STUPIDSID
Solve any one question from Q1 and Q2
1 (a)
What do you mean by convergence? Explain importance in brief.
2 M
1 (b)
Solve the following set of linear simultaneous equation using Gauss
elimination method.
x+3y+z=10
x+2y+5z=12
4x+y+2z=16
x+3y+z=10
x+2y+5z=12
4x+y+2z=16
8 M
2 (a)
Find the root of log10 x-x2+2=0 upto accuracy 0.01. Use false position method.
6 M
2 (b)
Write short note on Genetic Algorithm.
4 M
Solve any one question from Q3 and Q4
3 (a)
Write a flow chart for Bisection method for root finding.
4 M
3 (b)
Using Gauss Seidal iteration method solve the following equation.
x+20y+9z=-23
2x-7y-20z=-57
20x+2y+6z=28.
x+20y+9z=-23
2x-7y-20z=-57
20x+2y+6z=28.
6 M
4 (a)
Write short note on Simulated Annealing.
4 M
4 (b)
Write a flow chart for Thomas algorithm for tri-diagonal matrix solution.
6 M
Solve any one question from Q5 and Q6
5 (a)
The value of x and y obtained in an experiment are as follows, the law controlling them is y=axb,
Find the best value of the constant a and b.
Find the best value of the constant a and b.
| x | 1 | 2 | 3 | 4 | 5 |
| y | 0.5 | 2.0 | 4.5 | 8 | 12.5 |
8 M
5 (b)
From the tabulated values of x and y given below prepare forward difference table. Find the polynomial passing through the points and estimate the value of y when x = 1.5.
Also find the slope curve at x=1.5.
Also find the slope curve at x=1.5.
| x | 0 | 2 | 4 | 6 | 8 |
| y | 5 | 29 | 125 | 341 | 725 |
8 M
6 (a)
Fit the exponential curve y=aebx to the following data.
| x | 2 | 4 | 6 | 8 |
| y | 25 | 38 | 56 | 84 |
8 M
6 (b)
The velocity distribution of a fluid near a flat surface is given below.
Where x is the distance from the surface (mm) and V is the velocity (mm/sec). Use Lagrange's interpolation polynomial to obtain the velocity at x = 0.4.
Where x is the distance from the surface (mm) and V is the velocity (mm/sec). Use Lagrange's interpolation polynomial to obtain the velocity at x = 0.4.
| x | 0.1 | 0.3 | 0.6 | 0.8 |
| V=y | 0.72 | 1.81 | 2.73 | 3.47 |
8 M
Solve any one question from Q7 and Q8
7 (a)
Draw flow chart for Simpson's 3/8th rule.
8 M
7 (b)
Find double integration of f(x)=x2+y2+5 for x=0 to 2 and y=0 to 2 taking increment in both x and y as 0.5. Use Trapezoidal rule.
8 M
8 (a)
Find the area under the curve on X axis. The curve passes through the following points (1.00,2.00), (1.50,2.40), (2.00,2.70), (2.50,2.80), (3.00,3.00), (3.50,2.60), (4.00,2.10).
8 M
8 (b)
The velocity of car running on a straight road at the interval of 2 minutes is given below:
Find the distance covered by the car using Simpson's 1/3rd rule.
Find the distance covered by the car using Simpson's 1/3rd rule.
| Time (min) | 0 | 2 | 4 | 6 | 8 | 10 | 12 |
| Velocity (Km/hr) | 0 | 22 | 30 | 27 | 18 | 7 | 0 |
8 M
Solve any one question from Q9 and Q10
9 (a)
A second order ODE is transformed into first order ODE as, ( \dfrac {dy}{dx}=z, y(0)=2 \ and \ \dfrac {dz}{dx}=0.5 \ x-y , \ z(0)=0. ) Estimate the value of y and z at x=0.2 take h=0.1.
10 M
9 (b)
Explain the step by step solution procedure for solving parabolic equations.
8 M
10 (a)
The relationship between x and y is given by ( \dfrac {dy}{dx} +xy=2. ) Estimate y at x=5.1 using 2nd order Runge Kutta method. Assume y=2 at x=5.0. Take step size of 0.02.
8 M
10 (b)
Solve the Laplace's equation ( \dfrac {partial^2}{partial^{x^{2}}} + \dfrac {partial^2}{partial^{y^{2}}} =0 ) for the square mesh shown below:
10 M
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