Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech CHE (Chemical Engineering) 2020 March 5th Sem BTCH 501 Numerical Method Previous Question Paper
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech (Chemical Engg) (Sem.?5)
NUMERICAL METHOD
Subject Code : BTCH-501
M.Code : 70521
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) Differentiate between ?Interpolation? and ?Extrapolation?.
b) Define various types of errors in numerical computations.
c) Write the Simpson?s 3/8 rule.
d) Define significant digits. How many significant digits are there in 1.001?
e) Write any disadvantage of Newton-Raphson method.
f) Define algebraic equations and transcendental equations with example.
g) Define forward operator ? and shift operator E. Hence prove that E = 1 + ?.
h) Define eigen values and eigen vectors of a matrix.
i) Write the Langrage?s interpolation formula.
j) Write iterative methods to solve linear algebraic equations.
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1 | M-70521 (S2)-2717
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech (Chemical Engg) (Sem.?5)
NUMERICAL METHOD
Subject Code : BTCH-501
M.Code : 70521
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) Differentiate between ?Interpolation? and ?Extrapolation?.
b) Define various types of errors in numerical computations.
c) Write the Simpson?s 3/8 rule.
d) Define significant digits. How many significant digits are there in 1.001?
e) Write any disadvantage of Newton-Raphson method.
f) Define algebraic equations and transcendental equations with example.
g) Define forward operator ? and shift operator E. Hence prove that E = 1 + ?.
h) Define eigen values and eigen vectors of a matrix.
i) Write the Langrage?s interpolation formula.
j) Write iterative methods to solve linear algebraic equations.
2 | M-70521 (S2)-2717
SECTION-B
2. Evaluate
6
2
0
1
dx
x ?
?
using Trapezoidal rule and Simpson?s 1/3 rule taking h = 1.
3. Solve the following system of equations by using the relaxation method :
12x + y + z = 31
2x + 8y ? z = 24
3x + 4y + 10z = 58.
4. Fit a straight line to the given data : y (?4) = 4, y (1) = 6, y (2) = 10, and y (3) = 8 by the
method of least squares.
5. Find the cubic curve that passes through the points (?1, ?8), (0, 3), (2, 1) and (3, 2) using
Newton divided difference formula.
6. From the following table find the values of y ? and y ? ? at x = 0 :
x : 0 1 2 3 4 5
y : 4 8 15 7 6 2
SECTION-C
7. Determine the largest eigen value and the corresponding eigen vector of the matrix
1 3 2
A 4 4 1
6 3 5
? ? ?
? ?
? ?
? ?
? ?
? ?
By power method.
8. a) Use the method of triangularization to solve the system of equations
2x + y + 4z = 12
8x ? 3y + 2z = 20
4x + 11y ? z = 33
b) Find a real root of the equation f (x) = cos x ? 2x + 3 = 0 by fixed point iteration
method correct upto three decimal places.
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1 | M-70521 (S2)-2717
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech (Chemical Engg) (Sem.?5)
NUMERICAL METHOD
Subject Code : BTCH-501
M.Code : 70521
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) Differentiate between ?Interpolation? and ?Extrapolation?.
b) Define various types of errors in numerical computations.
c) Write the Simpson?s 3/8 rule.
d) Define significant digits. How many significant digits are there in 1.001?
e) Write any disadvantage of Newton-Raphson method.
f) Define algebraic equations and transcendental equations with example.
g) Define forward operator ? and shift operator E. Hence prove that E = 1 + ?.
h) Define eigen values and eigen vectors of a matrix.
i) Write the Langrage?s interpolation formula.
j) Write iterative methods to solve linear algebraic equations.
2 | M-70521 (S2)-2717
SECTION-B
2. Evaluate
6
2
0
1
dx
x ?
?
using Trapezoidal rule and Simpson?s 1/3 rule taking h = 1.
3. Solve the following system of equations by using the relaxation method :
12x + y + z = 31
2x + 8y ? z = 24
3x + 4y + 10z = 58.
4. Fit a straight line to the given data : y (?4) = 4, y (1) = 6, y (2) = 10, and y (3) = 8 by the
method of least squares.
5. Find the cubic curve that passes through the points (?1, ?8), (0, 3), (2, 1) and (3, 2) using
Newton divided difference formula.
6. From the following table find the values of y ? and y ? ? at x = 0 :
x : 0 1 2 3 4 5
y : 4 8 15 7 6 2
SECTION-C
7. Determine the largest eigen value and the corresponding eigen vector of the matrix
1 3 2
A 4 4 1
6 3 5
? ? ?
? ?
? ?
? ?
? ?
? ?
By power method.
8. a) Use the method of triangularization to solve the system of equations
2x + y + 4z = 12
8x ? 3y + 2z = 20
4x + 11y ? z = 33
b) Find a real root of the equation f (x) = cos x ? 2x + 3 = 0 by fixed point iteration
method correct upto three decimal places.
3 | M-70521 (S2)-2717
9. a) Using Runge-Kutta fourth order method to find y (0.4) given that
2 2
2 2
, (0) 1
y x
y y
y x
?
? ? ?
?
With h = 0.2
b) Solve the following system
x
2
? 2xy + 9.62 = 0,
xy ? 2y
2
+ 14.97 = 9,
by Newton-Raphson method with the initial values x
0
= 2 and y
0
= 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