7 + x8 = 1 An equation that is not linear is said to be a nonlinear equation.The following are examples of non-linear equations:a)   x2 - 9 = 0                                        b)   xy + 3x – 2y = 5

c)                                     d)   

e)                                           f)    y = ln(2x) + 3g)    y – 1 = 3ex + t                                h)  y + sin x = cos zThe quintuplet, or 5-tuple, (3, –4, –1, 0, 5) is a solution of the system     –x1 + 4x2 – 3x3 + 6x4 – 2x5 = –26                                                                                                              3x1 - 5x2 – 2x3 + 7x4 + 4x5 =  11                                                                                                                x1 + 2x2 + 5x3 - 5x4 – 3x5 = –25                                                                                                            -5x1 +  x2  – 4x3 + 8x4 + 5x5 =  10

                                                                                                              2x1 –  x2  +  x3  + 9x4 – 2x5 =  –1  

because when we substitute  x1 = 3,   x2 = –4, x3 = -1, x4 = 0, and x5 = 5 into each equation, we get a true equality.  That is, the quintuplet (3, –4, –1, 0, 5) is a solution of each of the five equations.