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

Seat No.: ________
Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER?IV (NEW) EXAMINATION ? WINTER 2020
Subject Code:2140606 Date:09/02/2021
Subject Name:Numerical and Statistical Methods for Civil Engineering
Time:02:30 PM TO 04:30 PM Total Marks:56
Instructions:
1. Attempt any FOUR questions out of EIGHT questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.


MARKS
Q.1 (a)
1
Prove that
1
2 = + .
03
2

(b) Fit a polynomial of degree three which takes the following values :
04
X:
3
4
5
6

Y:
6
24
60
120

(c) Use the Runge-Kutta method of fourth order to solve
07
= 1 + 2
Subject to (0) = 0, find (0.2) and (0.4).



Q.2 (a)
1
03
Evaluate
ex
2 dx
with n=10 using the trapezoidal rule.
0

(b) If 20 % of the bolts produced by a machine are defective, determine the
04
Probability that out of 4 bolts chosen, at most 2 bolts will be defective.

(c) Solve the following system of linear equations by Gauss Seidel method
07
6x y z 105
4x 8y 3z 155
5x 4 y 10z 65



Q.3 (a) Find a root of the equation 3
x 4x 9 0 using the Bisection method in
03
four stages.

(b) Determine the root of x
xe 2 0 by method of false position.
04

(c) Find a real root of the equation
x
x e ,using the Newton-Raphson
07
method.



Q.4 (a) Write sample space of random experiment of tossing three coins together
03
and obtain the probability of the event that one head and two tails obtained.

(b)
1
1
04
Evaluate
dx
with n=6 by using Simpson's 3/8 rule, and hence
1 x
0
calculate log 2.

(c) Fit a second degree parabola
2
y a bx to the following data :
07
x:
1
2
3
4
5
y:
1.8
5.1
8.9
14.1
19.8
1

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Q.5 (a) Use Lagrange's interpolation formula to find y( )
4 from the following
03
table:
x :
-1
0
2
3
y:
-8
3
1
2

(b) Using Newton's divided difference interpolation, compute the value of
04
f ( )
6 from the table given below:
x
1
2
7
8
f(x)
1
5
5
4

(c) Use the Gauss Elimination method to solve the following equations :
07
x 4 y z 5
x y 6z 12
3x y z 4



Q.6 (a) Using Taylor's series method, find the value of y(0. ),
1 given = +
03
and y( )
0 ,
1 correct to four decimal places.

(b) Using Stirling's formula, find y(25) from the following table :
04
x:
20
24
28
32
y:
0.01427
0.01581
0.01772
0.01996

(c)
1 2
07
Find the dominant eigen values of A
by power method and hence
3 4
find the other eigen value also.
Q.7 (a)
dy
2x
03
Use Euler's method, find y(0.2) given
y
, y( )
0 1with h
.
1
.
0
dx
y

(b) Fit a straight line for the following data:
04
X:
1
2
3
4
5
6
Y:
6
4
3
5
4
2

(c) Fit the curve
b
y ax to the following data:
07
x:
61
26
7
2.6
y:
350
400
500
600


OR

Q.8 (a) Define Discrete Random Variable and Continuous Random Variable.
03

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

(c) From the following results, obtain the two regression equations and
07
estimate the yield when rainfall is 29 cm and the rainfall, when the yield is
600Kg :
Yield in Kg
Rainfall in cm
Mean
508.4
26.7
S.D.
36.8
4.6
The coefficient of correlation between yield and rainfall is 0.52.

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