Download GTU BE/B.Tech 2019 Summer 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 Summer 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 ? SUMMER 2019
Subject Code:2140706 Date:15/05/2019
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.



MARKS

Q.1 (a) Find the percentage error in the area of an ellipse when errors of 2% and 3
% are made in measuring its major and minor axes respectively.
03



(b) Using the bisection method, find a root of
( ) 2 3sin 5 0 f x x x ? ? ? ? correct up to three decimal places.
04
(c) Interpolate the function () y f x ? at point 1.5 x ? using the following
tabulated data.
x 1 2 3 4 5 6 7 8
y 1 8 27 64 125 216 343 512

07

Q.2 (a)
Using trapezoidal rule find the value of the integral
5
0
1
dx
x ?
?
with h =1.
04
(b) Discuss false position method. 03
(c) Fit a second-degree parabola to the following data using method of least
squares.
x 0 1 2 3 4
y 1 1.8 1.3 2.5 6.3

07
OR
(c)
Find the cubic spline in the interval ? ? 0, 2 for the following data:
x 0 2 4 6
y 1 9 41 41

07
Q.3 (a) Apply Budan`s theorem to find the number of roots of the equation
32
3 4 13 x x x ? ? ? in the interval ? ? 3, 2 ?? and ? ? 2, 1 ??
03
(b)
Find an iterative formula for N , where N is a positive number and hence,
find 12 correct up to four decimal places.
04
(c) Using Gauss Seidel method solve the following equations:
5 10
2 4 14
8 20
x y z
x y z
x y z
? ? ?
? ? ?
? ? ?

07
OR
Q.3 (a)
Prove that ? ? ? ? ? ? ( ) 1 1 1 ( ) i ii ? ? ? ? ? ? ? ? ? ? ?
03
(b) Find (32) y from the following table:
x 25 30 35 40
y 0.2707 0.3027 0.3386 0.3794

04
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV(NEW) ? EXAMINATION ? SUMMER 2019
Subject Code:2140706 Date:15/05/2019
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.



MARKS

Q.1 (a) Find the percentage error in the area of an ellipse when errors of 2% and 3
% are made in measuring its major and minor axes respectively.
03



(b) Using the bisection method, find a root of
( ) 2 3sin 5 0 f x x x ? ? ? ? correct up to three decimal places.
04
(c) Interpolate the function () y f x ? at point 1.5 x ? using the following
tabulated data.
x 1 2 3 4 5 6 7 8
y 1 8 27 64 125 216 343 512

07

Q.2 (a)
Using trapezoidal rule find the value of the integral
5
0
1
dx
x ?
?
with h =1.
04
(b) Discuss false position method. 03
(c) Fit a second-degree parabola to the following data using method of least
squares.
x 0 1 2 3 4
y 1 1.8 1.3 2.5 6.3

07
OR
(c)
Find the cubic spline in the interval ? ? 0, 2 for the following data:
x 0 2 4 6
y 1 9 41 41

07
Q.3 (a) Apply Budan`s theorem to find the number of roots of the equation
32
3 4 13 x x x ? ? ? in the interval ? ? 3, 2 ?? and ? ? 2, 1 ??
03
(b)
Find an iterative formula for N , where N is a positive number and hence,
find 12 correct up to four decimal places.
04
(c) Using Gauss Seidel method solve the following equations:
5 10
2 4 14
8 20
x y z
x y z
x y z
? ? ?
? ? ?
? ? ?

07
OR
Q.3 (a)
Prove that ? ? ? ? ? ? ( ) 1 1 1 ( ) i ii ? ? ? ? ? ? ? ? ? ? ?
03
(b) Find (32) y from the following table:
x 25 30 35 40
y 0.2707 0.3027 0.3386 0.3794

04
2
(c)
Solve
4 3 2
8 39 62 50 0 x x x x ? ? ? ? ? by using Lin-Bairstow method up to
third iteration
00
0 pq ??
07
Q.4 (a)
Using Simpson`s 1/3 rule, find
2
0.6
0
x
e dx
?
?
, by taking 6 n ?
03
(b) Find the median of the following data:
Age
greater
than (in
years)
0 10 20 30 40 50 60 70
No. of
persons
230 218 200 165 123 73 28 8

04
(c)
Solve
2
, (0) 1
dy x
yy
dx y
? ? ? in the range 0 0.2 x ?? using modified Euler`s
method taking h = 0.1.
07
OR
Q.4 (a) Write the formula for Runge-Kutta second order method. 03
(b) Use Lagrange`s interpolation formula to find the value of y (10) for given
data:
x 5 6 9 11
y 12 13 14 16

04
(c) Using Runge- Kutta method of fourth order, solve for y (0.1),
y (0.2) and y (0.3) given that
2
, (0) 1. y xy y y ? ? ? ?
07
Q.5 (a) Develop a C program for bisection method. 03
(b) Two unbiased dice are thrown at random. Find the probability distribution
of the sum of the numbers on them. Also find the mean and variance.
04
(c) Calculate the coefficient of correlation for the following pairs of x and y:
x 17 19 21 26 20 28 26 27
y 23 27 25 26 27 25 30 33

07
OR

Q.5 (a) Discuss type of Regression. 03
(b) Find the regression coefficient of y on x for the following data:
x 1 2 3 4 5
y 160 180 140 180 200

04
(c)
Given
1
, (0) 2
dy
y
dx x y
??
?
, (0.2) 2.0933 y ?
(0.4) 2.1755, (0.6) 2.2493 yy ?? , find y (0.8) using Milne`s Predictor
Corrector method.
07

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