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

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

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expected number of Black balls.

**(b)**Construct an Interpolating polynomial of degree 2 which takes the following values

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:

*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

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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*3

*z*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-

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Raphson method.

**(c)**Using Newton's divided difference method, find

*f*(9) from the given data:

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*x*

5

7

11

13

17

*f*(

*x*)

150

392

1452

2366

5202

**OR**

**Q.3 (a)**

3

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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, 3

*x*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

3

*x*

*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

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*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

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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.

**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

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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