Punjab Technical University 2010-6th Sem B.Sc BioInformatics (BI) (th) NUMERICAL ANALYSIS - Question Paper
Roll No.
[Total No. of Pages : 02
Total No. of Questions : 13]
[2037] B.Sc. (BI) (Semester - 6th)
J-3189[S-1045]
NUMERICAL ANALYSIS (B.Sc. (BI) - 602)
Maximum Marks : 75
Time : 03 Hours
Instruction to Candidates:
1) Section - A is compulsory.
2) Attempt any Nine questions from Section - B.
Section - A
(15 x 2 = 30)
Q1)
a) Define inherent and rounding errors with example.
b) An approximate value of n is given by 3.1428571 and its true value is 3.1415926. Find absolute and relative errors.
c) Define Newtion Raphson Method.
d) Define Hermitian and skew Hermitian matrix with example.
2 7 9 0 0 5 - 2 -1
e) Find the rank of the matrix
f) State Crammers Rule.
g) State Triangular factorization method.
h) Solve the equations by matrix inversion method 2x1 + x2 = 1, 2x1 + 3x2 = 2.
i) Define Jacobi lteration method.
j) Define interpolation with example.
k) Prove A = E-1 and V = 1-E-1
l) Prove A = E V = V E = 5E/2
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m) State Simpsons One-Third Rule. |
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o) State Newtions forward difference interpolation formula. |
Q2) Solve X - 5X3 + 20X2 - 40x + 60 = 0. by Newtion Raphson Method. Given that all the roots of given equation are complex.
Q3) Using Mullers method find the roots of equation y(x) = x3 - 2x- 5 = 0, which lies between 2 and 3.
Q4) Solve by Crammers Rule. x + 2y+ 3z= 6, 2x + 4y+ z= 7, 3x + 3y+ 9z= 15.
2 -1 1
Q5) Find the characteristic equation of the matrixA=| it is satisfied by A.
and verify that
-1 2 -1 1 -1 2
. Express A6 - 4A5 + 8A4 - 12A3 + 14A2 as 9 Linear
1 2 -1 3 polynomial in A.
Q6) If A =
Q7) Solve the system of equations by Gauss Elimination method,
2x1 + 4x2 + x3 = 3, 3x1 + 2x2 - 2x3 = 2, x1 - x2 + x3 = 6.
Q8) Solve the following system of equations by matrix inversion method.
x+y+ z= 3, x + 2y+ 3z= 4, x + 4y+ 9z= 6.
Q9) Solve the system of equations by factorization method,
x1 + 2x2 + 3x3 = 14, 2x1 + 5x2 + 2x3 = 18, 3x1 + x2 + 5x3 = 20.
Q10) Sum the series 1 3 + 23 + 33 + ......................+ n3 using the calculus of
finite differences.
Q11) The population of town was as given below. Using Newtion backward difference formula. Estimate the population for the year 1925 Year x : 1891 1901 1911 1921 1931
Population y: 46 66 81 93 101 (in thousands)
Q12) Evaluate f dx using Simpsons 1/3 rule taking h =
01+ x2 4
Q13) If r = 3h(h6 - 2). Find percentage error in r at h = 1, if percentage error in h is 5.
J-3189[S-1045] -2-
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Attachment: |
| Earning: Approval pending. |
