A husband and wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is 18 and that of wife’s selection is ¼. What is the probability that:
(i) Both of them will be selected
(ii) Only one of them will be selected
(iii) None of them will be selected.

Use the Jacobi method to solve the following system of equations: 
3x + 4y + 15z = 54.8
x + 12y + 3z = 39.66
10x + y — 2z = 7.74

Solve the following system of equations by using the Gauss Elimination method: (8 Marks)
 x + 2y + z = 3
2x + 3y + 3z = 10
3x y + 2z = 13

Calculate the value of the integral

(i) Simpson's 1/3 rule,

(ii) Simpson's 3/8 rule.

Use Regula-Falsi method to find the roots of the equation f(x) =x³ + x – 1.

Write a program in Prolog to find and print prime numbers between 50 to 200.

What is the difference between Knowledge and Intelligence? Enumerate the various knowledge representation schemes, giving a brief description for each scheme.

Write BFS algorithm. Use the BFS to search the goal node . Show each step of the algorithm.

What is Means-Ends Analysis? How is Means-Ends Analysis used as a problem solving technique?

Define fuzzy inference system? What are the main steps in Fuzzy inference system? Make an inference system for food management system.

What are Semantic Nets? Briefly discuss the utility of semantic nets in knowledge management. Give suitable example in support of your answer.

What is Prenex Normal Form (PNF). Write the steps to transform a Well-Formed Formula (WFF) into PNF. Transform Ɐx(Q(x) →(ⱻx) R(x, y)).

Write a program in LISP to calculate the area of the circle, whose radius is given by the user. Write proper comments to enhance readability of your code.

What are Expert Systems? Briefly discuss the various categories of software tools, used for the development of expert systems.

If the propositions are described as follows: (8 Marks)
P : He needs a doctor
S : He is Sick
Q : He needs a lawyer
U : He is injured
R : He has an accident
Then represent the following formulas in English :
(i) (P ˄ Q) → R
(ii) (P ˄ Q) ↔ (S ˄ U)

Write a Program in C/C++ using Open GL that draws the following figure.

Write a Program in C/C++ using open GL that draws the following figure:

Write a program in C/C++ to implement a Bresenham's Circle generation algorithm (without using inbuilt circle ( ) function).

Write a program in C/C++ using OpenGL that draws the following figure:

Implement DDA Line Generation algorithm in C/C++ using OpenGL.