Suppose there are two coins. The first coin gives heads with probability 5/8 when tossed, while the second coin gives heads with probability 1/4. One of the two coins is picked up at random with equal probability and tossed. What is the probability of obtaining heads ?

Let A be the What is the maximum value of x^TAx where the maximum is taken over all x that are the unit eigenvectors of A?

Consider a weighted undirected graph with positive edge weights and let uv be an edge in the graph. It is known that the shortest path from the source vertex s to u has weight 53 and the shortest path from s to v has weight 65. Which one of the following statements is always true?

In the Spiral model of software development, the primary determinant in selecting activities in each iteration is

Which of the following systems is a most likely candidate example of a pipe and filter architecture ?

A processor takes 12 cycles to complete an instruction I. The corresponding pipelined processor uses 6 stages with the execution times of 3, 2, 5, 4, 6 and 2 cycles respectively. What is the asymptotic speedup assuming that a very large number of instructions are to be executed?

Which of the following input sequences for a cross-coupled R-S flip-flop realized with two NAND gates may lead to an oscillation?

The following circuit implements a two-input AND gate using two 2-1 multiplexers. What are the values of X₁, X₂, X₃ ?

Consider an ambiguous grammar G and its disambiguated version D. Let the language recognized by the two grammars be denoted by L(G) and L(D) respectively. Which one of the following is true ?

Processes P1 and P2 use critical_flag in the following routine to achieve mutual exclusion. Assume that critical_flag is initialized to FALSE in the main program.

        get_exclusive_access ( ) 
{ 
  if (critical _flag == FALSE) { 
      critical_flag = TRUE ; 
      critical_region () ; 
      critical_flag = FALSE; 
      } 
}

Consider the following statements. i. It is possible for both P1 and P2 to access critical_region concurrently. ii. This may lead to a deadlock.

Which of the following holds?

Let a memory have four free blocks of sizes 4k, 8k, 20k, 2k. These blocks are allocated following the best-fit strategy. The allocation requests are stored in a queue as shown below.

The time at which the request for J₇ will be completed will be

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. 

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?

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

Consider the following two statements:
(i) A hash function (these are often used for computing digital signatures) is an injective function.
(ii) An 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?

The minimum positive integer p such that 3^p modulo 17 = 1 is

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?

A firewall is to be configured to allow hosts in a private network to freely open TCP connections and send packets on open connections. However, it will only allow external hosts to send packets on existing open TCP connections or connections that are being opened (by internal hosts) but not allow them to open TCP connections to hosts in the private network. To achieve this the minimum capability of the firewall should be that of

Given below are HTML lines,

With reference to the HTML lines given above, consider the following statements.
(i) Clicking on the point <80, 75> does not have any effect.
(ii) 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.
(iii) The dots in the cgi-bin URL will be resolved by the web browser before it is sent to the web server.
(iv) 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?

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?

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