STUPIDSID
1 (a)
Discuss the types of errors in performing numerical calculations.
4 M
1 (b)
Does bisection method always converge?
Discuss the comparison of iterative methods .
5 M
1 (c)
Discuss the merits and demerits of the moving average method.
5 M
2 (a)
(1) Discuss the consequences of normalized floating point representation of
numbers with a suitable example.
(2) Evaluate \[\left ( \dfrac{\Delta ^{2}}{E} \right )x^{3}\]
(2) Evaluate \[\left ( \dfrac{\Delta ^{2}}{E} \right )x^{3}\]
7 M
2 (b)
Write an algorithm for cubic spline interpolation.
7 M
2 (c)
Find the first, second and third derivative of the function, tabulated below, at x=1.5:
| x | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 |
| f(x) | 3.375 | 7.000 | 13.625 | 24.000 | 38.875 | 59.000 |
7 M
3 (a)
(1) Obtain the function whose first difference is 9x2+11x+5. Show that its third difference is 18.
(2) Find the first term of the series whose second and subsequent terms are 8, 3, 0, -1, 0 .
(2) Find the first term of the series whose second and subsequent terms are 8, 3, 0, -1, 0 .
7 M
3 (b)
State Budan's theorem. Solve x3-8x2+17x-10=0 by Graffe's method,
squaring three times.
7 M
3 (c) (i)
Find the value of log 3 from \[\int_{0}^{1}\limits \dfrac{x^{2}}{1+x^{3}}dx\] using Simpson's rule by dividing the range into four equal parts.
3 M
3 (c) (ii)
Write an algorithm to solve a differential equation by Runge-Kutta
Method.
4 M
3 (d)
Using Taylor series method, solve \[\dfrac{dy}{dx}=x+y\].Starting from x=1,y=0 and carry to x=1.2 with h=0.1. Compute the final result with the value of the explicit solution.
7 M
4 (a) (i)
Find the value of x corresponding to y=12 using inverse interpolation:
| x | 1.2 | 2.1 | 2.8 | 4.1 | 4.9 | 6.2 |
| y | 4.2 | 6.8 | 9.8 | 13.4 | 15.5 | 19.6 |
4 M
4 (a) (ii)
Solve by Jacobi's iterative method:
2x-3y+20z=25, 3x+20y-z=18,20x+y-2z=17.
2x-3y+20z=25, 3x+20y-z=18,20x+y-2z=17.
4 M
4 (b)
By the method of least squares, fit a parabola to the following data; also
Estimate y at x=6.
| X | 1 | 2 | 3 | 4 | 5 |
| Y | 5 | 12 | 26 | 60 | 97 |
6 M
4 (c)
Define Chebyshev polynomial. Obtain Taylor series expansion of e-x in terms of x . Approximate it in terms of Chebyshev polynomials.
7 M
4 (d)
Determine the value of y(0.4) using predictor corrector method given \[\dfrac{dy}{dx}=xy+y^{2}\];y(0)=1; use Taylor series to get the values of y(0.1),y(0.2),y(0.3) Take h=0.1.
7 M
5 (a) (i)
The coefficient of correlation between two variables X and Y is 0.48. The
covariance is 36. The variance of X is 16. Find the standard deviation of Y.
4 M
5 (a) (ii)
From the following table calculate the coefficient of correlation by Karl
Pearson's method
| X | 39 | 65 | 62 | 90 | 82 | 75 | 25 | 98 | 36 | 78 |
| Y | 47 | 53 | 58 | 86 | 62 | 68 | 60 | 91 | 51 | 84 |
4 M
5 (b)
The sales of a company in million of rupees for the years 1994-2001 are given
below:
Find the linear trend equation. Estimate the sales for the year 1993. Find the slope of the straight line trend.
| Year | 1994 | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2001 |
| Sales | 550 | 560 | 555 | 585 | 540 | 525 | 545 | 585 |
Find the linear trend equation. Estimate the sales for the year 1993. Find the slope of the straight line trend.
6 M
5 (c) (i)
If the relation between two random variables x and y is 2x+3y=4, find the correlation coefficient between them.
5 M
5 (c) (ii)
Compute the seasonal index for the following data assuming that there is no need to adjust the data for the trend:
| Quarter | 1990 | 1991 | 1992 | 1993 | 1994 | 1995 |
| I | 3.5 | 3.5 | 3.5 | 4 | 4.1 | 4.2 |
| II | 3.9 | 4.1 | 3.9 | 4.6 | 4.4 | 4.6 |
| III | 3.4 | 3.7 | 3.7 | 3.8 | 4.2 | 4.3 |
| IV | 3.6 | 4.8 | 4 | 4.5 | 4.5 | 4.7 |
4 M
5 (d)
If the two lines of regression are
4x-5y+30=0 and 20x-9y-107=0 which of these line of regression of x on y, and y on x. Find rxy and σy when σx=3.
4x-5y+30=0 and 20x-9y-107=0 which of these line of regression of x on y, and y on x. Find rxy and σy when σx=3.
5 M
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