Solve the initial value problem )+ )% = y − x with y(0) = 2 and h = 0 ∙ 1, Using fourth order classical Runge –Kutta Method, find y(0 ∙ 1) and y(0 ∙ 2) correct to four decimal places.

Evaluate the integral ( using Gauss-Legendre formula. Compare the results with exact solution obtained by Simpson rule. The exact value of I = 1.

Solve by Jacobi’s method, the following system of linear equations:

A car hire firm has two cars which it hires out day by day. The number of demands for a car on each day is distributed as Poisson variate with mean 1 ∙ 5. Calculate the proportion of days on which

(i) neither car is used

(ii) some demand is refused

Use Lagrange’s Interpolation formula to find the value of Cos( � ⁄6) given y = Cos x.

What are the pitfalls of Gauss-Elimination method? Solve the following system, using Gauss Elimination Method:

2x + y + z = 10

Find the roots of the equation f(x) = # $ % − 5x + 2, by using Secant method.

Use the Newton-Raphson method to find a root of the equation X² − 2_X − 5 = 0.

If 0∙333 is the approximate value of ! " , find absolute, relative and percentage error. Explain how these errors measure accuracy.

Closed World Assumptions

Expert System and its architecture

Skolemization

Truth Maintenance System – TMS.

Classification of Agents in Artificial Intelligence

Express the following knowledge as a semantic network structure with Interconnected nodes and labeled arcs. “Ram is Vice President of ABC Company. He is married to Raj and has a male child RajaRam. RajaRam Goes to school. Ram plays golf and owns a silver color German made car Mercedez Benz”

Discuss the systems available to handle the incompleteness of a knowledge base. What do you understand by the term “Fuzzyfication”? Given below a fuzzy set to describe the term tall tall

= (5’/0. 0; 5’5”/0. 2; 5’8” /0. 5 6’/0. 7; 6’5”/0. 8; 7’/1. 0)

Discuss and describe membership function for the fuzzy sets for each of the terms:

(i) Very tall

(ii) More or less tall

(iii) Not tall

Compare and contrast the following

: (i) Frames and scripts

(ii) Informed search and uniformed search

Explain the difference between Forward and Backward Chaining. Under which situation which mechanism is best to use, for a given set of problem?

Write a recursive program is LISP to find factorial of a number given by the user.

With the help of a suitable example, describe the “member” function of PROLOG. How it can be used for searching of a data in a list, recursively.