Gate IT 2007

Question 11

The address sequence generated by tracing a particular program executing in a pure demand paging system with 100 bytes per page is
0100, 0200, 0430, 0499, 0510, 0530, 0560, 0120, 0220, 0240, 0260, 0320, 0410.
Suppose that the memory can store only one page and if x is the address which causes a page fault then the bytes from addresses x to x + 99 are loaded on to the memory.
How many page faults will occur ?

• 0
• 4
• 7
• 8

Question 12

Consider the following statements about the timeout value used in TCP. i. The timeout value is set to the RTT (Round Trip Time) measured during TCP connection establishment for the entire duration of the connection. ii. Appropriate RTT estimation algorithm is used to set the timeout value of a TCP connection. iii. Timeout value is set to twice the propagation delay from the sender to the receiver. Which of the following choices hold?

• (i) is false, but (ii) and (iii) are true
• (i) and (iii) are false, but (ii) is title
• (i) and (ii) are false, but (iii) is true
• (i), (ii) and (iii) are false

Question 13

Consider a TCP connection in a state where there are no outstanding ACKs. The sender sends two segments back to back. The sequence numbers of the first and second segments are 230 and 290 respectively. The first segment was lost, but the second segment was received correctly by the receiver. Let X be the amount of data carried in the first segment (in bytes), and Y be the ACK number sent by the receiver. The values of X and Y (in that order) are

• 60 and 290
• 230 and 291
• 60 and 231
• 60 and 230

Question 14

Consider the following two statements: i. A hash function (these are often used for computing digital signatures) is an injective function. A. encryption technique such as DES performs a permutation on the elements of its input alphabet. Which one of the following options is valid for the above two statements?

• Both are false
• Statement (i) is true and the other is false
• Statement (ii) is true and the other is false
• Both are true

Question 15

Exponentiation is a heavily used operation in public key cryptography. Which of the following options is the tightest upper bound on the number of multiplications required to compute bⁿ mod m,0≤b,n≤m ?

• O(logn)
• O(√n)
• O(n/logn)
• O(n)

Question 16

Consider the XML document fragment given below:

Consider the XPath expression: *[not (self ) : : TOC]
What would be the result of the given XPath expression when the current node is Book?

• The Title and Content elements
• The Content and TOC elements
• The Title and TOC elements
• The Title, Content and TOC elements

Question 17

Which one of these first-order logic formula is valid?

• ∀x(P(x) => Q(x)) => (∀xP(x) => ∀xQ(x))
• ∃x(P(x) ∨ Q(x)) => (∃xP(x) => ∃xQ(x))
• ∃x(P(x) ∧ Q(x)) <=> (∃xP(x) ∧ ∃xQ(x))
• ∀x∃y P(x, y) => ∃y∀x P(x, y)

Question 18

Consider the XML document fragment given below:

With reference to the HTML lines given above, consider the following statements.
1. Clicking on the point <80, 75> does not have any effect.
2. The web browser can identify the area applicable to the mouse-click within the image and the subsequent action to be taken without additional responses from the web server.
3. The dots in the cgi-bin URL will be resolved by the web browser before it is sent to the web server
4. The "fd.html" request when sent to the web server will result in a GET request.
Exactly how many of the statements given above are correct?

• 0
• 1
• 2
• 3

Question 19

The trapezoidal method is used to evaluate the numerical value of [Tex]\\int_0^1 $e^x$\\,dx[/Tex]. Consider the following values for the step size h.
i. 10^-2
ii. 10^-3
iii. 10^-4
iv. 10^-5
For which of these values of the step size h, is the computed value guaranteed to be correct to seven decimal places. Assume that there are no round-off errors in the computation.

• (iv) only
• (iii) and (iv) only
• (ii), (iii) and (iv) only
• (i), (ii), (iii) and (iv)

Question 20

A partial order P is defined on the set of natural numbers as follows. Here x/y denotes integer division.
i. (0, 0) ∊ P.
ii. (a, b) ∊ P if and only if a % 10 ≤ b % 10 and (a/10, b/10) ∊ P.
Consider the following ordered pairs:
i. (101, 22)
ii. (22, 101)
iii. (145, 265)
iv. (0, 153)
Which of these ordered pairs of natural numbers are contained in P?

• (i) and (iii)
• (ii) and (iv)
• (i) and (iv)
• (iii) and (iv)