Seat No.: Enrolment No.
GUJARAT TECHNOLOGICAL UNIVERSITY
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BE - SEMESTER-V (Old) EXAMINATION — WINTER 2019Subject Code: 151601 Date: 27/11/2019
Subject Name: Computer Oriented Statistical Methods
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
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- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
Q.1 (a) Explain the concept of significant digits. Also explain the difference between accuracy and precision.
(b) Write an algorithm of Regula False position method.
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Q.2 (a) Find a root of x3 — x2+ 10x + 7 = 0, correct up to three decimal places between -2 and -1 by the Newton-Raphson method.
(b) Find all roots of the equation x3 — 2x2 — 5x + 6 = 0 by Graeffe’s method, squaring thrice.
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 7th stage.
Q.3 (a) The following data gives the melting point of an alloy of lead and zinc, where t is the temperature in °C and p is the percentage of lead in the alloy.
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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.
(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
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y: -0.25 2 20OR
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 25
W: 50 70 100 120
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Where P and W, are taken in kg-wt. Compute P when W = 150kg.
(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
Q.4 (a) What is meaning of diagonally dominant system? Solve the following system of equation using Gauss Jacobi method
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20x +y—-2z=17, 3x+20y—-z=-18, 2x - 3y + 20z =25
(b) Solve the equation dy/dx = xy + y2 where y = 0 when x = 1 find y (0.1) using Runge-Kutta method.
OR
Q.4 (a) Given dy/dx =2ex—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.
(b) Following table shows speed in km/min and time in minute of a moped
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t: 2 4 6 8 10 12 14 16 18 20
v: 10 18 25 29 32 20 11 5 2 0
Using Simpson’s 1/3rd and Simpson’s 3/8th 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
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Judge X: 20 22 28 23 30 30 23 24Judge Y: 28 24 24 25 26 27 32 30
(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
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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
(b) Obtain Seasonal fluctuation from the following data using moving average method:
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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
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This download link is referred from the post: GTU BE/B.Tech 2019 Winter Question Papers || Gujarat Technological University
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