UGC-NET CS 2017 Nov - III

Question 51

If b is the branching factor and m is the maximum depth of the search tree, what is the space complexity of greedy search?

• O(b+m)

• O(bm)

• O(b^m)

• O(m^m)

Question 52

Let P, Q, R and S be Propositions. Assume that the equivalences P ⇔ (Q ∨ ¬ Q) and Q ⇔ R hold. Then the truth value of the formula (P ∧ Q) ⇒ ((P ∧ R) ∨ S) is always:

• True
• False
• Same as truth table of Q
• Same as truth table of S

Question 53

“If X, then Y unless Z” is represented by which of the following formulae in propositional logic?

• (X ∧ Y) → ¬ Z
• (X ∧ ¬ Z) → Y
• X → (Y ∧ ¬ Z)
• Y → (X ∧ ¬ Z)

Question 54

Consider the following two well-formed formulas in prepositional logic.

F1 : P ⇒ ¬ P
F2 : (P ⇒ ¬ P) ∨ (¬ P ⇒ P)

Which of the following statements is correct?

• F1 is Satisfiable, F2 is valid
• F1 is unsatisfiable, F2 is Satisfiable
• F1 is unsatisfiable, F2 is valid
• F1 and F2 both are Satisfiable

Question 55

Which of the following statements is not correct?

• Every recursive language is recursively enumerable.
• L = {0ⁿ1ⁿ 0ⁿ │n=1, 2 , 3, ....} is recursively enumerable.
• Recursive languages are closed under intersection.
• Recursive languages are not closed under intersection.

Question 56

Context free grammar is not closed under:

• Concatenation
• Complementation
• Kleene Star
• Union

Question 57

Consider the following languages: 
L₁ = {a^m bⁿ │ m ≠ n} 
L₂ = {a^m bⁿ │ m = 2n+1} 
L₃ = {a^m b^m │ m ≠ 2n} 
Which one of the following statement is correct ?

• Only L₁ and L₂ are context free languages

• Only L₁ and L₃ are context free languages

• Only L₂ and L₃ are context free languages

• L₁, L₂ and L₃ are context free languages

Question 58

A 4×4 DFT matrix is given by : (j² = −1) Where values of x and y are _____, _____ respectively.

• 1, −1
• −1, 1
• −j, j
• j, −j

Question 59

Entropy of a discrete random variable with possible values {x1, x2, ..., xn} and probability density function P(X) is : The value of b gives the units of entropy. The unit for b=10 is : (1) bits (2) bann (3) nats (4) deca

• (1) and (3)
• (2) and (3)
• (1),(2)and(3)
• All are correct.

Question 60

For any binary (n, h) linear code with minimum distance (2t+1) or greater

• 2t+1
• t+1
• t
• t-1