MTH202 Assignment # 2 Solution

MTH202 Assignment # 4 Solution

MTH202 Assignment # 4 Solution:

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MTH202 GDB

MTH202 GDB Solution…..
Question:-
Discuss the Role of Probability for solving problems in different fields of life.
Answer:-
Probability's is branching of Statistics and statistics itself a branch of mathematics. It helps us in decision making in every field of life. With this help .in computing field we making loop and in medical field we inferences that what need of hospital in these areas .probability itself a math.Statistics refers to a branch of mathematics that deals with collection, analysis, interpretation and presentation of data. It is widely used in all fields of life including social and natural sciences
Answer:-2
By Sherry
"Probability is the mathematical way to deal with problems of uncertainty. It is a tool formeasuring the appearance chance of events. In this regard, probabilistic thinking is fundamentally different from deterministic thinking that is used in other mathematical topics that generally relate to the present or the past.The strength of probability, what makes it important and powerful, is also an important aspect of teacher subject matter knowledge. Probability opened new possibilities for dealing with uncertain and random situations that occur in almost every field of our life.Today, probability has become an integral component in every area. Probability applies in everyday situations, in games, in data processing, in insurance, in economics, in natural sciences. There is no part of mathematics that is as universally applied, except, of course, elementary arithmetic. "

MTH202

MTH202 Assignment Solution:

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MTH202

Question 1; Mark: 10Use Mathematical Induction to prove that.
Sol:

Induction given statement is true for all set of whole numbers.
Question 2; Mark: 5
If 3x+1 is odd then x is even (prove by contradiction).

Sol: Suppose 3x + 1 is odd and x is not evenx is not even à x is odd (x is either even or odd but not both)à x = 2k + 1 ( x is not divisible by 2)à 3x + 1 = 3 ( 2k +1) + 1 (substitute 2k +1 from x)
3x +1 = 6k + 3 + 1
= 6k + 4
= 2 ( 3k + 2) (Divisible by 2)
à 3x + 1 is even which is contradiction
Therefore 3x + 1 is odd then x is even

Question 3; Marks: 5

Find the number of arrangements of balls having colors Red, Yellow, Blue Green and Pink such that Red and Green balls must place next to each other.

Sol:

Red, Yellow, Blue, Green, Pink

Total numbers of balls = 5

Considering two balls Red and Green as a single ball ( due to restriction), we have to make the arrangements of 4 balls taken all together

No. of Arrangements = 4!

= 4 × 3 × 2 × 1= 24

But two balls (restricted) permuted among themselves in two ways

i.e. 2! = 2 × 1 = 2 ways

Therefore total numbers of arrangements = 4! × 2!= 24 × 2
= 48

MTH202

MTH202 Assignment Solution:
Question 1
Let a function f: R®R be defined by
f(x) =2x3 + 7 Show that f is bijective.
Solution:
f is one-to-one
Let f(x1) = 2 x13 + 7 and f(x2) = 2 x23 + 7
By the definition we know that,

f(x1) = f(x2) for x1 , x2 Î R
2 x13 + 7 = 2 x23 + 7
2 x13 - 2 x23 = 7 – 7
2( x13 - x23 ) = 0
x13 - x23 = 0
(x1 - x2)( x12 + 2x1 x2 + x22) = 0
x1 - x2 = 0 ; x12 + 2x1 x2 + x22 = 0
x1 = x2 (The second equation gives no real solution)

Accordingly f is one-to-one.

f is onto
f(x) =2x3 + 7

let y Î R. We search for x Î R such that

f(x) = y
2x3 + 7 = y
x3 = OR x =

f(x) = f [ ]

f(x) = 2 + 7 = y – 7 + 7
f(x) = y

Thus f is a Bijective

Question 2;
Find the sum of the series whose nth term is .
Solution


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