GATE 2016 CS Set 2

33) Anarkali digitally signs a message and sends it to Salim. Verification of the signature by Salim requires

Anarkali's public key.
Salim's public key.
Salim's private key.
Anarkali's private key.

Answer: A

Explanation:

We know that in the digital signature, the sender encrypts the message by using her private key and receiver decrypts the message by using the sender's public key. Hence verification of the signature by Salim requires Anarkali's public key. Therefore option (A) will be the right answer.

34) In an Ethernet local area network, which one of the following statements is TRUE?

A station stops to sense the channel once it starts transmitting a frame.
The purpose of the jamming signal is to pad the frames that are smaller than the minimum frame size.
A station continues to transmit the packet even after the collision is detected.
The exponential backoff mechanism reduces the probability of collision on retransmissions.

Answer: D

Explanation:

The exponential backoff mechanism reduces the probability of collision on retransmissions is the true answer. This algorithm does this by selecting the waiting time for each station = k*rtt. Here k will be from 0 to 2n-1. Hence option (D) is the right answer.

35) Identify the correct sequence in which the following packets are transmitted on the network by a host when a browser requests a webpage from a remote server, assuming that the host has just been restarted.

HTTP GET request, DNS query, TCP SYN
DNS query, HTTP GET request, TCP SYN
DNS query, TCP SYN, HTTP GET request
TCP SYN, DNS query, HTTP GET request

Answer: C

Explanation:

Step-1: FIrst we send DNS request which converts the domain name into IP address.
Step-2: Then we established a connection with IP by using TCP Syn.
Step-3: Finally HTTP Get Request will be sent to access the webpage.
Therefore option (C) will be the right answer.

36) A binary relation R on N × N is defined as follows: (a, b)R(c, d) if a ≤ c or b ≤ d. Consider the following propositions:

P: R is reflexive
Q: R is transitive

Which one of the following statements is TRUE?

Both P and Q are true.
P is true and Q is false.
P is false and Q is true.
Both P and Q are false.

Answer: B

Explanation:

Given: (a, b)R(c, d) if a ≤ c or b ≤ d

For Reflexive property: True because (a, b)R(a, b)

For Transitive property: False. Example (5, 2)R(1, 5) and (1, 5)R(4, 1) but not (5, 2)R(4, 1)

Hence option (B) is the right answer.

37) Which one of the following well-formed formulae in predicate calculus is NOT valid?

(∀x p(x) ⇒ ∀x q(x)) ⇒ (∃x ¬p(x) ∨ ∀x q(x))
(∃x p(x) ∨ ∃x q(x)) ⇒ ∃x (p(x) ∨ q(x))
∃x (p(x) ∧ q(x)) ⇒ (∃x p(x) ∧ ∃x q(x))
∀x (p(x) ∨ q(x)) ⇒ (∀x p(x) ∨ ∀x q(x))

Answer: D

Explanation:

If we take a set of natural numbers, then option D will not be satisfied. Example:
Given: ∀x (p(x) ∨ q(x)) ⇒ (∀x p(x) ∨ ∀x q(x)). Then
For all x ( x is even no or x is odd no ) ⟹ For all x( x is even no ) or For all x ( x is odd no)
According to the set of natural numbers LHS is true, but RHS is not satisfied because not all natural numbers are even or odd.

Therefore option (D) will be the right answer.

38. Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of 9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following statements:

I. Each compound in U \ S reacts with an odd number of compounds.
II. At least one compound in U \ S reacts with an odd number of compounds.
III. Each compound in U \ S reacts with an even number of compounds.

Which one of the above statements is ALWAYS TRUE?

Only I
Only II
Only III
None

Answer: B

Explanation:

Suppose an undirected graph G with each of the 23 different compounds as a vertex, and if two compounds react, then there will be an edge between the corresponding vertices. As there are 9 compounds in S⊆U such that each of the compounds, the graph G will have at least 9 odd vertices. We know that in an undirected graph, there is an even number of odd vertices. Thus, there exist at least one compound in U/S that reacts with an odd number of compounds. Therefore option (B) will be the right answer.

39) The value of the expression 13⁹⁹ (mod 17), in the range 0 to 16, is ______________.

Answer: A

Explanation:

According to Fermat's Little Theorem, if p is prime and a should not devide p then

a^p-1 ? 1 mod p.

From question, we get p = 17 and a = 13

So, 13^17-1 ? 1 mod 17 <=> 13¹⁶ ? 1 mod 17

∴ 13⁹⁶ = (13¹⁶)⁶ ? 1 mod 17

Hence, 13⁹⁹ = 13⁹⁶ * 13³ ? 133 mod 17 ? 2197 mod 17 = 4

Therefore option (A) is the right answer.

40) Suppose the functions F and G can be computed in 5 and 3 nanoseconds by functional units U_F and U_G, respectively. Given two instances of U_F and two instances of U_G, it is required to implement the computation F(G(X_i )) for 1 ≤ i ≤ 10. Ignoring all other delays, the minimum time required to complete this computation is ______________ nanoseconds.

Answer: C

Explanation:

According to the question, U_F takes 5 ns, and U_G takes 3 ns only. Calculations = 10 and we have 2 instances of U_F and U_G respectively. So, U_F can be done in: (10*5) / 2 = 50/2 = 25 ns.
Now, for the starts, U_F needs to wait for U_G output for 3 ns and rest all are pipelined. Hence there is no more wait happens. So, answer is: 25 + 3 = 28ns

Therefore option (C) is the right answer.

GATE 2016 CS Set 2-1
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