Download GTU B.Tech 2020 Summer 4th Sem 2140706 Numerical And Statistical Methods For Computer Engineering Question Paper

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

Seat No.: ________
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
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 7x 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:
8x y 2z 13
x 10y 3z 17
3x 2y 12z 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 8x 39x 62x 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 xlog 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 4x 3x 10x 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:
3x 0.1y 0.2z 7.85
0.1x 7 y 0.3z 1
9.3
0.3x 0.2y 10z 71.4
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2

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