PTU Punjab Technical University B-Tech May 2019 Question Papers 6th Semester Mechanical Engineering (MECH)

Total No. of Pages : 02

Total No. of Questions : 09

B.Tech.(ME) (2011 Onwards) (Sem.?6)

STATISTICAL AND NUMERICAL METHODS IN ENGINEERING

Subject Code : BTME-604

M.Code : 71188

Time : 3 Hrs. Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :

1.

SECTION-A is COMPULSORY consisting of TEN questions carrying T WO marks

each.

2.

SECTION-B contains FIVE questions carrying FIVE marks each and students

have to attempt any FOUR questions.

3.

SECTION-C contains T HREE questions carrying T EN marks each and students

have to attempt any T WO questions.

SECTION-A

1.

Write briefly :

a) The mean of 5 observations is 7. Later on it was found that two observations 4 and 8

were wrongly taken instead of 5 and 9. Find the correct mean.

b) Define Conditional Probability.

c) Find the mean and the standard deviation of the number of heads in 100 tosses of a

fair coin.

d) Define level of Significance.

e) If u = 26 ? 5, find the percentage error in u at v = 1 if error in v is 0.05.

f) Show that the following rearrangement of the equation :

x3 + 6x2 + 10x ? 20 = 0 does not yield a convergent sequence of successive

2

3

(20 6x x )

approximations by iteration method near x = 1, x

.

10

g) Prove = E ? 1.

h) Write Simpson's 1/3rd formula for numerical integration.

i) Define Pivoting and type of Pivoting.

j) Show that Euler's formula is R-K method of first order.

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SECTION-B

2.

It is known from the past experience that the average number of industrial accidents in a

factory per month in a plant is 4. Find the probability that during a particular month, there

will be lower than 4 accidents. Use Poisson Distribution (Given e?4) = 0.0183.

3.

Evaluate 12 to four decimal places by Newton's iterative method.

4.

Find y (10) from the following table :

X

5

6

9

11

Y

12

13

14

16

5.

The table given below reveals the velocity `v' of a body during the time `t' specified.

Find its acceleration at t = 1.1

T

1.0

1.1

1.2 1.3 1.4

V 43.1

47.7

52.1 56.4 60.8

6.

Solve the following system of equations using Gauss Elimination Method.

x + y + z = 7

3x + 3y + 4z = 24

2x + y + 3z = 16

SECTION-C

7.

In a test given to two groups of students the marks obtained are as follows :

First group

18

20

36

50

49

36

34

49

41

Second group 29

28

26

35

30

44

46

Examine the significance of difference between the mean marks secured by students of

the above two groups. (The value of t at 5% level for 4d.f = 2.14).

8.

Find the smallest Eigen value of the matrix

1

2

2

4

2 12

3

5

A =

using Power Method.

3 13 0

7

2 11

2

2

9.

Use Milne's method to solve y = 1 + y2 with:

y(0) = 0, y (0.2) = 0.2027, y (0.4) = 0.4228, y (0.6) = 0.6841 obtain y (0.8), y(1) and

y(-0.2).

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any

page of Answer Sheet will lead to UMC against the Student.

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This post was last modified on 04 November 2019