Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 4th Sem New 2140706 Numerical And Statistical Methods For Computer Engineering Previous Question Paper
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV (NEW) EXAMINATION ? WINTER 2018
Subject Code:2140706 Date:01/12/2018
Subject Name:Numerical and Statistical Methods for Computer 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)
(b)
Discuss about mathematical modeling.
Discuss various types of errors used for numerical calculations.
03
04
(c) Obtain cubic spline approximation for the function defined by the data given below for
the first two subintervals. Take 0
3 0
? ? M M .
x 0 1 2 3
) (x f 1 2 33 244
07
Q.2 (a)
(b)
Write an algorithm for Simpson?s rule.
Using Simpson?s rule, find
?
?
6 . 0
0
2
dx e
x
taking seven ordinates. Show the calculations up
to four decimal places.
03
04
(c) Define divided difference. Using Newton?s divided difference interpolation, find ) 6 ( f
from the following table:
x 1 2 7 8
) (x f 1 5 5 4
07
OR
(c) Define interpolation. Using Lagrange interpolation, fit a second degree polynomial
passing through the points ) 0 , 0 ( , ) 1 , 1 ( and ) 20 , 2 ( .
07
Q.3 (a)
(b)
State Budan?s theorem. Define diagonally dominant system with example.
Use Newton-Raphson method to find a positive root of 0 1
2 3
? ? ? x x correct up to
four decimal places taking 1
0
? x .
03
04
(c) What do you mean by diagonally dominant system? Solve the following system of
linear equations using Gauss-Seidel method:
0 11 4 3 , 19 3 10 2 , 10 9 ? ? ? ? ? ? ? ? ? z y x z y x z y x .
07
OR
Q.3 (a)
(b)
Explain geometrically the method of false position.
Using Euler?s method, find ) 1 ( y if y x
dx
dy
? ? and 1 ) 0 ( ? y . Take 10 ? n .
03
04
(c) Perform one iteration of the Bairstow method to extract a quadratic factor from the
polynomial 1 2
2 3 4
? ? ? ? x x x x with initial factor 5 . 0 5 . 0
2
? ? x x .
07
Q.4 (a)
Write the steps for engineering problem solving. 03
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV (NEW) EXAMINATION ? WINTER 2018
Subject Code:2140706 Date:01/12/2018
Subject Name:Numerical and Statistical Methods for Computer 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)
(b)
Discuss about mathematical modeling.
Discuss various types of errors used for numerical calculations.
03
04
(c) Obtain cubic spline approximation for the function defined by the data given below for
the first two subintervals. Take 0
3 0
? ? M M .
x 0 1 2 3
) (x f 1 2 33 244
07
Q.2 (a)
(b)
Write an algorithm for Simpson?s rule.
Using Simpson?s rule, find
?
?
6 . 0
0
2
dx e
x
taking seven ordinates. Show the calculations up
to four decimal places.
03
04
(c) Define divided difference. Using Newton?s divided difference interpolation, find ) 6 ( f
from the following table:
x 1 2 7 8
) (x f 1 5 5 4
07
OR
(c) Define interpolation. Using Lagrange interpolation, fit a second degree polynomial
passing through the points ) 0 , 0 ( , ) 1 , 1 ( and ) 20 , 2 ( .
07
Q.3 (a)
(b)
State Budan?s theorem. Define diagonally dominant system with example.
Use Newton-Raphson method to find a positive root of 0 1
2 3
? ? ? x x correct up to
four decimal places taking 1
0
? x .
03
04
(c) What do you mean by diagonally dominant system? Solve the following system of
linear equations using Gauss-Seidel method:
0 11 4 3 , 19 3 10 2 , 10 9 ? ? ? ? ? ? ? ? ? z y x z y x z y x .
07
OR
Q.3 (a)
(b)
Explain geometrically the method of false position.
Using Euler?s method, find ) 1 ( y if y x
dx
dy
? ? and 1 ) 0 ( ? y . Take 10 ? n .
03
04
(c) Perform one iteration of the Bairstow method to extract a quadratic factor from the
polynomial 1 2
2 3 4
? ? ? ? x x x x with initial factor 5 . 0 5 . 0
2
? ? x x .
07
Q.4 (a)
Write the steps for engineering problem solving. 03
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2
(b)
Determine the condition number of the matrix
?
?
?
?
?
?
?
?
?
?
25 16 9
16 9 4
9 4 1
.
04
(c) State direct and iterative methods to solve system of linear equations. Solve the
following system of linear equations using Gauss elimination method:
40 5 4 3 , 13 4 3 2 , 9 ? ? ? ? ? ? ? ? ? z y x z y x z y x .
07
OR
Q.4 (a)
(b)
Write the formula for Runge-Kutta fourth order method.
Fit a second degree polynomial to the following data using least square method.
y
-3 -2 -1 0 1 2 3
x 12 4 1 2 7 15 30
03
04
(c) Calculate the first four moments of the following distribution about the mean.
x
0 1 2 3 4 5 6 7 8
) (x f 1 8 28 56 70 56 28 8 1
07
Q.5 (a)
(b)
Develop a C program to fit regression line of y on x through given set of points using the
least square method.
The probability distribution of a commodity is given below.
Demand 5 6 7 8 9 10
Probability 0.05 0.10 0.30 0.40 0.10 0.05
Find expected demand.
03
04
(c) For the following data, obtain trend values using five years moving average.
Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Value 3 7 14 8 10 11 14 12 16 20 25
07
OR
Q.5 (a)
(b)
Discuss the pitfalls of Gauss elimination.
Define the following terms with examples:
1. Ill-conditioned system
2. Significant figure
03
04
(c) Obtain the correlation coefficient for the following data:
x 100 98 78 85 110 93 80
y
85 90 70 72 98 81 74
07
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This post was last modified on 20 February 2020