Download AKTU B-Tech 3rd Sem 2015-2016 NCS 303 Computer Based Numerical And Statistical Techniques Question Paper

Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 3rd Semester (Third Semester) 2015-2016 NCS 303 Computer Based Numerical And Statistical Techniques Question Paper

Printed Pages : 5 616 NCS-303
(Following Paper [D and Roll No. to be filled in your
Answer Book) '
Roll No.
B.Tech.
(SEM. III) THEORY EXAMINATION, 2015-16
COMPUTER BASED NUMERICAL AND
STATISTICAL TECHNIQUES
[Time:3 hours] [Tomi Marks:100]
Section-A
1. Attempt all parts.A11 parts carry equal marks. Write
answer of each part in short. (10x2=20)
(a) Describe brie?y the ?oating point representation
ofnumbers.
(b) Suppose 1.414 is used as an approximation to ~12.
Find the absolute and relative errors.
(c) Express 2 To(x)-% 'l?2(x)- 1/ 8 T4 (x) as polynomials
in x.
(d) Differentiate between ill conditioned and well
conditioned methods.
(e) Explain under?ow and over?ow conditions of
error in ?oating point?s addition and subtraction.
17025 (1) P.T.O.

(f)
(g)
(h)
(i)
0)
Write diffemcebetween the truncation error and
round off error.
Differentiate false position method and secant
method.
How can the rate of convergme-e of two methods
be compared, explain by taking an example?
Find the number ofterms of the exponential series
such that their sum gives the value of e?K correct to
six decimal places at x=1.
The numbers 0.01850x105 and 386755
have ........... and ...................... signi?cant digits
respectively.
? Section-B
Attempt any ?ve questions from this section. (5 X 10:50)
2. The following table gives the marks obtained by 100
students in Statistics:
?I 7025
Marks Number of Students
30 40 25
40-50 35
50-60 22
60-70 1 1
70-80 7
(2) NCS-303
Use Newton?s forward?fmh to ?nd the number of
students who got more than 55 marks.
3. Solve the fo?owing system of equation by Gauss
elimination method:
Jr1+2x2+3Jc3+4x4 :10
7x, +Mbr2+5x3 +21:4 :40
13171 +6):2 + 2x3 ?3x4 = 34
llu+l4x3+8x3?x4=64
4. The speed v meters per second of a car. tseconds after
its starts, is shown in fellowing table:
l V
0 0
12 3.6
24 10.08
.36 18.9
48 21.6
60 1854
72 10.26
34 5.40
96 4.50
108 5.40
120 9.00
Using Simpson?s l/3rd rule ?nd the distance traveled by
the car in 2 minutes.
17025 (3) p.10.

1 7025 (4)
Find the {mm of function F (x) of the following table
using Lagrange?s method.
x 0 V 1 ,.4 ,. S
F(x) 8 11 68 123
Find a real root of the equation 2x-log 10x=7 c, correct
to three decimal places using Aitken;s method and
Iteration method, Also show how the rate of convergence
of Aitken?s method is rapid than iteration method.
A real root of the equation f(x) =x3-5x+1=0, lies in the
interval (0.1). Perform four iterations of the secant
method.
Evaluate the intergral I=dx/(x2+ 1) in the interval [0,1]
using the Lobatto and Radau 3 point formula.
F ind the value of integral, using Gauss-Legendre three
point integration rule.
I- jcostdx
1+sinx
NCS-303
Attempt any two questions from this section.
10.
11.
12.
17025 (5)
Section?C
(15X2=30)
Using Gram-Schmidt orthogonalization process.
compute the ?rst three orthogonal polynomials PU(X),
P1(X ). P2(X) which are orthogonal on interval [0,1] w.r.t.
weight function W (x)=1. Using these polynomials
obtain least square approximation of first degree for
f(x)=x'/? 0n interval [0. 1 J.
Fit a natural cubic Spline to every subinterval for the
following data. ?
Hence compute: y (2.5)
(a) Apply Milne?s predictor?corrector method, ?nd y
(0.8) if y (x) is the solution of dy/dx= 1 +y2. Given
y(0)=0, y (0.2) =0.2027, y(0.4) =0.4228 and y
(0.6) = 0.6841.
(b) Apply Runge kutta fourth order method to ?nd y
(0. 1) for the initial value problem, dy/dx=y-x Given
y(0)=2-
NCS-303