Download OU B.Sc 2016 April 3rd Year 2020E Mathematics Question Paper

Download OU (Osmania University) B.Sc (Bachelor of Science) 2016 April 3rd Year 2020E Mathematics Previous Question Paper

Code No. 2020 I E
FACULTIES OF ARTS AND SCIENCE '
B.A.'I B.Sc. IIE?Year Examination, MarchIApril 2016.
Subject :' MATHEMATICS
Paper ? IV (a)
Numerical Analysis
Time : 3 hours Max. Marks : 100
Note: Answer Six questions from Part-A 8. Four questions from Part-B.
Choosing atleast one from each Unit. Each question in Part-A carries
6 marks and' In Part-B carries 16 marks.
Part? A (6 X 6.= 36 Marks)
Unit -|
1 If u = 5xy2 I 23 then find maximum relative error in u given that Ax 2 Ay = A2 = 0.001,
x = y = z = 1.
2 Explain bisectioh method of finding a real root of f(x) =
7_ Unit- ll
' 3 Derive Lagrange?sformula.
4 Define the" operators A,V, E and 6 show that
i) A=VE=6EW ii) y=1ll+i52
Unit- III ?" '
5 Explain the method of fitting a straight line to the giveh data using the principiel of
least squares. / 2x?)
2
6 Evaluate I _5~t?2?t dt using Trapezoidal rule with 8 stripV
_2 + ,9
Unit- EV
/7 Apply Euler' 5 method to compute y(O. 4) y(O. 6) given thatd? d: ? x + y, y(0) = O with
6/1 h=0.2.
//\,\2?
i ? \ 8 Solve the following system of equation using Jacobi? s iterative method
10x+2y+z= 9, 2x+20y?- 22=?44-2x+3y+102= 22
Part? B (4 X 16 = 64 Marks)
Unit - l
9 3) Find the reai root of x3 - x 2 - 1 = 0 upto three decimal places using bisection
method.
b) Find a double root of x3 ? 3x2 - 4 = o by generaiized Newton?s method.

Code No. 2020 I E
_ 2 -
10 a)' Using Newton Raphson method find a root of x4 - x - 10 = 0.
b) Calculate the vatue of x/102 ? #101 correct to four decimal places.
Unit - ll
11 a) Find the cubic polynomial which takes the following values.
y(0) = 1, y(1) = O, y(2) = 1, y(3) = 10, hence obtain y(4).
b) Prove that Nux :ux+n ? "C,ux+n_l +? Czumh2 +....+(?1)?ux.
12 a) Derive Newton?s forward difference interpolation formula.
b) Using Newton?s forward difference formula, find the sum Sn=13+23+33+...n3.
Unit - III
13 a) Derive Simpsons 1/3 rule and find error in it.
7
b) Find the value of sz logx dx by taking 8 strips using Boote?s rule.
3,
l t /2
14 a') Using Trapezoidal rule find the value of J: 1I(cose) d6 by dividing interval
into 6 parts.
b) Fit a straight line to the following data :
x 1 2 3 4 5 6?
y 1200 900 600 200 '11?0" 50" ' ,
Unit ? Iv
15 a) Sotve the fotiowing systems of equations using Gauss elimination method
2x+y+z= 10, 3x+2y+32= 18,x+4y+92= 16.
b) Find the?value of y for x = 0.1 by Picard?s method given that 91 = y?x
dx y + x ?
y(0)=1. ?
16 a) Use Runge?Kutta?s method of fourth order to compute y(0.1), y(0.2) given
Ell=x+y, y(0)=1.
dx
b) Use Tayior?s series method to find y(0.1) correct to four decimal places if y(x)
satisfies y' = x ? yz, y(0) = 1.
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