UGC NET CS 2017 Jan - III

Question 21

Consider the languages L1 = φ and L2 = {1}. Which one of the following represents L*₁∪ L*₁ L*₂ ?

• {∈}
• {∈, 1}
• φ
• 1*

Question 22

Given the following statements : (A) A class of languages that is closed under union and complementation has to be closed under intersection. (B) A class of languages that is closed under union and intersection has to be closed under complementation. Which of the following options is correct ?

• Both (A) and (B) are false.
• Both (A) and (B) are true.
• (A) is true, (B) is false.
• (A) is false, (B) is true.

Question 23

Let G = (V, T, S, P) be a context-free grammar such that every one of its productions is of the form A → v, with |v| = K > 1. The derivation tree for any W ∈ L(G) has a height h such that

• logK|W| ≤ h ≤ logK((|W|-1)/k-1)
• logK|W| ≤ h ≤ logK(K|W|)
• logK|W| ≤ h ≤ K logK|W|
• logK|W| ≤ h ≤ ((|W|-1)/k-1)

Question 24

Given the following two languages : L1 = {aⁿ bⁿ | n ≥ 0, n ≠ 100} L2 = {w ∈ {a, b, c}*| n_a(w) = n_b(w) = n_c(w)} Which of the following options is correct ?

• Both L₁ and L₂ are not context free language
• Both L₁ and L₂ are context free language.
• L₁ is context free language, L₂ is not context free language.
• L₁ is not context free language, L₂ is context free language.

Question 25

A recursive function h is defined as follows :

h(m) = k, if m = 0
     = 1, if m = 1
     = 2 h(m – 1) + 4h(m – 2), if m ≥ 2

If the value of h(4) is 88 then the value of k is :

• 0

• 1

• 2

• -1

Question 26

Suppose there are n stations in a slotted LAN. Each station attempts to transmit with a probability P in each time slot. The probability that only one station transmits in a given slot is _______.

• nP(1 – P)^{n – 1}
• nP
• P(1 – P)^{n – 1}
• n^P(1 – P)^{n – 1}

Question 27

Station A uses 32 byte packets to transmit messages to station B using sliding window protocol. The round trip delay between A and B is 40 milliseconds and the bottleneck bandwidth on the path between A and B is 64 kbps. The optimal window size of A is ________.

• 20
• 10
• 30
• 40

Question 28

Let G(x) be generator polynomial used for CRC checking. The condition that should be satisfied by G(x) to correct odd numbered error bits, will be:

• (1 + x) is factor of G(x)
• (1 – x) is factor of G(x)
• (1 + x²) is factor of G(x)
• x is factor of G(x)

Question 29

In a packet switching network, if the message size is 48 bytes and each packet contains a header of 3 bytes. If 24 packets are required to transmit the message, the packet size is ________.

• 2 bytes
• 1 bytes
• 4 bytes
• 5 bytes

Question 30

In RSA public key cryptosystem suppose n = p ∗ q where p and q are primes. (e, n) and (d, n) are public and private keys respectively. Let M be an integer such that o < M < n and φ(n) = (p – 1)(q – 1). Which of the following equations represent RSA public key cryptosystem ?

     I. C ≡ Me(mod n)         
        M ≡ (C)d(mod n) 
    II.ed ≡ 1(mod n)
   III.ed ≡ 1(mod φ(n))           
    IV. C ≡ Me(mod φ(n))
        M ≡ Cd(mod φ(n))

Codes :

• I and II
• I and III
• II and III
• I and IV