Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 3rd Semester (Third Semester) 2016-2017 NCS 303 Computer Based Numerical And Statistical Techniques Question Paper
(F ollowing Paper ID and Roll No. to be ?lled in your
Answer Books)
Paper ll) : 2289953 Roll No.
4B.TECH '
Regular Theory Examination (Odd Sem-III) 2016-17
COMPUTER BASED NUMERICAL AND
STATISTICAL TECHNIQUES
Time : 3 Hours ' 'Max. Marks .' 100
Note: Attempt all Sections. If require any missing data;
then choose suitably.
Section - A ~
1. Attempt all questions in bi'iefi ._ (10X2=20)
a) Discuss the signi?cant digits with suitable example.
b) The error in the measurement of the area of a circle
is not allowed to exceed 0. 1%. How accurately
shoilld the diameter be measured?
0) De?ne testing of Statistical hypothesis. ?
303/12/2016/15680 ? (1) [P.T.O.
. VNCS - 303
Express 1+x?x2 +x3' as sum Of Chebyshev
d)
polynomial.
e) What is the condition of natural spline.
f) Write the normal equation for a y = a + bx + cx2
g) Write a short note on ?oating point arithmetic.
, I 1 . AE" A
h) Prove that [15 = ?(A+V) = ????+?
2 2 2
i) Determine the condition number of the matrix
2 -1 1 .
1 0 1 using the maximum absolute row sum
3 ?1 4
norm:
j) Differentiate between ill conditioned and well
conditioned methdds.
Section - B
2. Attempt three questions from this section
(3 x 1 0=30)
a) Use synthetic division and perform two interations
for?the Birge-Vieta method to ?nd the smallest
positive root of the equation '
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b)
d)
NCS - 303
-x4_3x3+3x2_3x+2=0. Use the initial
approximation R, = 0.5.
Write down the computer algorithms of least square
curve ?tting.
_ Derive the formula for error analysis of trapezmdal
1:.
rule. If {6 dx, then estimate I using the
Trapezoidal rule with the 10 subinte'rvals. F ind an
error bound also. '
Use (Iauss-Eliminatien method to solve the
followmg system of equations:
2x+y+z=10
3x+2y+3z=18
x+4y+9z=16
Use secant method to determine the root of the
equation cosx? xe"= 0. Choose suitable initial
approximation.
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NCS. ? '303
Section - C
Attempt any one part of the following: (1 x 10'=.10)
a) Find the condition for convergence of ?xed point
interation method. Find by ?xed point iteration
method, the real root Of the equation
sinx=10(x?1).'
b) De?ne Aitken?s A2 method. Find areal root of the '
equation 2x? log,0 x = 7, correct to?three decimal
places using Aitken?s . A2 method and iteration
' method. Also show how the rate ofconvergence of
Aitken?s A2 method is rapid than iteration method.
Attempt any one part of the following: (1 X'10=10)
a) Write the algorithm for Lagrange?s interpolation
' formula. Determine the step size that can be used
in the tabulation of f (x) = sinx in the interval ,
[0, 7r/ 4] at equally spaced nodal points so that the
truncation error of the quadratic interpolation is less
than 5 ><10?8
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NCS - 303
b) Obtain an approximation in the sense of the
principle of least squares in the form of a polynomial
of the degree 2 to the function 1/ (1 +x2) in the 1
range ?1 s x :1 - ?
Attempt any one, part of the following: (1 ><10=10)
a) Calculate y?( 0.398) as accurately as possible using
the table below and with the aid of the approximation
S(h). Give the error estimate (the values In the table
are correctly rounded. )
X: 0.398 0.399 0.400 0.401 0.402
f(x): 0.408591 0.409671 0.410752 0.411834 0.412915
b) Find a quadrature formula
=(0a1f )+a2f[1]+a3f(l) which is
exact for polynomials of highest possible degree.
?f(x)dx)
{?? x(1? x)
1
dx
Then se th f l ' ?
u e ormu a on i \/-x???x3 and compare
with the exact value.
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(5) '
NCS _ 303 , NCS - 303
6. Attempt any one hart of the following: (1 x 10:10) 11) Find a uniform polynomial approxnmatlon of
V degree four or less to e" on [?1, 1] using
a) Apply Runge-Kutta method to ?nd an approximate Lanczos economization with a tolerance of
y2 _ x2 a = 0.02
y2 +X2
. d
value ofy for x = 0.2 and x = 0.4 if 7: =
with y(0) = l
b) SOlVe by? supcessive over relaxation method, the
equations.
10x?2y?22=6
.?x+10y?22=7
?x?y+lOz=8
7. Attempt any one part of the following: (1X10=10)
a) Evaluate
12!??? 22): + 2x +1 , using the Lobatto 3 point and
Radau 3-point formula. Compare with the exact
solution.
b) i) A random sample of 900 memb?rs has a mean
3.4 cms. Can it be reasonably regarded as a
sample from a large population of mean 3.2
cins and SD. 2.3 cms.
/1 7
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This post was last modified on 29 January 2020