MTH222 Numerical Analysis B.Sc Question Bank : nmu.ac.in

Name of the University : North Maharashtra University
Degree : B.Sc
Department : Mathematics
Year : II
Name Of The Subject : MTH222 Numerical Analysis
Document type : Question Bank
Website : nmu.ac.in

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Numerical Analysis Model Paper :

NORTH MAHARASHTRA UNIVERSITY,
Question Bank
New syllabus w.e.f. June 2008
Class : S.Y. B. Sc. Subject : Mathematics
Paper : MTH – 222 (B) (Numerical Analysis)
Unit – I

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1 : Questions of 2 marks
1) What is meant by “Inherent error”-
2) Define Rounding error.
3) Define Truncation error.
4) Explain : Absolute error and relative error.
5) What is meant by “Percentage error”-
6) State with usual notation the Newton Raphson formula.

7) In the method of false position, state the formula for the first approximation of the root of given equation, where symbol have their usual meaning.
8) Find the root of the equation x3 – x – 1 = 0 lying between 1 and 2 by Bisection method up to first iteration.
9) Show that a real root of the equation x3 – 4x – 9 = 0 lies between 2 and 3 by Bisection method.
10) Using Bisection method, show that a real root of the equation 3x – 1+ sin x = 0 lies between 0 and 1.
11) Find the first approximation of x for the equation x = 0.21sin(0.5+x) by iteration method starting with x = 0.12.
12) Find an iterative formula to find N where N is a positive number by Newton Raphson method.
13) Using Newton Raphson method find first approximation x1 for finding 10 , taking x0 = 3.1.
14) Using Newton Raphson method find first approximation x1 for finding 3 13 , taking x0 = 2.5.
15) Obtain Newton Raphson formula for finding a rth root of a given number c.
16) Show that a real root of a equation xlog10x – 1.2 = 0 lies between 2 and 3.
17) What is meant by significant figure? Find the significant figures in 0.00397.
18) If true value of a number is 36.25and its absolute error is 0.002. find the relative error and percentage error.
19) If the absolute error is 0.005 and relative error is 3.264×10-6, then find the true value and percentage error.

2 : Fill in the blanks/Multiple choice Questions of 1 marks
1) If X is the true value of the quantity and X1 is the approximate value then the relative error is ER = – – – – and percentage error is EP
2) If X is the true value and X1 is the approximate value of the given quantity then its absolute error is EA = – – – – and relative is error ER
3) Every algebraic equation of the nth degree has exactly roots.
4) After rounding of the number 2.3762 to the two decimal places, we get the number

5) Rounding off the number 32.68673 to 4 significant digits, we get a number
a) 32.68
b) 32.69
c) 32.67
d) 32.686

8) The root of the equation x3 – 2x – 5 = 0 lies between – – – –
a) 0 and 1
b) 1 and 2
c) 2 and 3
d) 3 and 4

3 : Questions of 4 marks :
1) Explain the Bisection method for finding the real root of an equation f(x) = 0.
2) Explain the method of false position for finding the real root of an equation f(x) = 0.
3) Explain the iteration method for finding the real root of an equation f(x) = 0. Also state the required conditions.
4) State and prove Newton-Raphson formula for finding the real root of an equation f(x) = 0.
5) Explain in brief Inherent error and Truncation error. What is meant by absolute, relative and percentage errors? Explain.

6) Using the Bisection method find the real root of each of the equation :
(i) x3 – x – 1 = 0.
(ii) x3 + x2 + x + 7 = 0.
(iii) x3 – 4x – 9 = 0.
(iv) x3 – x – 4 = 0.
(v) x3 – 18 = 0.
(vi) x3 – x2 – 1 = 0.
(vii) x3 – 2x – 5 = 0.
(viii) x3 – 9x + 1 = 0.
(ix) x3 – 10 = 0.
(x) 8×3 – 2x – 1 = 0.
(xi) 3x – 1+ sin x = 0.
(xii) xlog10x = 1.2.
(xiii) x3 – 5x + 1 = 0.
(xiv) x3 – 16×2 + 3 = 0.
(xv) x3 – 20×2 – 3x + 18 = 0. (up to three iterations).

7) Using Newton-Raphson method, find the real root of each of the equations given bellow (up to three iterations) :
(i) x2 – 5x + 3 = 0
(ii) x4 – x – 10 = 0
(iii) x3 – x – 4 = 0
(iv) x3 – 2x – 5 = 0
(v) x5 + 5x + 1 = 0
(vi) sinx = 1 – x
(vii) tanx = 4x
(viii) x4 + x2 – 80 = 0
(ix) x3 – 3x – 5 = 0
(x) xsinx + cosx = 0
(xi) x3 + x2 + 3x + 4 = 0
(xii) x2 – 5x + 2 = 0
(xiii) 3x = cosx + 1
(xiv) xlog10x – 1.2 = 0
(xv) x5 – 5x + 2 = 0
(xvi) x3 + 2×2 + 10x – 20 = 0