Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 5th Sem Old 151601 Computer Oriented Statistical Methods Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?V (Old) EXAMINATION ? WINTER 2019
Subject Code: 151601 Date: 27/11/2019
Subject Name: Computer Oriented Statistical Methods
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.
Q.1 (a) Explain the concept of significant digits. Also explain the difference between
accuracy and precision.
07
(b) Write an algorithm of Regula False position method. 07
Q.2 (a) Find a root of x
4
? x
3
+ 10x + 7 = 0, correct up to three decimal places between -
2 and -1 by the Newton-Raphson method.
07
(b) Find all roots of the equation x
3
? 2x
2
? 5x + 6 = 0 by Graeffe?s method, squaring
thrice.
07
OR
(b) Using bisection method, find an approximate root of the equation sinx = 1/x, that
lies between x = 1 and x = 1.5. Carry out computations up to the 7
th
stage.
07
Q.3 (a) The following data gives the melting point of an alloy of lead and zinc, where t
is the temperature in
0
C and p is the percentage of lead in the alloy.
p (%): 60 70 80 90
t: 226 250 276 304
Find the melting point of the alloy containing 84% of lead, using Newton?s
interpolation formula.
07
(b) Using Lagrange interpolation method find f (x) and hence find y at x =4 from the
given data below.
x: 1.5 3 6
y: -0.25 2 20
07
OR
Q.3 (a) If P is the pull required to lift a load W by means of pulley block, find a linear
law of the form P = mW + c connecting P and W using following data:
P: 12 15 21 2
W: 50 70 100 120
Where P and W are taken in kg-wt. Compute P when W = 150kg.
07
(b) Find cos (1.74), from the following data using proper numerical method:
x: 1.7 1.74 1.78 1.82 1.86
sin x: 0.9916 0.9857 0.9781 0.9691 0.9584
07
Q.4 (a) What is meaning of diagonally dominant system? Solve the following system of
equation using Gauss Jacobi method
20x + y ? 2z = 17, 3x + 20y ? z = -18, 2x ? 3y + 20z = 25
07
(b) Solve the equation dy/dx = xy + y
2
where y = 0 when x = 1 find y (0.1) using
Runge-Kutta method.
07
OR
Q.4 (a) Given dy/dx = 2e
x
? y with y (0) = 2, y (0.1) = 2.01, y (0.2) = 2.04, y (0.3) = 2.09.
Find y at x = 0.4 with step size of 0.1 by Predictor-Corrector method.
07
(b) Following table shows speed in km/min and time in minute of a moped
t: 2 4 6 8 10 12 14 16 18 20
07
FirstRanker.com - FirstRanker's Choice
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?V (Old) EXAMINATION ? WINTER 2019
Subject Code: 151601 Date: 27/11/2019
Subject Name: Computer Oriented Statistical Methods
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.
Q.1 (a) Explain the concept of significant digits. Also explain the difference between
accuracy and precision.
07
(b) Write an algorithm of Regula False position method. 07
Q.2 (a) Find a root of x
4
? x
3
+ 10x + 7 = 0, correct up to three decimal places between -
2 and -1 by the Newton-Raphson method.
07
(b) Find all roots of the equation x
3
? 2x
2
? 5x + 6 = 0 by Graeffe?s method, squaring
thrice.
07
OR
(b) Using bisection method, find an approximate root of the equation sinx = 1/x, that
lies between x = 1 and x = 1.5. Carry out computations up to the 7
th
stage.
07
Q.3 (a) The following data gives the melting point of an alloy of lead and zinc, where t
is the temperature in
0
C and p is the percentage of lead in the alloy.
p (%): 60 70 80 90
t: 226 250 276 304
Find the melting point of the alloy containing 84% of lead, using Newton?s
interpolation formula.
07
(b) Using Lagrange interpolation method find f (x) and hence find y at x =4 from the
given data below.
x: 1.5 3 6
y: -0.25 2 20
07
OR
Q.3 (a) If P is the pull required to lift a load W by means of pulley block, find a linear
law of the form P = mW + c connecting P and W using following data:
P: 12 15 21 2
W: 50 70 100 120
Where P and W are taken in kg-wt. Compute P when W = 150kg.
07
(b) Find cos (1.74), from the following data using proper numerical method:
x: 1.7 1.74 1.78 1.82 1.86
sin x: 0.9916 0.9857 0.9781 0.9691 0.9584
07
Q.4 (a) What is meaning of diagonally dominant system? Solve the following system of
equation using Gauss Jacobi method
20x + y ? 2z = 17, 3x + 20y ? z = -18, 2x ? 3y + 20z = 25
07
(b) Solve the equation dy/dx = xy + y
2
where y = 0 when x = 1 find y (0.1) using
Runge-Kutta method.
07
OR
Q.4 (a) Given dy/dx = 2e
x
? y with y (0) = 2, y (0.1) = 2.01, y (0.2) = 2.04, y (0.3) = 2.09.
Find y at x = 0.4 with step size of 0.1 by Predictor-Corrector method.
07
(b) Following table shows speed in km/min and time in minute of a moped
t: 2 4 6 8 10 12 14 16 18 20
07
2
v: 10 18 25 29 32 20 11 5 2 0
Using Simpson?s 1/3
rd
and Simpson?s 3/8
th
rule to find the distance travelled by
the moped in 20 minutes.
Q.5 (a) Compute Spearman?s rank correlation for the following observations. Marks are
awarded out of 35.
Candidate: 1 2 3 4 5 6 7 8
Judge X: 20 22 28 23 30 30 23 24
Judge Y: 28 24 24 25 26 27 32 30
07
(b) Calculate the first four moments about the mean.
Marks: 0-10 10-20 20-30 30-40 40-50 50-60 60-70
No. of
students:
8 12 20 30 15 10 5
07
OR
Q.5 (a) Obtain regression equation of Y on X and estimate Y when X = 55 from the
following:
X: 40 50 38 60 65 50 35
Y: 38 60 55 70 60 48 30
07
(b) Obtain Seasonal fluctuation from the following data using moving average
method:
Year I II III IV
1984 65 58 56 61
1985 68 63 63 67
1986 70 59 56 52
1987 60 55 51 58
07
*************
FirstRanker.com - FirstRanker's Choice
This post was last modified on 20 February 2020