Download GTU BE/B.Tech 2018 Winter 4th Sem New 2140606 Numerical And Statistical Methods For Civil Engineering Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 4th Sem New 2140606 Numerical And Statistical Methods For Civil Engineering Previous Question Paper

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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ?IV (NEW) EXAMINATION ? WINTER 2018
Subject Code:2140606 Date:22/11/2018

Subject Name:Numerical and Statistical Methods for Civil Engineering

Time: 02:30 PM TO 05:00 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

Q.1

(a) In usual notations show that
?
?
?
?
?
? ? ? ?
03
(b) Find the cubic polynomial which takes on the values
. 71 ) 5 ( , 32 ) 4 ( , 11 ) 3 ( , 2 ) 2 ( , 1 ) 1 ( , 4 ) 0 ( ? ? ? ? ? ? f f f f f f Also find ) 6 ( f
and ). 5 . 2 ( f
04
(c) Obtain by Power method the numerically largest eigen value of the matrix
?
?
?
?
?
?
?
?
?
?
? ?
? ?
? ?
?
2 4 20
6 12 10
3 4 15
A

07

Q.2 (a) In how many different ways can the director of a research laboratory choose 2
chemists from among 7 applicants and 3 physicists from among 9 applicants?
03
(b) A class consists of 6 girls and 10 boys. If a committee of three is chosen at random
from the class, find the probability that, (i) three boys are selected; (ii) exactly
two girls are selected.
04
(c) Solve the following system of equations using Gauss Jacobi iteration method:
4 3 2 ; 6 2 5 ; 2 4
3 2 1 3 2 1 3 2 1
? ? ? ? ? ? ? ? ? ? ? x x x x x x x x x

07
OR
(c) At checkout counter customers arrive at an average of 2.0 per minute. Find the
probabilities that
(i) At most 3 will arrive in any given minute
(ii) At least 3 will arrive during an interval of 4 minutes
(iii) At most 10 will arrive during an interval of 6 minutes.
07
Q.3 (a) Using Regula ? Falsi method determine the root of the equation . 2 . 1 log ? x x 03


(b)
Use Euler?s method to solve the initial value problem
2
y x
dx
dy ?
? on the interval
] 3 , 0 [ with . 1 ) 0 ( ? y Compare the numerical solution with exact solution for the step
size . 25 . 0 ? h
04


(c) Using Runge ? Kutta fourth order method solve . 1 ) 0 ( ;
2
? ? ? y
y
x
y
dx
dy

Evaluate the value of y when , 4 . 0 2 . 0 ? ? x x take step size 0.2.
07
OR
Q.3 (a) Using Taylor?s series method, find ) 1 . 1 ( y correct to four decimal place, given by
. 1 ) 1 ( ;
3
1
? ? y xy
dx
dy

03
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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ?IV (NEW) EXAMINATION ? WINTER 2018
Subject Code:2140606 Date:22/11/2018

Subject Name:Numerical and Statistical Methods for Civil Engineering

Time: 02:30 PM TO 05:00 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

Q.1

(a) In usual notations show that
?
?
?
?
?
? ? ? ?
03
(b) Find the cubic polynomial which takes on the values
. 71 ) 5 ( , 32 ) 4 ( , 11 ) 3 ( , 2 ) 2 ( , 1 ) 1 ( , 4 ) 0 ( ? ? ? ? ? ? f f f f f f Also find ) 6 ( f
and ). 5 . 2 ( f
04
(c) Obtain by Power method the numerically largest eigen value of the matrix
?
?
?
?
?
?
?
?
?
?
? ?
? ?
? ?
?
2 4 20
6 12 10
3 4 15
A

07

Q.2 (a) In how many different ways can the director of a research laboratory choose 2
chemists from among 7 applicants and 3 physicists from among 9 applicants?
03
(b) A class consists of 6 girls and 10 boys. If a committee of three is chosen at random
from the class, find the probability that, (i) three boys are selected; (ii) exactly
two girls are selected.
04
(c) Solve the following system of equations using Gauss Jacobi iteration method:
4 3 2 ; 6 2 5 ; 2 4
3 2 1 3 2 1 3 2 1
? ? ? ? ? ? ? ? ? ? ? x x x x x x x x x

07
OR
(c) At checkout counter customers arrive at an average of 2.0 per minute. Find the
probabilities that
(i) At most 3 will arrive in any given minute
(ii) At least 3 will arrive during an interval of 4 minutes
(iii) At most 10 will arrive during an interval of 6 minutes.
07
Q.3 (a) Using Regula ? Falsi method determine the root of the equation . 2 . 1 log ? x x 03


(b)
Use Euler?s method to solve the initial value problem
2
y x
dx
dy ?
? on the interval
] 3 , 0 [ with . 1 ) 0 ( ? y Compare the numerical solution with exact solution for the step
size . 25 . 0 ? h
04


(c) Using Runge ? Kutta fourth order method solve . 1 ) 0 ( ;
2
? ? ? y
y
x
y
dx
dy

Evaluate the value of y when , 4 . 0 2 . 0 ? ? x x take step size 0.2.
07
OR
Q.3 (a) Using Taylor?s series method, find ) 1 . 1 ( y correct to four decimal place, given by
. 1 ) 1 ( ;
3
1
? ? y xy
dx
dy

03
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2

(b)
Evaluate
?
?
1
0
1 x
dx
by Simpson?s
rd
3
1
rule taking eleven ordinates and hence find the
value of 2 log
e
correct to five significant digits.
04
(c) Use Newton?s divided difference method to evaluate ) 4 ( f from the below data:
x : 0 1 2 3
: ) (x f 2 3 12 147


07
Q.4 (a) The runs scored by two batsmen A and B in 9 consecutive matches are given
below. Find which batsman is more consistent?
A 85 20 62 28 74 5 69 4 13
B 72 4 15 30 59 15 49 27 26

03


(b) Derive an iteration formula for
3
N and hence find
3
58 .
04
(c) Solve the following system of equation using Gauss ? Seidel method:
20 8 ; 14 4 2 ; 10 5 ? ? ? ? ? ? ? ? ? z y x z y x z y x
07
OR
Q.4 (a) Find the mean and standard deviation for the following data:
Class Interval 0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 6 14 10 8 1 3 8


03
(b)
Find the equation of the cubic curve which passes through the points ? ? 5 , 0 ? ,
? ? 10 , 1 ? , ? ?, 9 , 2 ? ? ? 4 , 3 , and ? ? 35 , 4 .
04
(c) Solve the following system of equations using Gauss elimination method with
partial pivoting. 16 3 2 ; 24 4 3 3 ; 7 ? ? ? ? ? ? ? ? ? z y x z y x z y x
07
Q.5 (a) Find the median from the following data.
Class limits 0-30 30-60 60-90 90-120 120-150 150-180
Frequency 8 13 22 27 18 7


03
(b) Compute the correlation coefficient between X and Y using the following data:
X 2 4 5 6 8 11
Y 18 12 10 8 7 5

04
(c) Following table gives the data on rainfall and discharge in a certain river. Obtain
the line of regression of Y on X.
Rainfall(inch) X: 1.53 1.78 2.60 2.95 3.42
Discharge(1000cc) Y: 33.5 36.3 40.0 45.8 53.5

07
OR

Q.5 (a) A train is moving at the speed of 30 m/s suddenly brakes are applied. The speed
of the train per second after t seconds is given by the following table:
Time(t) 0 5 10 15 20 25 30
Speed(v) 30 24 19 16 13 11 10
Apply Simpson?s 3/8
th
rule to determine the distance moved by the train 30 sec.
03
(b) An unbiased coin is tossed 6 times. Find the probability of getting (i) exactly 4
heads, (ii) at least 4 heads.
04
(c) At constant temperature, the pressure P and the volume V of a gas are connected
by the relation
?
PV = constant. Find the best fitting equation of this form to the
following data and estimate V when P=4.
P(Kg. Sq. cm) 0.5 1.0 1.5 2.0 2.5 3.0
V(cc) 1620 1000 750 620 520 460

07

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