Gate IT 2008

Question 11

For problems X and Y, Y is NP-complete and X reduces to Y in polynomial time. Which of the following is TRUE?

• If X can be solved in polynomial time, then so can Y
• X is NP-complete
• X is NP-hard
• X is in NP, but not necessarily NP-complete

Question 12

Match the programming paradigms and languages given in the following table.

• I-c, II-d, III-b, IV-a
• I-a, II-d, III-c, IV-b
• I-d, II-c, III-b, IV-a
• I-c, II-d, III-a, IV-b

Question 13

A processor that has carry, overflow and sign flag bits as part of its program status word (PSW) performs addition of the following two 2\'s complement numbers 01001101 and 11101001. After the execution of this addition operation, the status of the carry, overflow and sign flags, respectively will be:

• 1, 1, 0
• 1, 0, 0
• 0, 1, 0
• 1, 0, 1

Question 14

A paging scheme uses a Translation Look-aside Buffer (TLB). A TLB-access takes 10 ns and a main memory access takes 50 ns. What is the effective access time(in ns) if the TLB hit ratio is 90% and there is no page-fault?

• 54
• 60
• 65
• 75

Question 15

Find if the following statements in the context of software testing are TRUE or FALSE.
(S1) Statement coverage cannot guarantee execution of loops in a program under test.
(S2) Use of independent path testing criterion guarantees execution of each loop in a program under test more than once.

• True, True
• True, False
• False, True
• False, False

Question 16

Which of the following is TRUE only of XML but NOT HTML?

• It is derived from SGML
• It describes content and layout
• It allows user defined tags
• It is restricted only to be used with web browsers

Question 17

Provide the best matching between the entries in the two columns given in the table below:

• I-a, II-d, III-c, IV-b
• I-b, II-d, III-c, IV-a
• I-a, II-c, III-d, IV-b
• I-b, II-c, III-d, IV-a

Question 18

Which of the following first order formula is logically valid? Here α(x) is a first order formula with x as a free variable, and β is a first order formula with no free variable.

• [β→(∃x,α(x))]→[∀x,β→α(x)]
• [∃x,β→α(x)]→[β→(∀x,α(x))]
• [(∃x,α(x))→β]→[∀x,α(x)→β]
• [(∀x,α(x))→β]→[∀x,α(x)→β]

Question 19

Which of the following is the negation of [∀ x, α → (∃y, β → (∀ u, ∃v, y))]

• [∃ x, α → (∀y, β → (∃u, ∀ v, y))]
• [∃ x, α → (∀y, β → (∃u, ∀ v, ¬y))]
• [∀ x, ¬α → (∃y, ¬β → (∀u, ∃ v, ¬y))]
• [∃ x, α ʌ (∀y, β ʌ (∃u, ∀ v, ¬y))]

Question 20

What is the probability that in a randomly chosen group of r people at least three people have the same birthday?

• A
• B
• C
• D