North Maharashtra University 2008 B.Sc Mathematics S.Y. - MTH – 222 (B) (Numerical Analysis) - exam paper

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NORTH MAHARASHTRA UNIVERSITY, JALGAON

Class : S.Y. B. Sc. Subject : Mathematics
Paper : MTH – 222 (B) (Numerical Analysis)

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Unit – I
1 : ques. of two marks
1) What is meant by “Inherent error”?
2) describe Rounding fault.
3) describe Truncation fault.
4) discuss : Absolute fault and relative fault.
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 provided equation, where symbol have
their usual meaning.
8) obtain the root of the formula x3 – x – one = 0 lying ranging from one and 2
by Bisection method up to 1st iteration.
9) Show that a real root of the formula x3 – 4x – nine = 0 lies ranging from 2
and three by Bisection method.
10) Using Bisection method, show that a real root of the formula 3x -
1 + sin x = 0 lies ranging from 0 and 1.
11) obtain the 1st approximation of x for the formula x =
0.21sin(0.5+x) by iteration method starting with x = 0.12.
2
12) obtain an iterative formula to obtain N where N is a positive number
by Newton Raphson method.
13) Using Newton Raphson method obtain 1st approximation x1 for
finding 10 , taking x0 = 3.1.
14) Using Newton Raphson method obtain 1st approximation x1 for
finding three 13 , taking x0 = 2.5.
15) find Newton Raphson formula for finding a rth root of a provided
number c.
16) Show that a real root of a formula xlog10x – 1.2 = 0 lies ranging from 2
and 3.
17) What is meant by significant figure? obtain the significant figures in
0.00397.
18) If actual value of a number is 36.25and its absolute fault is 0.002.
obtain the relative fault and percentage fault.
19) If the absolute fault is 0.005 and relative fault is 3.264×10-6, then
obtain the actual value and percentage fault.
2 : Fill in the blanks/Multiple option ques. of 1
marks
1) If X is the actual value of the volume and X1 is the approximate
value then the relative fault is ER = - - - - and percentage fault is
EP = - - - -
2) If X is the actual value and X1 is the approximate value of the provided
volume then its absolute fault is EA = - - - - and relative is fault
ER = - - - -
3) Every algebraic formula of the nth degree has exactly - - - -
roots.
3
4) After rounding of the number 2.3762 to the 2 decimal places, we
get the number - - - -.
5) Rounding off the number 32.68673 to four significant digits, we get a

Earning:   Approval pending.