West Bengal Institute of Technology (WBIT) 2009-4th Sem B.C.A Computer Application - BM401 Statistics, Numerical Methods & Algorithms ( ) - Question Paper
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CS/BCA/SEM-4/BM-401/2010
STATISTICS, NUMERICAL & METHODS $ ALGORITHMS
Time Allotted : 3 Hours . Full Marks : 70
The figures In the margin Indicatefull marks.
Candidates are required to give their answers In their own words
as far as practicable.
GROUP-A ( Muftipte ChoiceType Questions)
iii) First order forward difference of a constant function is a) 0 ;V b) 4
iv) Inverse of a matrix A is given by
" a, A'.!*L b) A-'.m
detA adjA
c) A-1-(detA)T d) A-l-(adJA)T.
.. i-' ? ' ' '. : . " '
v) bE2 is equal to .
a) V b) A
c) E d) none of these.
Vi) The inherent error in the Runge-Kutta method is of .-s' : order ' ' .
.....a) h* b) h4
c) h8 d) h6.
vii) The value <rf is
a) 6x b) 6x2
v C) 6x3 d) 6x.
viii) If E is the shift operator and A is the forward difference
operator, then relationship between them is
' - \ '
a) E = A + 1 b) A-1
d) E+1*A d) none of these.
ix) Let/ ( x ) 0 be the equation of. a curve. Then the condition that one of the roots of / ( x ) lies between x = a and x * b is
a) /(a ) > 0 b) / (a ) / (b ) < 0
c) /(a J /(b ) > 0 d) none of these.
x) Simpsons rd rule gives us exact result for a polynomial of degree
a) less than 3
b) less than equal to 3
c) greater than 3
d) greater than equal to 3.
xi) If u0 -1, ! aAd u2-21, thpn A2u0 is
a) 10 b) 11
c) 0 d) 20.
dx
xii) By evaluating f -j- by numerical integration method,
' o l*x ,
we can obtain the approximate value of
a) loge 2 b) ~
. ' ' ' '
_ .. .
c) e d) logl0 2.
xiii) For a system of equation Ax = b, a solution exists if and only if A is
. : ' - i
a) symmetric b) singular
c) orthogonal d) diagonal.
' " - i . '
jtfv) Equation AX = B has unique solution If
a) Rank (A) * Rank (A B)
b) Rank (A) < Rank ( A B)
c) Rank (A )*Rank(AB)* No. of unknowns
d) Rank {A ) = Rank {A B \ * No. of unknowns.
GROW-B (Short Answer Type Question#)
Answer any three of the following. 3x5= 15
2 Prove that D-ilog, where D is differential operator
h (1-V)
and V is backward difference operator.
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3 Find the value of for x = 1 0 from the following table : dx ___ | ||||||||||||||
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4. Find a root of the equation x3-3x-5-0 by the method of false position correct to 2 decimal places.
' / .
5. Using Taylors method obtain an approximate value of y at x = 0-2 for the differential equation ~-2y + 3ex, y ( 0 ) = 0.
CS/BGA/SEM-4/BM-401/2010
Solve the system of equations by Gauss elimination method :
2x + 3y + 2*9 x + 2y + 32 6
3x,+ y+ 2z*=8 correct upto three significant figures.
GROUP-C
3 x 15 * 45
Answer any three of the following.
a) Evaluate y ( M ) using Runge-Kutta method of order 4 3fer the proteka
dx
1 2 6 2 5 15 0 15 46
b) Find the inverse of the matrix by Gauss elimination method.
8.
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a) Compute / ( 0-29 ) from the following table by using Newtons backward interpolation formula | ||||||||||||||
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CS/BGA/SBM-4/BM-401 /2010
- ; s ' .
b) The following are the mean temperature ( Fahrenheit ) cm the three days, 30 days apart round the periods of summer and winter. Estimate the approximate dates and the values of the maximum dates and the values of the maximum and minimum temperature.
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Day |
Summer |
Winter | ||
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Date |
Temperature |
' Date |
Temperature | |
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0 |
15th June |
58-8 |
16th December |
40-7 |
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' 30 |
15 th July |
63-4 |
15th January |
381 |
|
60 |
14th August |
62-5 |
14th Februaiy |
39-3 |
9. a) Using Newtons divided difference formula, construct
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the interpolation polynomial and hence compute dy d 2u dx 311 dx* at * = 5 by using the following data : | ||||||||||||||
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b) Evaluate J x3 dx by Trapezoidal rule with n = 5.
. o . ' - ' \ '
10. a) Evaluate one root of the following equation, by
Newton - Raphson method : .
ex-3x0
correct up to 3 decimal places. .
b) Use Eulers method to find the numerical solution of the following differential equation :
f'(x)-l+x-x2, y ( 0 ) - 1, h = 0*02; find y (01 ).
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11. a) Find the missing term in the following table : | ||||||||||||||
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b) What is the lowest degree polynomial which takes the |
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following values : | ||||||||||||||
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Hence calculate/(x) and also find/( 6 ). |
Choose the correct alternatives for any ten of the following: 10x1 = 10
i) tff(x) is a polynomial of degree n, then,....................is
a constant.
a) ( n + 1 )th order difference
. . i - ' .
b) nth order difference
c) ( n - 1 )th order difference
d) ( n - 2 )th order difference.
ii) One of the roots of the equation x2 + 2x - 20 lies in between /
a) 1 & 2 b) 0& 0-5
c) 0*5 & 1-0 d) none of these.
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Attachment: |
| Earning: Approval pending. |
