Download PTU B.Tech 2020 March EEE 5th Sem Numerical Analysis Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech EEE (Electrical And Electronics Engineering) 2020 March 5th Sem Numerical Analysis Previous Question Paper

1 | M-57027 (S2)-2714
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(EE/EEE) (Sem.?5)
NUMERICAL ANALYSIS
Subject Code : EE-311/AM-351
M.Code : 57027
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. Write briefly :
a) State intermediate value property.
b) State the condition where Newton?s method fails.
c) Using Euler?s method, find y (1), given that y ? = x + y and y (0) = 1 with h = 1.
d) Write the normal equations for fitting a straight line to the data using a method of
least squares.
e) Show that Newton?s method has quadratic rate of convergence.
f) Use Picard?s method to solve
dy
dx
= 2x + y
2
upto third approximation where y(0) = 0.
g) Write the iterative formula for method of false position.
h) What is the condition of convergence of fixed point iteration method ?
i) Write a short note on finite difference method.
j) Use Taylor?s series method to solve 2 3
dy
x y
dx
? ? at x = 0.1, given that y (0) = 1.

SECTION-B
2. Use iteration method to obtain the root of equation x
3
? 15x + 8 = 0 correct to four
decimal places.
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1 | M-57027 (S2)-2714
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(EE/EEE) (Sem.?5)
NUMERICAL ANALYSIS
Subject Code : EE-311/AM-351
M.Code : 57027
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. Write briefly :
a) State intermediate value property.
b) State the condition where Newton?s method fails.
c) Using Euler?s method, find y (1), given that y ? = x + y and y (0) = 1 with h = 1.
d) Write the normal equations for fitting a straight line to the data using a method of
least squares.
e) Show that Newton?s method has quadratic rate of convergence.
f) Use Picard?s method to solve
dy
dx
= 2x + y
2
upto third approximation where y(0) = 0.
g) Write the iterative formula for method of false position.
h) What is the condition of convergence of fixed point iteration method ?
i) Write a short note on finite difference method.
j) Use Taylor?s series method to solve 2 3
dy
x y
dx
? ? at x = 0.1, given that y (0) = 1.

SECTION-B
2. Use iteration method to obtain the root of equation x
3
? 15x + 8 = 0 correct to four
decimal places.

2 | M-57027 (S2)-2714
3. Solve the following system of equation using the Gauss-elimination method :
3x ? y + 2z = 12
x + 2y + 3z = 11
2x ? 2y ? z = 2.
4. Fit a curve of the form y = ab
x
to the given data :
y(2) = 144, y (3) = 172.8, y (4) = 207.4. y(5) = 248.8, y(6) = 298.5.
5. Using modified Euler?s method, find an approximate value of y (0.3), given that y(0) = 0
and
1
x
dy
y e
dx
? ? ?
with h = 0.1
6. Find the value of at 40
dy
x
dx
? from the following data :
x : 0 10 20 30 40
y : 1 0.984 0.939 0.866 0.766

SECTION-C
7. Use the method of triangularization to solve the system of equations
x + 3y + z = 3
x + 4y + 2z = 3
x + 2y ? 3z = 6
8. For the given initial value problem (IVP),
2
, (0) 1,
dy
x y y
dx
? ? ? estimate the value of y
(0.2) using Runge-Kutta method of fourth order with step size h = 0.1.
9. The velocities of a car running on a straight road from rest position at intervals of 2
minutes are given below :
Times (in minutes) : 2 4 6 8 10 12
Velocity (in km/hr) : 22 30 27 18 7 0
Find the total distance covered by the car in 12 minutes.
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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