Bhaskaracharya College of Applied Sciences
B.Sc.(H) Electronics Semester V : Paper# DSE 2 Numerical Analysis
Internal Assessment Test : Max. Marks 50: Monday October 5, 2020 : Time 2hrs
(Ordinary Calculators allowed. All questions compulsory)
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1a What is an error of observation? Distinguish between systematic and random errors.
The velocity of light in km/sec obtained using different methods are 299782,
299798, 299774, 299771 and 299776. Find the mean and its standard error.
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1b Find the relative error if the number x=0.00646819 is
a. Chopped off upto 3 decimal places
b. Rounded off upto 3 decimal places.
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2a Write calculation in the tabular form using Regula Falsi to find root of the equation
xSin(x)+Cos(x)=0 in the interval (0,3) upto an accuracy of 10-4 How Regula Falsi
differ from secant method.
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2b Define rate of convergence and calculate it for Newton Raphson method. Compare
different methods on this criterion.
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3a Solve the system of equations using Gauss Elimination
2𝑥𝑥 + 2𝑦𝑦 + 4𝑧𝑧 = 14
3𝑥𝑥 − 𝑦𝑦 + 2𝑧𝑧 = 13
5𝑥𝑥 + 2𝑦𝑦 − 2𝑧𝑧 = 2
3b Solve the system of equations using Cholesky’s method.
𝑥𝑥 + 2𝑦𝑦 + 3𝑧𝑧 = 7
2𝑥𝑥 + 7 𝑦𝑦 + 15𝑧𝑧 = 26
3𝑥𝑥 + 15𝑦𝑦 + 41𝑧𝑧 = 26
4a Solve the system of equations using Jacobi’s method.
10𝑥𝑥 − 𝑦𝑦 − 𝑧𝑧 = 13
𝑥𝑥 + 10 𝑦𝑦 + 𝑧𝑧 = 36
−𝑥𝑥 − 𝑦𝑦 + 10𝑧𝑧 = 35
4b Solve the system of equations using Gauss Seidal method.
𝑥𝑥 + 10𝑦𝑦 + 𝑧𝑧 = 6
10𝑥𝑥 + 𝑦𝑦 + 𝑧𝑧 = 6
𝑥𝑥 + 𝑦𝑦 + 10𝑧𝑧 = 35
5a Find the inverse of the given matrix using Gauss Jordan
2 1 1
�3 2 3�
1 4 9
5b Solve the system of equations using LU decomposition method.
2𝑥𝑥 + 3𝑦𝑦 + 𝑧𝑧 = 9
𝑥𝑥 + 2𝑦𝑦 + 3𝑧𝑧 = 6
3𝑥𝑥 + 𝑦𝑦 + 2𝑧𝑧 = 8
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