# Download GTU B.Tech 2020 Summer 4th Sem 2140606 Numerical And Statistical Methods For Civil Engineering Question Paper

Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Summer 4th Sem 2140606 Numerical And Statistical Methods For Civil Engineering Previous Question Paper

Seat No.: ________
Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER? IV EXAMINATION ? SUMMER 2020
Subject Code: 2140606 Date:29/10/2020
Subject Name: NUMERICAL AND STATISTICAL METHODS FOR
CIVIL ENGINEERING

Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

MARKS
Q.1 (a) There are 3 Red and 2 Black balls in a box. If 2 balls are selected at random, find the
03
expected number of Black balls.

(b) Construct an Interpolating polynomial of degree 2 which takes the following values
04
:
x
-1
0
1
3
y
2
1
0
-1

(c) By using Method of least squares , fit a second degree parabola
2
y a b x c x
to
07
the following data.
x
0
1
2
3
4
y
1
1.8
1.3
2.5
2.3

Q.2 (a) Considering following tabular values, Determine the area bounded by the given
03
curve and X-axis between x 7.47 to x 7.52 by Trapezoidal rule.
x
7.47
7.48
7.49
7.50
7.51
7.52
y
1.93
1.95
1.98
2.01
2.03
2.06

(b)
1
04
Using Simpson's 3/8 rule, evaluate sin x dx
with n = 6
x
0

(c) Use Gauss-Seidel method to obtain the solution of the system
07
6 x y z 105, 4 x 8 y 3z 155, 5 x 4 y 10 z 65

OR

(c) 4 Coins are tossed simultaneously. What is the probability of getting (a) Two heads
07
(b) At least two heads (c) At most two heads
Q.3 (a) Use Bisecti
on method to find the real root of equation 2sin x x 0 .
03

(b) Find a real root of 3
x x 1 0, correct to four decimal places using Newton-
04
Raphson method.

(c) Using Newton's divided difference method, find f (9) from the given data:
07
x
5
7
11
13
17
f (x)
150
392
1452
2366
5202

OR

Q.3 (a)
3
03
Using Simpson's 1/3 rule, evaluate
2
cos x dx
taking 6 sub intervals.
0

(b) Solve the following linear system using Gauss Elimination method:
04
2 x y z 10, 3x 2 y 3 z 18, x 4 y 9 z 16
1

(c)
dy
07
Use second order Runge-Kutta method to solve

3x y , y (1)1.3 and find

dx
y(1.2) with h 0.1
Q.4 (a) Use the Secant method to find approximate root of equation
x
xe 1 0 .
03

(b)
1
dy
04
Using Taylor's series method, obtain the solution of
3
x y
, y(1) 1
. Find the
dx
value of y (1.1)

(c) Use Fourth order Runge-Kutta method to find y(0.2) with h 0.1, given that
07
dy
2
2
10
x y , y(0) 1
dx

OR

Q.4 (a) Use Euler's Method to find y(0.2) from the differential equation
03
dy
2 x
y
, y (0) 1
dx
y

(b) Evaluate 1 1 dx
using the Gaussian Integration formula with n = 2.
04
0 1 x

(c)
dy
07
Given that
2
x y , y(0) 0, y(0.2) 0.02, y(0.4) 0.0795, y(0.6) 0.1762
dx
Evaluate y (0.8) by Milne's Predictor ? Corrector method.
Q.5 (a) The following table gives marks obtained by 50 students in a subject of Civil. Find
03
the Median.
Marks
0-10
10-20
20-30
30-40
40-50
No. of Students
16
12
18
3
1

(b) Find the correlation coefficient from the following data:
04
X
1
2
3
4
5
6
7
Y
6
8
11
9
12
10
14

(c) Calculate karl Pearson's co-efficient of skewness from the following data:
07
x
0-100 100-
200-
300-
400-
500-
600-
700-
200
300
400
500
600
700
800
f
6
10
18
20
15
12
10
9

OR
Q.5 (a) Find the mean and standard deviation of a group of data points:
03
3, 4, 6, 7, 9, 15
(b) Ten Students got the following percentage of marks in Mathematics and Statistics.
04
Calculate the correlation coefficient.
Roll no.
1
2
3
4
5
6
7
8
9
10
Maths
78
36
98
25
75
82
90
62
65
39
Statistics 84 51
91
60
68
62
86
58
53
47
(c) A study of the amount of rainfall and the quality of air pollution removed produced the
07
following data:
Daily
4.3
4.5
5.9
5.6
6.1
5.2
3.8
2.1
7.5
rainfall x
Particulate 126
121
116
118
114
118
132
141 108
removed y
(a) Find the equation of the regression line to predict the particulate removed
from the amount of daily rainfall.
(b) Find the amount of particulate removed when daily rainfall is x = 4.8 units.
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This post was last modified on 04 March 2021