# PTU B.Tech Mechanical Engineering 6th Semester May 2019 71188 STATISTICAL AND NUMERICAL METHODS IN ENGINEERING Question Papers

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

Roll No.
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.
1 | M-71188

(S2)-1152

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).

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