Deemed University 2011 B.Tech Automobile Engineering University: Lingayas University Term: V Title of the : Applied Numerical Methods - Question Paper
Roll No. ..
Lingayas University
B.Tech. 2nd Year (Term V)
Examination Feb 2011
Applied Numerical Methods (MA - 202)
[Time: 3 Hours] [Max. Marks: 100]
Before answering the question, candidate should ensure that they have been supplied the correct and complete question paper. No complaint in this regard, will be entertained after examination.
Note: Attempt five questions in all. All questions carry equal marks. Question no. 1 is compulsory. Select two questions from Section B and two questions from Section C.
Section A
Q-1. Select the correct answer of the following multiple choice questions. [10x2=20]
(i) The number of significant digits in the number 0.01850 x 103 are
(a) 3 (b) 4 (c) 5 (d) 6
(ii) If a number is correct to n decimal places, then the error is
(a) 
(b)
(c)
(d)
(iii) If for a real continuous function f (x), f (a) f (b) < 0, then in the range of [a,b] for f (x) = 0, there is (are)
(a) One root (b) Infinite number of roots
(c) No root (d) Atleast one root
(iv) For finding a root of sin x = 0 by secant method, the following choice of initial guess would not be appropriate
(a) 
(b)
(c) 
(d)
(v) The goal of forward elimination step in the Gauss elimination method is to reduce the coefficient matrix to
(a) Diagonal matrix (b) Identity matrix
(c) Lower triangular (d) Upper triangular
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x |
15 |
18 |
22 |
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y |
24 |
37 |
25 |
(vi) The Lagranges polynomial f(x) = L0(x) (24) + L1(x) (37) + L2(x) (25) passes through the three data points given by
What is the value of L1(x) at x = 16?
(a) 0.071430 (b) 0.50000
(c) 0.57143 (d) 4.3333
(vii) The number of strips required in Simpsons 3/8th rule is a multiple of
(a) 1 (b) 2 (c) 3 (d) 6
(viii) The second order Runge-Kutta method is
(a) Eulers method (b) Modified Eulers method
(c) Runges method (d) None of these
(ix) To use Adam-Bashforth method, atleast values of y, prior to the desired value are required
(a) 1 (b) 2 (c) 3 (d) 4
(x) The equation fxx + 2 fxy + fyy = 0 is
(a) Elliptic (b) Parabolic
(c) Hyperbolic (d) None of these
Section B
Q-2. (a) Find the iterative
formula for finding 
where
N is a real number, using Newton-Raphson formula. Hence, evaluate the cube root
of 24 upto four places of decimal.
(b) Find a root of the equation xex = cos x using the secant method correct upto three decimal places. [2x10=20]
Q-3. (a) Solve the following equations by Gauss-Jordan method.
x + 2y + z = 8 ; 2x + 3y + 4z = 20 ; 4x + 3y + 2z = 16
(b) Solve by Jacobis method
4x + y + 3z = 17
x + 5y + z = 14
2x y + 8z = 12 [2x10=20]
Q-4. (a) Define the term divided differences. Find f(x) as a polynomial in x from the given data using Newtons divided difference formula and also find f(8)
x : 3 7 9 10
f(x) : 168 120 72 63
[2+6+2]
(b) Fit a straight line to the following data by the method of least squares.
x : 5 10 15 20 25
y : 16 19 23 26 30
[10]
Section C
Q-5. (a) Find the value of cos 1.74, using the values given in the table below:
x : 1.70 1.74 1.78 1.82 1.86
sin x : 0.9916 0.9857 0.9781 0.9691 0.9584
(b) Find the approximate
value of loge5 by calculating to four decimal places, the integral 
by
Simpsons 1/3 rd rule dividing the range into 10 equal parts. [2x10=20]
Q-6. (a) Using modified Eulers
method, find an approximate value of y when x = 0.3 given that 
and
y = 1 when x = 0. (Take h = 0.1).
(b) Solve the initial
value problem 
for
x = 0.4, given that y (0) = 1 and
x : 0.1 0.2 0.3
y : 1.1169 1.2773 1.5040
Use Milnes predictor corrector method. [2x10=20]
Q-7. Solve the equation uxx + uyy = 0 for the square mesh at the pivotal points with the boundary values as shown.
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11.1 17 19.7
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8.7 12.1 12.8
| Earning: Approval pending. |
