## UGC Net Computer Science December 13 Paper 3 Page 3 Solved

21. Given the following statements :
S1 : The grammars S → asb | bsa |
ss | a and S → asb | bsa | a are not equivalent.
S2 : The grammars S → ss | sss |
asb | bsa | λ and S → ss | asb | bsa | λ are equivalent.

Which of the following is true ?

(A) S1 is correct and S2 is not correct.
(B) Both S1 and S2 are correct.
(C) S1 is not correct and S2 is correct.
(D) Both S1 and S2 are not correct.
Explanation :-

22. What are the final values of Q1 and Q0 after 4 clock cycles, if initial values are 00 in the sequential circuit shown below :

(A) 11
(B) 10
(C) 01
(D) 00
Explanation :-
 T flip-flop operation Characteristic table Excitation table {\displaystyle T} {\displaystyle Q} {\displaystyle Q_{\rm {next}}} Comment {\displaystyle Q} {\displaystyle Q_{\rm {next}}} {\displaystyle T} Comment 0 0 0 hold state (no clk) 0 0 0 No change 0 1 1 hold state (no clk) 1 1 0 No change 1 0 1 toggle 0 1 1 Complement 1 1 0 toggle 1 0 1 Complement

23. High level knowledge which relates to the use of sentences in different contexts and how the
context affect the meaning of the sentences ?
(A) Morphological
(B) Syntactic
(C) Semantic
(D) Pragmatic

Explanation :-

A process in which the speaker implies and a listener infers. Simply Pragmatics studies language that is not directly spoken. The speaker hints at or suggests a meaning , and the listener assume the correct intention. Pragmatics study how words can be interpreted in different ways based on the situation.

24. The objective of ________ procedure is to discover at least one ________ that causes two literals to match.
(A) unification, validation
(B) unification, substitution
(C) substitution, unification
(D) minimax, maximum

Explanation :-

25. If h* represents an estimate of the cost of getting from the current node N to the goal node and h
represents actual cost of getting from the current node to the goal node, then A* algorithm gives an optimal solution if
(A) h* is equal to h
(B) h* overestimates h
(C) h* underestimates h
(D) none of these

26. The mean-end analysis process centers around the detection of differences between the current state and goal state. Once such a difference is isolated, an operator that can reduce the difference must be found. But perhaps that operator can not be applied to the current state. So a sub-problem of getting to a state in which it can be applied is set up. The kind of backward chaining in which
operators are selected and then sub goals are set up to establish the precondition of operators is called
(A) backward planning
(B) goal stack planning
(C) operator subgoaling

Explanation :-

Most of the search strategies either reason forward of backward however, often a mixture o the two directions is appropriate. Such mixed strategy would make it possible to solve the major parts of problem first and solve the smaller problems the arise when combining them together. Such a technique is called "Means - Ends Analysis".

Operator subgoaling is a computer problem solving method in which the inability of the computer to take the desire  next step at any point in the problem solving process leads to a subtotal of making step feasible

Steps:
1. Computing the current state s1 to a goal state s2 and computing their difference D12.
2. Satisfy the preconditions for some recommended operator op is selected, then to reduce the difference D12.
3. The operator OP is applied if possible. If not the current state is solved a goal is created and means- ends analysis is applied recursively to reduce the sub goal.
27. In alpha-beta pruning, _________ is used to cut off the search at maximizing level only and
_________ is used to cut off the search at minimizing level only.
(A) alpha, beta
(B) beta, alpha
(C) alpha, alpha
(D) beta, beta
Explanation :-
Alpha-Beta pruning is not actually a new algorithm, rather an optimization technique for minimax algorithm. It reduces the computation time by a huge factor. This allows us to search much faster and even go into deeper levels in the game tree. It cuts off branches in the game tree which need not be searched because there already exists a better move available. It is called Alpha-Beta pruning because it passes 2 extra parameters in the minimax function, namely alpha and beta.

Let’s define the parameters alpha and beta.
Alpha is the best value that the maximizer currently can guarantee at that level or above.
Beta is the best value that the minimizer currently can guarantee at that level or above.

 An illustration of alpha–beta pruning. The grayed-out subtrees need not be explored (when moves are evaluated from left to right), since we know the group of subtrees as a whole yields the value of an equivalent subtree or worse, and as such cannot influence the final result. The max and min levels represent the turn of the player and the adversary, respectively.
image source : https://en.wikipedia.org/wiki/Alpha%E2%80%93beta_pruning

28. If A and B are two fuzzy sets with membership functions μA(x) = {0.2, 0.5, 0.6, 0.1, 0.9}
μB(x) = {0.1, 0.5, 0.2, 0.7, 0.8}Then the value of μA ∩ B will be
(A) {0.2, 0.5, 0.6, 0.7, 0.9}
(B) {0.2, 0.5, 0.2, 0.1, 0.8}
(C) {0.1, 0.5, 0.6, 0.1, 0.8}
(D) {0.1, 0.5, 0.2, 0.1, 0.8}
Explanation :-
Explanation:-  The fuzzy intersection of two fuzzy sets A and B on universe of discourse X: μA∩B(x) = min [μA(x), μB(x)] , where x∈X But here in the question, they are asking for complement of A intersection B and so the answer would be 1-min[A(x),B(x)].
The minimum of 0.2 and 0.1 will be 0.1, and 1-0.1 will be 0.9
The second value is min(0.4,0.3)=0.3 and 1-0.3=0.7
The third value is min(0.8,0.6)=0.6 and 1-0.6=0.4
The fourth value is min(0.5,0.3)=0.3 and 1-0.3=0.7
The last value is min(0.1,0.2)=0.1 and 1-0.1=0.9
The only option which has got the values 0.9,0.7,0.4,0.7 and 0.9, although the fourth value is given as 0.8 instead of 0.7 is option A.
So the answer is option A.

29. The height h(A) of a fuzzy set A is defined as
h(A) = sup A(x)
x ∈ A
Then the fuzzy set A is called normal when
(A) h(A) = 0
(B) h(A) < 0
(C) h(A) = 1
(D) h(A) < 1