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

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Subject Code: 2140706

GUJARAT TECHNOLOGICAL UNIVERSITY

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BE - SEMESTER- IV (New) EXAMINATION - WINTER 2019
Date: 12/12/2019
Subject Name: Numerical and Statistical Methods for Computer Engineering
Time: 10:30 AM TO 01:00 PM
Total Marks: 70

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Instructions:

1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

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Q.1

(a) If X = 3.1416, find the absolute and relative errors if :

1. X is truncated to three decimal places.
2. X is rounded off to three decimal places.

(b) Construct an Interpolating polynomial which takes the following values :

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x	0	1	2	3	4	5
y	-10	-8	-8	-4	10	40

MARKS

03

04

(c) By using Method of least squares , fit a second degree parabola y=a +bx+cx’ to the following data:

x	0	1	2	3	4
Y	1	1.8	1.3	2.5	23

07

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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

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(c) Obtain Cubic spline for any of given subinterval from the following data:

x	1	2	3	4
S(x)	1	2	5	11

07

OR

(c) Using Lagrange’s interpolating polynomial, find Interpolating polynomial from the given data:

X	2	3	5	7
S(x)	0.1506	0.3001	0.4517	0.6259

Q.3

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(a) Use Secant method to find the real root of equation x³-5x-7=0.

03

(b) Find a real root of x³—x—1=0, correct to three decimal places using Newton-Raphson method.

04

(c) Use Gauss-Seidel method to obtain the solution of the system

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83x+11y—4z =95, 7x+52y+132z =104, 3x+8y+29z=71

07

OR

(c) Apply Budan’s theorem to the equation x⁴—7x²+6x—1=0 to draw the inference about the roots in the interval (-2,—1).

Q.3

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(a) Solve the given System of Linear equations by using Gauss Elimination method:
x+y+z=7, 3x+3y+4z=24, 2x+y+3z=16

03

(b) Given that dy/dx =y²+x²y² , y(0)=1, y(0.1)=1.06, y(0.2) =1.12, y(0.3) =1.21
Estimate y(0.4) using Milne’s predictor-corrector method.

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04

Q.4

(a) Considering following tabular values, Determine the area bounded by the given curve and X-axis between x =10 to x =16 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 ∫₀¹ 1/(1+x) dx by taking 4 sub intervals.

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04

(c) Use Fourth order Runge-Kutta method to find y(0.2) with h=0.1, given that dy/dx =2x+y, y(0) =1

07

OR

Q.4

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(a) Use Euler’s Method to find y(0.10) in five steps from the differential equation dy/dx =x+y+xy ,y(0)=1

03

(b) Use Modified Euler’s method to solve dy/dx =x+3y , y(0)=1. Hence find y(0.5) with h=0.1.

04

(c) (i) Write an algorithm for Newton’s Forward Interpolation Formula

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(ii) Using Newton’s divided difference formula, calculate the value of f(6)

x	2	7	8
S(x)	1	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

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(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)

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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

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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.

1st Judge	1	6	5	10	3	2	4	9	7	8
2nd Judge	3	5	8	4	7	10	2	1	6	9
3rd 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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