Download PTU B.Tech 2020 March Aero 4th Sem ANE 204 Numerical Analysis Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech Aero (Aerospace-Engg) 2020 March 4th Sem ANE 204 Numerical Analysis Previous Question Paper

1 | M-60512 (S2)-1658
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(Aerospace Engg.) (2012 Onwards)/B.Tech.(ANE) (Sem.?4)
NUMERICAL ANALYSIS
Subject Code : ANE-204
M.Code : 60512
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
1. Answer briefly :
a) Evaluate the sum 3 5 7 S ? ? ? to four significant digits and find its absolute and
relative errors.
b) Write the Newton-Cote?s quadrature formula.
c) Using Euler?s method, find y (1), given that y ? = x + y and y (0) = 1.
d) Write the normal equations for fitting a straight line to the data using a method of
least squares.
e) Find a root of x
3
? x ? 1 = 0 using a bisection method correct to two decimal places.
f) Evaluate
12
5
dx
x
?
by Gauss quadrature formula.
g) Using Taylor?s series method find y (0.2) for y ? = 2y + 3e
x
, y (0) = 0.
h) What is the condition of convergence of fixed point iteration method?
i) Write a short note on finite difference method.
j) Classify the partial differential equation :
y
2
u
xx
? 2 xyu
xy
+ x
2
u
yy
+ 2u
x
? 3u = 0
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1 | M-60512 (S2)-1658
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(Aerospace Engg.) (2012 Onwards)/B.Tech.(ANE) (Sem.?4)
NUMERICAL ANALYSIS
Subject Code : ANE-204
M.Code : 60512
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
1. Answer briefly :
a) Evaluate the sum 3 5 7 S ? ? ? to four significant digits and find its absolute and
relative errors.
b) Write the Newton-Cote?s quadrature formula.
c) Using Euler?s method, find y (1), given that y ? = x + y and y (0) = 1.
d) Write the normal equations for fitting a straight line to the data using a method of
least squares.
e) Find a root of x
3
? x ? 1 = 0 using a bisection method correct to two decimal places.
f) Evaluate
12
5
dx
x
?
by Gauss quadrature formula.
g) Using Taylor?s series method find y (0.2) for y ? = 2y + 3e
x
, y (0) = 0.
h) What is the condition of convergence of fixed point iteration method?
i) Write a short note on finite difference method.
j) Classify the partial differential equation :
y
2
u
xx
? 2 xyu
xy
+ x
2
u
yy
+ 2u
x
? 3u = 0
2 | M-60512 (S2)-1658
SECTION-B
2. Find a root of xe
x
= cos x using Regula-falsi method correct to four decimal places.
3. Solve the following system of equation using the Gauss-Seidel iteration method :
6x + 3y + 1 = 9
2x ? 5y + 2z = ? 5
3x + 2y + 8z = ? 4
4. Estimate the values of f (22) and f (42) from the following available data :
x : 20 25 30 35 40 45
f (x) : 354 332 291 260 231 204
5. Use Runge-Kutta method to approximate y when x = 1.2. given that y = 1.2 when x = 1 and
2
3
dy
x y
dx
? ? .
6. Evaluate
/2
0
sin , x dx
?
?
using Simpson?s 1/3 rule.

SECTION-C
7. Use the power method to find the largest eigen value and the associated eigen vectors of
the matrix A =
1 3 1
3 2 4
1 4 10
? ? ?
? ?
? ?
? ? ?
? ?
starting with [0, 0, 1]
t
as initial eigen vector.
8. For IVP y ? = x ? y
2
, y (0) = 1, estimate y (0.8) using the Milne?s predictor-corrector method
with h = 0.2.
9. Solve the equation ?
2
u = ? 10 (x
2
+ y
2
+ 10) over the square with sides x = 0 = y, x = 3 = y
with u = 0 on the boundary and mesh length equal to one.

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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