BABSc, B.Com & BCA Questions _III - Nalanda Open University

Nalanda Open University
Annual Exam-2010,
Bachelor of Science (Mathematics) Hons, Part-III
Paper-VIII
Time: 3Hrs Full Marks: 75
Answer any Five questions. All questions carry equal marks.
Calculator are Allowed.
1. (a) Evaluate
2 2
∆
∆
E Sin x h Sin( x + h)
( + ) +
ESin( x + h)
h being the differencing interval.
(b) Given that log 10 654 = 2.8156, log 10 658 = 2.8182, log 10 659 = 2.8189, log 10 661 =
2.8202 find the value of log 10 656 by Lagrange's Interpolation formula.
2. (a) Establish Gauss Forward Interpolation formula for equal Interval.
(b) Find the missing term in the following table
x: 16 18 20 22 24 26
y: 39 85 - 151 264 388
3. (a) Find the first and 2nd derevatives of the function y = f(x) tabulated below at the
point x = 1.1
x 1 1.2 1.4 1.6 1.8 2.00
f(x) 0.00 0.1280 0.5440 1.2960 2.4320 4.00
(b) Prove that the nth divided differences of a polynomial of the nth degree are
constant.
4. (a) Derive trapezoidal Rule for numerical evaluation of integrals.
z5.
2
lo g x d x
4
(b) Find by Weddle's rule the value of
e .
5. (a) Solve 2U x+2 - 5U x+1 +2U x =0 find the Particular solution when U o =1, U 1 = 1.
dy y x
(b) Given dx
y x Euler's method.
6. (a) Explain Picard's method of successive Approximation.
dy 1
= x + y
(b) Find y(2) if y(x) is the solution of dx 2 ( ) assuming y(0) = 2, y(0.5) =
2.636,
y(1) = 3.595, y(1.5)=4.968 by Milne's Method.
7. (a) Explain Gauss elimination method.
(b) Solve the system of Equations by Gauss - Seidal Iteration method
27x+6y-z=85
6x+15y+2z=72
x+y+54z=110
8. (a) Explain method of finding the roots and equation by Bisection Method.
(b) Find the real roots of the Equation with the help of Reguli falsi method xlog 10 x -
1.2 = 0.
9. Explain Newton-Raphson's method and find the root of x 4 - x - 10 nearer to x = 2
correct to three decimal places with the help of Newton Raphson's method.
10. Use Greaff's method to solve the Equation x 3 - 5x 2 - 17x + 20 = 0.
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