Gate IT 2007

Question 61

Consider the following implications relating to functional and multivalued dependencies given below, which may or may not be correct.
i. If A ↠ B and A ↠ C then A → BC
ii. If A → B and A → C then A ↠ BC
iii. If A ↠ BC and A → B then A → C
iv. If A → BC and A → B then A ↠ C
Exactly how many of the above implications are valid?

• 0
• 1
• 2
• 3

Question 62

Consider the following relation schemas :

• b-Schema = (b-name, b-city, assets)
• a-Schema = (a-num, b-name, bal)
• d-Schema = (c-name, a-number)

Let branch, account and depositor be respectively instances of the above schemas. Assume that account and depositor relations are much bigger than the branch relation. Consider the following query: П_c-name (σ_{b-city = "Agra" ⋀ bal < 0} (branch ⋈ (account ⋈ depositor) Which one of the following queries is the most efficient version of the above query ?

• П_c-name (σ_{bal < 0} (σ_{b-city = "Agra"} branch ⋈ account) ⋈ depositor)
• П_c-name (σ_{b-city = "Agra"}branch ⋈ (σ_{bal < 0} account ⋈ depositor))
• П_c-name (σ_{b-city = "Agra"} branch ⋈ σ_{b-city = "Agra" ⋀ bal < 0} account) ⋈ depositor)
• П_c-name (σ_{b-city = "Agra" ⋀ bal < 0} account ⋈ depositor))

Question 63

Consider the following clauses: i. Not inherently suitable for client authentication. ii. Not a state sensitive protocol. iii. Must be operated with more than one server. iv. Suitable for structured message organization. v. May need two ports on the serve side for proper operation. The option that has the maximum number of correct matches is

• IMAP-(i), FTP-(ii), HTTP-(iii), DNS-(iv), POP3-(v)
• FTP-(i), POP3-(ii), SMTP-(iii), HTTP-(iv), IMAP-(v)
• POP3-(i), SMTP-(ii), DNS-(iii), IMAP-(iv), HTTP-(v)
• SMTP-(i), HTTP-(ii), IMAP-(iii), DNS-(iv), FTP-(v)

Question 64

Your are given the following four bytes : 10100011            00110111            11101001            10101011 Which of the following are substrings of the base 64 encoding of the above four bytes ?

• zdp
• fpq
• qwA
• oze

Question 65

Consider the regular expression R = (a + b)* (aa + bb) (a + b)*<br> Which of the following non-deterministic finite automata recognizes the language defined by the regular expression R? Edges labeled λ denote transitions on the empty string.

• A
• B
• C
• D

Question 66

Consider the regular expression R = (a + b)* (aa + bb) (a + b)* Which deterministic finite automaton accepts the language represented by the regular expression R ?

• A
• B
• C
• D

Question 67

Consider the regular expression R = (a + b)* (aa + bb) (a + b)*<br> Which one of the regular expressions given below defines the same language as defined by the regular expression R?

• (a(ba)* + b(ab)*)(a + b)⁺
• (a(ba)* + b(ab)*)*(a + b)*
• (a(ba)* (a + bb) + b(ab)*(b + aa))(a + b)*
• (a(ba)* (a + bb) + b(ab)*(b + aa))(a + b)⁺

Question 68

Consider a token ring topology with N stations (numbered 1 to N) running token ring protocol where the stations are equally spaced. When a station gets the token it is allowed to send one frame of fixed size. Ring latency is t_p, while the transmission time of a frame is t_t. All other latencies can be neglected.
The maximum utilization of the token ring when t_t =3 ms, t_p = 5 ms, N = 10 is

• 0.545
• 0.6
• 0.857
• 0.961

Question 69

Consider a token ring topology with N stations (numbered 1 to N) running token ring protocol where the stations are equally spaced. When a station gets the token it is allowed to send one frame of fixed size. Ring latency is t_p, while the transmission time of a frame is t_t. All other latencies can be neglected.
The maximum utilization of the token ring when t_t = 5 ms, t_p = 3 ms, N = 15 is :

• 0.545
• 0.655
• 0.9375
• 0.961

Question 70

Consider the sequence <x_n>, n>= 0 defined by the recurrence relation x_{n + 1} = c . x_n²- 2, where c > 0. Suppose there exists a non-empty, open interval (a, b) such that for all x₀ satisfying a < x₀ < b, the sequence converges to a limit. The sequence converges to the value?

• (1 + (1 + 8c)^1/2)/2c
• (1 - (1 + 8c)^1/2)/2c
• 2
• 2/(2c-1)