Download GTU BE/B.Tech 2019 Winter 4th Sem New 2140706 Numerical And Statistical Methods For Computer Engineering Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 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 2019
Subject Code: 2140706 Date: 12/12/2019

Subject Name: Numerical and Statistical Methods for Computer 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) If X = 3.1416, find the absolute and relative errors if :
(a) X is truncated to three decimal places.
(b) X is rounded off to three decimal places.
03
(b) Construct an Interpolating polynomial which takes the following values :
x 0 1 2 3 4 5
y
-10 -8 -8 -4 10 40

04
(c)
By using Method of least squares , fit a second degree parabola
2
y a bx cx ? ? ?
to the following data:
x 0 1 2 3 4
y
1 1.8 1.3 2.5 2.3

07

Q.2 (a) Write an algorithm for Bisection Method. 03
(b) If P is the pull required to lift a load W by means of pulley block, find a linear law
of the form P = m W + c connecting P and W using following data:
P 12 15 21 25
W 50 70 100 120

04
(c) Obtain Cubic spline for any of given subinterval from the following data:
x 1 2 3 4
() fx 1 2 5 11

07
OR
(c) Using Lagrange?s interpolating polynomial, find Interpolating polynomial from the
given data:
x 2 3 5 7
() fx 0.1506 0.3001 0.4517 0.6259

07
Q.3 (a) Use Secant method to find the real root of equation
3
5 7 0 xx ? ? ? . 03
(b)
Find a real root of
3
10 xx ? ? ? , correct to three decimal places using Newton-
Raphson method.
04
(c) Use Gauss-Seidel method to obtain the solution of the system
83 11 4 95, 7 52 13 104, 3 8 29 71 x y z x y z x y z ? ? ? ? ? ? ? ? ?
07
OR
Q.3 (a)
Apply Budan?s theorem to the equation
42
7 6 1 0 xxx ? ? ? ? to draw the inference
about the roots in the interval ( 2, 1) ? .
03
(b) Solve the given System of Linear equations by using Gauss Elimination method:
7, 3 3 4 24, 2 3 16 x y z x y z x y z ? ? ? ? ? ? ? ? ?
04
(c)
Given that
2 2 2
2
dy
y x y
dx
? , (0) 1, (0.1) 1.06, (0.2) 1.12, (0.3) 1.21 y y y y ? ? ? ?
07
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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? IV (New) EXAMINATION ? WINTER 2019
Subject Code: 2140706 Date: 12/12/2019

Subject Name: Numerical and Statistical Methods for Computer 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) If X = 3.1416, find the absolute and relative errors if :
(a) X is truncated to three decimal places.
(b) X is rounded off to three decimal places.
03
(b) Construct an Interpolating polynomial which takes the following values :
x 0 1 2 3 4 5
y
-10 -8 -8 -4 10 40

04
(c)
By using Method of least squares , fit a second degree parabola
2
y a bx cx ? ? ?
to the following data:
x 0 1 2 3 4
y
1 1.8 1.3 2.5 2.3

07

Q.2 (a) Write an algorithm for Bisection Method. 03
(b) If P is the pull required to lift a load W by means of pulley block, find a linear law
of the form P = m W + c connecting P and W using following data:
P 12 15 21 25
W 50 70 100 120

04
(c) Obtain Cubic spline for any of given subinterval from the following data:
x 1 2 3 4
() fx 1 2 5 11

07
OR
(c) Using Lagrange?s interpolating polynomial, find Interpolating polynomial from the
given data:
x 2 3 5 7
() fx 0.1506 0.3001 0.4517 0.6259

07
Q.3 (a) Use Secant method to find the real root of equation
3
5 7 0 xx ? ? ? . 03
(b)
Find a real root of
3
10 xx ? ? ? , correct to three decimal places using Newton-
Raphson method.
04
(c) Use Gauss-Seidel method to obtain the solution of the system
83 11 4 95, 7 52 13 104, 3 8 29 71 x y z x y z x y z ? ? ? ? ? ? ? ? ?
07
OR
Q.3 (a)
Apply Budan?s theorem to the equation
42
7 6 1 0 xxx ? ? ? ? to draw the inference
about the roots in the interval ( 2, 1) ? .
03
(b) Solve the given System of Linear equations by using Gauss Elimination method:
7, 3 3 4 24, 2 3 16 x y z x y z x y z ? ? ? ? ? ? ? ? ?
04
(c)
Given that
2 2 2
2
dy
y x y
dx
? , (0) 1, (0.1) 1.06, (0.2) 1.12, (0.3) 1.21 y y y y ? ? ? ?
07
2
Evaluate (0.4) y by Milne?s Predictor ? Corrector method.
Q.4 (a) Considering following tabular values, Determine the area bounded by the given
curve and X-axis between 10 x ? to 16 x ? by Trapezoidal rule.
x 10 11 12 13 14 15 16
y
1.02 0.94 0.89 0.79 0.71 0.62 0.55

03
(b)
Using Simpson?s 1/3 rule, evaluate
1
2
0
1
(1 )
dx
x ?
?
by taking 4 sub intervals.
04
(c) Use Fourth order Runge-Kutta method to find (0.2) y with 0.1 h ? , given that
2 , (0) 1
dy
x y y
dx
? ? ?
07
OR
Q.4 (a) Use Euler?s Method to find (0.10) y in five steps from the differential equation
, (0) 1
dy
x y xy y
dx
? ? ? ?
03
(b)
Use Modified Euler?s method to solve 3 , (0) 1
dy
x y y
dx
? ? ? . Hence find (0.5) y with
0.1 h ? .
04
(c) (i) Write an algorithm for Newton?s Forward Interpolation Formula
(ii) Using Newton?s devided difference formula, calculate the value of (6) f
x 1 2 7 8
() fx 1 5 5 4

07
Q.5 (a) Compute the Median from the data:
Class 0-30 30-60 60-90 90-120 120-150 150-180
Frequency 8 13 22 27 18 7

03
(b) Find the correlation coefficient between the sales and expenses of the following 10
firms:
Firms 1 2 3 4 5 6 7 8 9 10
Sales 50 50 55 60 65 65 65 60 60 50
Expenses 11 13 14 16 16 15 15 14 13 13

04
(c) In a state, data shows the demand of towers for the sufficient network for each of
the last 7 weeks.
Week 1 2 3 4 5 6 7
Demand 23 29 33 40 41 43 49
(a) Calculate a two week moving average for weeks two to seven
(b) Calculate mean square error (M. S. E)
07
OR

Q.5 (a) Find the standard deviation of a group of data points:
101.8 , 103.2, 104.0, 102.5, 103.5
03
(b) 10 Participants in a musical test were ranked by the three judges in the following
order. Using Spearman?s Rank Correlation Co-efficient method, determine which
pair of judges has the nearest approach to common liking music.
1
st
Judge 1 6 5 10 3 2 4 9 7 8
2
nd
Judge 3 5 8 4 7 10 2 1 6 9
3
rd
Judge 6 4 9 8 1 2 3 10 5 7

04
(c) Obtain the two lines of regression for the following data :
X 190 240 250 300 310 335 300
Y 5 10 15 20 20 30 30

07
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