STUPIDSID
1 (a)
Define Truncation error, Round off error, Inherent error.
Find the relative error and percentage error if 0.005998 is truncated to three
decimal digits.
7 M
1 (b)
Show that the Successive approximation method is linearly convergent.
7 M
2 (a)
Find all the roots of the equation x3+x2-x+2=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 x3-2x2-5x+6=0 using Graeffe's method squaring thrice.
7 M
2 (c)
Solve the non linear system of equations xy=1,x2+4y2=5 using Newton- Raphson method.
7 M
3 (a)
Derive the Recurrence relation for Chebyshev polynomials and using it define.
T2(x),T3(x) and T4(x).
T2(x),T3(x) and T4(x).
7 M
3 (b)
Derive Lagrange's interpolation formula and using inverse interpolation find the
value of x corresponding to y=12 from the following data.
| x | 1.2 | 2.1 | 2.8 | 4.1 | 4.9 | 6.2 |
| f(x) | 4.2 | 6.8 | 9.8 | 13.4 | 15.5 | 19.6 |
7 M
3 (c)
Obtain the cubic spline for every subinterval from the following data
| x | 1 | 2 | 3 | 4 |
| f(x) | 1 | 2 | 5 | 11 |
7 M
3 (d)
The pressure and volume of a gas are related by the equation pVa=c . Fit this
curve to the following data.
| p | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 |
| V | 1.62 | 1.0 | 0.75 | 0.62 | 0.52 | 0.46 |
7 M
4 (a)
Solve \[\dfrac{dy}{dx}=2y+3e^{x}\] with y(0)=0 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 \[\dfrac{dy}{dx}=xy+y^{2}\] with y(0)=1 for x=0.1,0.2,0.3 by Runge-Kutta method.
7 M
4 (c)
Derive the formula of Simpson's 1/3 rd rule and use it to evaluate \[\int_{0}^{6}\limits \dfrac{1}{1+x}dx\]. Hence obtain the value of log e 7 .
7 M
4 (d)
Explain ill conditioned system of equations and solve the following system of equations using Gauss - Jacobi method.
3x+20y-z=-18, 2x-3y+20z=25, 20x+y-2z=17.
3x+20y-z=-18, 2x-3y+20z=25, 20x+y-2z=17.
7 M
5 (a)
Find the first four moments of the following data about assumed mean 25 and actual mean.
| Class limit | 0-10 | 10-20 | 20-30 | 30-40 |
| Frequency | 1 | 3 | 4 | 2 |
7 M
5 (b)
Find the correlation coefficient from the following data
| X | 307 | 259 | 341 | 317 | 274 | 416 | 267 | 320 | 274 | 336 |
| Y | 80 | 75 | 90 | 74 | 75 | 110 | 70 | 85 | 88 | 78 |
7 M
5 (c)
Find both Regression lines for the data
The correlation coefficient is 0.5.
| x | y | |
| Mean | 60 | 67.5 |
| Standard Deviation | 15 | 13.5 |
The correlation coefficient is 0.5.
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 |
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