Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Summer 4th Sem 2140706 Numerical And Statistical Methods For Computer Engineering Previous Question Paper

Enrolment No.___________

**GUJARAT TECHNOLOGICAL UNIVERSITY**

**BE - SEMESTER? IV EXAMINATION ? SUMMER 2020**

**Subject Code: 2140706**

**Date:29/10/2020**

**Subject Name: NUMERICAL AND STATISTICAL METHODS FOR**

COMPUTER ENGINEERING

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)**Find the relative error if the number

*X*0.004997 is

**03**

(i)

truncated to three decimal places.

(ii)

rounded off to three decimal places.

**(b)**Find the negative root of 3

*x*7

*x*3 0 by the bisection method

**04**

correct up to three decimal places.

**(c)**Using Gauss Jacobi method solve the following system of the

**07**

equations:

8

*x*

*y*2

*z*13

*x*10

*y*3

*z*17

3

*x*2

*y*12

*z*25

**Q.2 (a)**

2

*x*

**03**

Using trapezoidal rule to evaluate

*dx*

, dividing the

2

0

2

*x*

interval into four equal parts.

**(b)**By using Lagrange's interpolation formula, find

*y*(10).

**04**

x

5

6

9

11

y

12

13

14

16

**(c)**Using the Runge-Kutta method of fourth order, solve

**07**

*dy*

2

2

10

*x*

*y*,

*y*(0) 1at

*x*0.1,

*x*0.2 taking

*h*0.1

*dx*

**OR**

**(c)**Using Euler's method find the approximate value of y at

*x*1.5

**07**

*dy*

*y*

*x*

taking

*h*0.1. Given that

and

*y*(1) 2.

*dx*

*xy*

**Q.3 (a)**Using Newton Raphson method find the positive root of

**03**

4

*x*

*x*10 0 correct up to three decimal places.

**(b)**Fit a least square quadratic curve to the following data:

**04**

x

1

2

3

4

y

1.7

1.8

2.3

3.2

Estimate

*y*(2.4) .

**(c)**Find the regression coefficients

*b*and

*b*hence, find the

**07**

*yx*

*yx*

correlation coefficient between x and y for the following data

x

4

2

3

4

2

y

2

3

2

4

4

1

**OR**

**Q.3 (a)**

0.6

**03**

Using Simpson's 1/3 rule, find

2

*x*

*e dx*

, by taking n = 6.

0

**(b)**Using Newton's divided difference formula, compute

*f*(10.5)

**04**

from the following data:

x

10

11

13

17

f(x)

2.3026

2.3979

2.5649

2.8332

**(c)**Solve 4

3

2

*x*8

*x*39

*x*62

*x*50 by using Lin Bairstow method up

**07**

to third iteration starting with

*p*

*q*0.

0

0

**Q.4 (a)**Find a real root of the equation

*x*log

*x*1.2 by the regula falsi

**03**

10

method.

**(b)**The first four moments of distribution about

*x*2 are 1, 2.5, 5.5

**04**

and 16. Calculate the four moments about

*x*and about zero.

**(c)**

*dy*

**07**

Given that

2

2 2

2

*y*

*x y*,

*y*(0) 1,

*y*(0.1) 1.06,

*dx*

*y*(0.2) 1.12,

*y*(0.3) 1.21 evaluate

*y*(0.4) by Milne's predictor-

corrector method.

**OR**

**Q.4 (a)**Find the arithmetic mean form the following data:

**03**

Marks less

10

20

30

40

50

60

than

No. of

10

30

60

110

150

180

students

**(b)**(i) Obtain relation between and E.

**04**

(ii) Obtain relation between D and E.

**(c)**Obtain cubic spline for every subinterval from the following data

**07**

x

0

1

2

3

f(x)

1

2

33

244

**Q.5 (a)**Two unbiased coins are tossed. Find expected value of number of

**03**

heads.

**(b)**

1 sin

*x*

1

**04**

By Simpson's 3/8 rule, evaluate

*dx*

taking

*h*.

*x*

6

0

**(c)**From the following table, estimate the number of students who

**07**

obtained marks between 40 and 45.

Marks

30-40

40-50

50-60

60-70

70-80

No. of

31

42

51

35

31

students

**OR**

**Q.5 (a)**Using Budan's theorem find the number of roots of the equation

**03**

4

3

2

*f*( )

*x*

*x*4

*x*3

*x*10

*x*8 0 in the interval 1

,0.

**(b)**Find the positive solution of

*x*2sin

*x*0, correct up to three

**04**

decimal places starting from

*x*2 and

*x*1.9 . Using secant

0

1

method.

**(c)**Using Gauss Siedel method solve the following system of the

**07**

equations:

3

*x*0.1

*y*0.2

*z*7.85

0.1

*x*7

*y*0.3

*z*1

9.3

0.3

*x*0.2

*y*10

*z*71.4

*****************

2

This post was last modified on 04 March 2021