NTA UGC NET 2019 June - II

Question 21

Which of the following problems is/are decidable problem(s) (recursively enumerable) on a Turing machine M? (a) G is a CFG with L(G)=∅ (b) There exist two TMs M​1​ and M2​ such that L(M) ⊆{L(M​1​)UL(M​2​)}= language of all TMs (c) M is a TM that accepts w using a most 2​|w|​ cells of tape

• a and b only
• a only
• a, b and c
• c only

Question 22

Consider the Euler’s phi function given by ϕ(n)=nΠp/n(1–1p) where p runs over all the primes dividing n. What is the value of ϕ(45)?

• 3
• 12
• 6
• 24

Question 23

Consider double hashing of the form h(k,i)=(h​ 1​ (k)+ih​ 2​ (k)) mod m Where h​ 1​ (k)=k mod m h​ 2​ (k)=1+(k mod n) Where n=m-1and m=701 for k=123456, what is the difference between first and second probes in terms of slots?

• 255
• 256
• 257
• 258

Question 24

At a particular time of computation, the value of a counting semaphore is 7. Then 20 P(wait) operations and 15 V(signal) operations are completed on this semaphore. What is the resulting value of the semaphore?

• 28
• 12
• 2
• 42

Question 25

Software validation mainly checks for inconsistencies between

• Use cases and user requirements
• Implementation and system design blueprints
• Detailed specifications and user requirements
• Function specifications and use cases

Question 26

Shift-reduce parser consists of (a) input buffer (b) stack (c) parse table choose the correct option from those given below:

• (a) and (b) only
• (a) and (c) only
• (c) only
• (a), (b) and (c)

Question 27

For a statement, " A language L ⊆ Σ* is recursive if there exists some Turing machine M Which of the following conditions is satisfied for any string w"?

• If ω∈L, then M accepts ω and M will not halt
• If ω∉L, then M accepts ω and M will halt by reaching at final state
• If ω∉L, then M halts without reaching to acceptable state
• If ω∈L, then M halts without reaching to an acceptable state

Question 28

K-mean clustering algorithm has clustered the given 8 observations into 3 clusters after 1st iteration as follows: C1 : {(3,3), (5,5), (7,7)} C2 : {(0,6), (6,0), (3,0)} C3 : {(8,8),(4,4)} What will be the Manhattan distance for observation (4,4) from cluster centroid C1 in second iteration?

• 2
• √2
• 0
• 18

Question 29

What is the output of the following JAVA program? public class Good{ Private int m; Public Good(int m){this.m=m;} public Boolean equals(Good n){return n.m=m;} public static void main(String args [ ]){ Good m1=new Good(22); Good m2=new Good(22); Object S1=new Good(22); Object S2=new good(22); System.out.println(m1.equals(m2)); System.out.println(m1.equals(s2)); System.out.println(m1.equals(s2)); System.out.println(s1.equals(m2)); } }

• True, True, False, False
• True, False, True, False
• True, True, False, True
• True, False, False, False
• None o the above.

Question 30

In relational database, if a relation R is in BCNF, then which of the following is true about relation R?

• R is in 4NF
• R is not in 1NF
• R is in 2NF and not in 3NF
• R is in 2NF and 3NF