Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech ECE (Electronics And Communications Engineering) 2020 March 4th Sem BTEL 401 Numerical Methods Previous Question Paper
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech (ECE) (Sem.?4)
NUMERICAL METHODS
Subject Code : BTEL-401
M.Code : 62021
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) If U = 2V
6
? 5V, find the percentage error in u at V = 1 if error in u at V = 1 if error in
V is 0.05.
b) Show that the following rearrangement of equation x
3
+ 6x
2
+ 10x ? 20 = 0 does not
yield a convergent sequence of successive approximations by iteration method near
x = 1 ..
c) Write Geometrical Interpretation of regula Falsi Method.
d) Construct a backward difference table for y = log x given that :
x : 10 20 30 40 50
y : 1 1.3010 1.4771 1.6021 1.6990
and find
3
? log40,
4
? log 50
e) Write Newton?s general interpolation formula.
f) Write normal equations for fitting the straight line using Method of least square
method.
g) Write formula of Simpson?s
1
3
I rule for numerical integration.
h) Define Pivoting and types of pivoting.
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1 | M-62021 (S2)-2803
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech (ECE) (Sem.?4)
NUMERICAL METHODS
Subject Code : BTEL-401
M.Code : 62021
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) If U = 2V
6
? 5V, find the percentage error in u at V = 1 if error in u at V = 1 if error in
V is 0.05.
b) Show that the following rearrangement of equation x
3
+ 6x
2
+ 10x ? 20 = 0 does not
yield a convergent sequence of successive approximations by iteration method near
x = 1 ..
c) Write Geometrical Interpretation of regula Falsi Method.
d) Construct a backward difference table for y = log x given that :
x : 10 20 30 40 50
y : 1 1.3010 1.4771 1.6021 1.6990
and find
3
? log40,
4
? log 50
e) Write Newton?s general interpolation formula.
f) Write normal equations for fitting the straight line using Method of least square
method.
g) Write formula of Simpson?s
1
3
I rule for numerical integration.
h) Define Pivoting and types of pivoting.
2 | M-62021 (S2)-2803
i) Define initial value problem and Boundary value problem.
j) Write formula of Runga Kutta method of third order.
SECTION-B
2. Find a real root of 2x-log
10
x = 7 correct to four decimal places using Newton Raphson
Method.
3. Use Lagrange?s Interpolation formula to fit a polynomial to the data :
x -1 0 2 3
u
x
-8 3 1 12
Hence or otherwise find the value of u
1
.
4. Fit the curve pv
v
= k to the following data :
p(kg/cm
2
) 0.5 1 1.5 2 2.5 3
v(liters) 1620 1000 750 620 520 460
5. The velocity ?v? of a particle at distance ?s? from a point on its linear path is given in the
following table :
s(m): 0 2.5 5 7.5 10 12.5 15 17.5 20
v(m/sec): 16 19 21 22 20 17 13 11 9
Estimate the time taken by the particle to traverse the distance of 20 meters.
6. Solve the system of equations
x + y + z = 6
3x + (3 + ?) y + 4z = 20
2x + y + 3z = 13
Using Gauss Elimination method where ? is small such that
2
1 1 ? ? ? . What happens if we
do not use partial pivoting at second step?
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1 | M-62021 (S2)-2803
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech (ECE) (Sem.?4)
NUMERICAL METHODS
Subject Code : BTEL-401
M.Code : 62021
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) If U = 2V
6
? 5V, find the percentage error in u at V = 1 if error in u at V = 1 if error in
V is 0.05.
b) Show that the following rearrangement of equation x
3
+ 6x
2
+ 10x ? 20 = 0 does not
yield a convergent sequence of successive approximations by iteration method near
x = 1 ..
c) Write Geometrical Interpretation of regula Falsi Method.
d) Construct a backward difference table for y = log x given that :
x : 10 20 30 40 50
y : 1 1.3010 1.4771 1.6021 1.6990
and find
3
? log40,
4
? log 50
e) Write Newton?s general interpolation formula.
f) Write normal equations for fitting the straight line using Method of least square
method.
g) Write formula of Simpson?s
1
3
I rule for numerical integration.
h) Define Pivoting and types of pivoting.
2 | M-62021 (S2)-2803
i) Define initial value problem and Boundary value problem.
j) Write formula of Runga Kutta method of third order.
SECTION-B
2. Find a real root of 2x-log
10
x = 7 correct to four decimal places using Newton Raphson
Method.
3. Use Lagrange?s Interpolation formula to fit a polynomial to the data :
x -1 0 2 3
u
x
-8 3 1 12
Hence or otherwise find the value of u
1
.
4. Fit the curve pv
v
= k to the following data :
p(kg/cm
2
) 0.5 1 1.5 2 2.5 3
v(liters) 1620 1000 750 620 520 460
5. The velocity ?v? of a particle at distance ?s? from a point on its linear path is given in the
following table :
s(m): 0 2.5 5 7.5 10 12.5 15 17.5 20
v(m/sec): 16 19 21 22 20 17 13 11 9
Estimate the time taken by the particle to traverse the distance of 20 meters.
6. Solve the system of equations
x + y + z = 6
3x + (3 + ?) y + 4z = 20
2x + y + 3z = 13
Using Gauss Elimination method where ? is small such that
2
1 1 ? ? ? . What happens if we
do not use partial pivoting at second step?
3 | M-62021 (S2)-2803
SECTION-C
7. Find the largest Eigen value and the associated Eigen vector of the matrix A
2 3 2
4 3 5
3 2 9
? ?
? ?
? ?
? ?
? ?
by Power?s method.
8. Using Milne?s method, solve
2
1
dy
y
dx
? ? with y(0) = 0, y(0.2) = 0.2027,
y(0.4) = 0.4228, y(0.6) = 0.6841, obtain y(0.8), y(1) and y(-0.2).
9. Obtain cubic spline for the following given data :
x : 0 1 2 3
f(x) : 2 -6 -8 2
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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This post was last modified on 21 March 2020