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
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
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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
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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
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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
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(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 .
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(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
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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 .
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(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
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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
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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
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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:
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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:
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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:
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3, 4, 6, 7, 9, 15
(b) Ten Students got the following percentage of marks in Mathematics and Statistics.
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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
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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