STUPIDSID
1 (a)
Define Absolute error, Relative error, Percentage error. The approximate solution of a problem is 3.436. If the absolute error in the
solution is less than 0.01 then find the interval within which the exact solution
lies.
7 M
1 (b)
Show that the False Position method is linearly convergent.
7 M
2 (a)
Find all the roots of the equation x4+x3+2x2+x+1=0 using Lin-
Bairstow method. Start with the initial factor x2+0.9x+0.9.
7 M
2 (b)
Find all the roots of the equation x3-6x2+11x-6=0 using Graeffe's method squaring thrice.
7 M
2 (c)
Solve the non linear system of equations xy=1,x2+4x2=5 using Newton Raphson method.
7 M
3 (a)
Derive Newton's divided difference formula and use it to find the interpolating
polynomial from the following table
| x | 1 | 2 | 7 | 8 |
| f(x) | 1 | 5 | 5 | 4 |
7 M
3 (b)
Show that 1+Δ=E=ehD.
7 M
3 (c)
Obtain the cubic spline for every subinterval from the following data
| x | 0 | 1 | 2 | 3 |
| f(x) | 1 | 2 | 33 | 244 |
7 M
3 (d)
Fit a curve of the type y= abx to the following data.
| x | 50 | 450 | 780 | 1200 | 4400 | 4800 | 5300 |
| y | 28 | 30 | 32 | 36 | 51 | 58 | 69 |
7 M
4 (a)
Solve \[\dfrac{dy}{dx}=x^{2}y\] with y(0)=1 for x=0.1,0.2,0.3 by Taylor's series method. Extend the solution to x=0.4 by Milne's method.
7 M
4 (b)
Solve \[\dfrac{dy}{dx}=\dfrac{y^{2}-x^{2}}{y^{2}+x^{2}}\] y(0)=1 for x=0.2,0.4 by Runge-Kutta method.
7 M
4 (c)
Derive the formula of Trapezoidal rule and use it to evaluate \[\int_{0}^{1}\limits exp(-x^{2})dx\] with n=10.
7 M
4 (d)
Explain ill conditioned system of equations and solve the following system of equations using Gauss Elimination method.
2x1+x2+2x3+x4=6
6x1-x2+6x3+12x4=36
4x1+3x2+3x3-3x4=1
2x1+2x2-x3+x4=10.
2x1+x2+2x3+x4=6
6x1-x2+6x3+12x4=36
4x1+3x2+3x3-3x4=1
2x1+2x2-x3+x4=10.
7 M
5 (a)
Find the first four moments of the following data about assumed mean 112.45
and actual mean.
| Class limit | 100-104.9 | 105-109.9 | 110-114.9 | 115-119.9 | 120-124.9 |
| Frequency | 7 | 13 | 25 | 25 | 30 |
7 M
5 (b)
Find the correlation coefficient from the following data.
| X | 50 | 50 | 55 | 60 | 65 | 65 | 65 | 60 | 60 | 50 |
| Y | 11 | 13 | 14 | 16 | 16 | 15 | 15 | 14 | 13 | 13 |
7 M
5 (c)
Find both Regression lines for the data.
| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| y | 10 | 12 | 16 | 28 | 25 | 36 | 41 | 49 | 40 | 50 |
7 M
5 (d)
Calculate 7-yearly moving averages for the following data showing the number
of students of an engineering college clearing GATE.
| Year | Number of students | Year | Number of students |
| 1999 | 23 | 2007 | 9 |
| 2000 | 26 | 2008 | 13 |
| 2001 | 28 | 2009 | 11 |
| 2002 | 32 | 2010 | 14 |
| 2003 | 20 | 2011 | 12 |
| 2004 | 12 | 2012 | 9 |
| 2005 | 12 | 2013 | 3 |
| 2006 | 10 | 2014 | 1 |
7 M
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