GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER-IV (NEW) EXAMINATION - WINTER 2020
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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:
- Attempt any FOUR questions out of EIGHT questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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MARKS
Q1 (a) prove that £z = u+ %6. 03
(b) Fit a polynomial of degree three which takes the following values : 04
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X: 3 4 5 6
Y: 6 24 60 120
(c) Use the Runge-Kutta method of fourth order to solve 07
Y' = 1+y?
Subject to ¥(0) = 0, find y(0.2) and y(0.4).
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Q2 (a) Evaluate ?01exdx with n=10 using the trapezoidal rule. 03
(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
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4x +8y+3z=155
5x+4y-10z =65
Q.3 (a) Find a root of the equation x³ —4x —9 = 0 using the Bisection method in 03
four stages.
(b) Determine the root of xe? —2 = 0 by method of false position. 04
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(c) Find a real root of the equation 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) Evaluate ?01 dx / (1+x) with n=6 by using Simpson’s 3/8 rule, and hence 04
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calculate log 2.
(c) Fit a second degree parabola y = a + bx² to the following data : 07
X: 1 2 3 4 5
y: 1.8 5.1 8.9 14.1 19.8
Q.5 (a) Using Newton’s divided difference interpolation, compute the value of 03
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f(6) from the table given below:
X: -1 0 1 2 3
y: -8 3 1 1 2
(b) Use the Gauss Elimination method to solve the following equations : 04
x+4y-z=-5
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x+y-6z=-12
3x-y-z=4
(c) Using Taylor’s series method, find the value of y(0.1), given y' =x² + 07
y² and y(0) =1, correct to four decimal places.
Q.6 (a) Using Stirling’s formula, find y(25) from the following table : 03
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X: 20 24 28 32
y: 0.01427 0.01581 0.01772 0.01996
(b) Find the dominant eigen values of A = [[1, 2], [3, 4]] by power method and hence 04
find the other eigen value also.
(c) Use Euler’s method, find y(0.2) given y' =y- x²-x,y(0) =1with h=0.1. 07
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Q.7 (a) Fit a straight line for the following data: 03
X: 1 2 3 4 5 6
Y: 6 4 3 5 4 2
(b) Fit the curve y = ax? to the following data: 04
X: 6 1 2 6 7 2.6
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y: 350 400 500 600
(c) OR 07
Define Discrete Random Variable and Continuous Random Variable.
Q.8 (a) Find the correlation coefficients from the following data : 03
X: 1 2 3 4 5 6 7
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Y: 6 8 11 9 12 10 14
(b) From the following results, obtain the two regression equations and 04
estimate the yield when rainfall is 29 cm and the rainfall, when the yield is
600Kg :
Yield in Kg Rainfall in cm
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Mean 508.4 26.7
S.D. 36.8 4.6
(c) The coefficient of correlation between yield and rainfall is 0.52. 07
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