GATE Computer Science & IT 2011 — GATE 2011 · CS

In a compiler, keywords of a language are recognized during

A layer-4 firewall (a device that can look at all protocol headers up to the transport layer) CANNOT

If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?

Consider different activities related to email.

• m1: Send an email from a mail client to a mail server

• m2: Download an email from mailbox server to a mail client

• m3: Checking email in a web browser

Which is the application level protocol used in each activity?

A company needs to develop a strategy for software product development for which it has a choice of two programming languages L1 and L2. The number of lines of code (LOC) developed using L2 is estimated to be twice the LOC developed with L1. The product will have to be maintained for five years. Various parameters for the company are given in the table below.

Total cost of the project includes cost of development and maintenance. What is the LOC for L1 for which the cost of the project using L1 is equal to the cost of the project using L2?

Let the time taken to switch from user mode to kernel mode of execution be $t1$ while time taken to switch between two user processes be $t2$. Which of the following is correct?

A company needs to develop digital signal processing software for one of its newest inventions. The software is expected to have 40,000 lines of code. The company needs to determine the effort in person-months using the basic COCOMO model. The multiplicative factor for embedded systems is 2.8, and the exponentiation factor is 1.20. What is the estimated effort in person-months?

Which of the following pairs have DIFFERENT expressive power?

HTML (Hypertext Markup Language) has language element which permits certain actions other than describing the structure of the web document. Which one of the following actions is NOT supported by pure HTML (without any server or client side scripting) pages?

Which one of the following is NOT desired in a good Software Requirement Specifications (SRS) document?

A computer handles several interrupt sources of which of the following are relevant for this question.

• Interrupt from CPU temperature sensor (raises interrupt if CPU temperature is too high)

• Interrupt from Mouse (raises Interrupt if the mouse is moved or a button is pressed)

• Interrupt from Keyboard (raises Interrupt if a key is pressed or released)

• Interrupt from Hard Disk (raises Interrupt when a disk read is completed)

Which one of these will be handled at the HIGHEST priority?

Consider a relational table with a single record for each registered student with the following attributes:

1. Registration_Num: Unique registration number for each registered student

2. UID: Unique identity number, unique at the national level for each citizen

3. BankAccount_Num: Unique account number at the bank. A student can have multiple accounts or joint accounts. This attribute stores the primary account number.

4. Name: Name of the student

5. Hostel_Room: Room number of the hostel

Which of the following options is INCORRECT?

Which one of the following circuits is NOT equivalent to a 2-input XNOR (exclusive NOR) gate?

The simplified SOP (Sum of Product) from the Boolean expression 

$(P + \bar{Q} + \bar{R}) . (P + \bar{Q} + R) . (P + Q +\bar{R})$ is

The minimum number of D flip-flops needed to design a mod-258 counter is

A thread is usually defined as a light weight process because an Operating System (OS) maintains smaller data structure for a thread than for a process. In relation to this, which of the following statement is correct?

K4 and Q3 are graphs with the following structures.

Which one of the following statements is TRUE in relation to these graphs?

If the difference between the expectation of the square of a random variable $\left(E\left[X^2\right]\right)$ and the square of the expectation of the random variable $\left(E\left[X\right]\right)^2$ is denoted by $R$, then

The lexical analysis for a modern computer language such as Java needs the power of which one of the following machine models in a necessary and sufficient sense?

Let the page fault service time be 10 milliseconds(ms) in a computer with average memory access time being 20 nanoseconds (ns). If one page fault is generated every 10^6 memory accesses, what is the effective access time for memory?

Consider a hypothetical processor with an instruction of type LW  R1, 20(R2), which during execution reads a 32-bit word from memory and stores it in a 32-bit register R1. The effective address of the memory location is obtained by the addition of a constant 20 and the contents of register R2. Which of the following best reflects the addressing mode implemented by this instruction for the operand in memory?

What does the following fragment of C program print?

char c[] = "GATE2011";
char *p = c;
printf("%s", p + p[3] - p[1]);

A max-heap is a heap where the value of each parent is greater than or equal to the value of its children. Which of the following is a max-heap?

Let $P$ be a regular language and $Q$ be a context-free language such that $Q \subseteq P$. (For example, let $P$ be the language represented by the regular expression $p^*q^*$ and $Q$ be $\{p^nq^n \mid n \in N\})$. Then which of the following is ALWAYS regular?

An algorithm to find the length of the longest monotonically increasing sequence of numbers in an array $A[0:n-1]$ is given below.Let $L_i$, denote the length of the longest monotonically increasing sequence starting at index $i$ in the array.Initialize $L_{n-1} = 1$.For all $i$ such that $0 \leq i \leq n-2$$L_i = \begin{cases} 1+ L_{i+1} & \quad\text{if A[i] < A[i+1]} \\ 1 & \quad\text{Otherwise}\end{cases}$Finally, the length of the longest monotonically increasing sequence is $\text{Max}(L_0,L_1,\ldots,L_{n-1})$.Which of the following statements is TRUE?

Consider the languages L1, L2 and L3 as given below.

$L_1=\{0^p1^q \mid p,q\in N\},$

$L_2=\{0^p1^q \mid p,q\in N\text{ and }p=q\}$ and

$L_3=\{0^p1^q0^r \mid p,q,r\in N\text{ and }p=q=r\}.$ Which of the following statements is NOT TRUE?

Consider two binary operators $\text{‘} \uparrow \text{’}$  and $\text{‘} \downarrow \text{’}$ with the precedence of operator $\downarrow$ being lower than that of the operator $\text{} \uparrow \text{}$. Operator $\text{} \uparrow \text{}$ is right associative while operator $\downarrow$ is left associative. Which one of the following represents the parse tree for expression $(7 \downarrow 3 \uparrow 4 \uparrow 3 \downarrow 2)$

On a non-pipelined sequential processor, a program segment, which is the part of the interrupt service routine, is given to transfer 500 bytes from an I/O device to memory.

        Initialize the address register

Initialize the count to 500

LOOP: Load a byte from device

Store in memory at address given by address register

Increment the address register

Decrement the count

If count !=0 go to LOOP Assume that each statement in this program is equivalent to a machine instruction which takes one clock cycle to execute if it is a non-load/store instruction. The load-store instructions take two clock cycles to execute.

The designer of the system also has an alternate approach of using the DMA controller to implement the same transfer. The DMA controller requires 20 clock cycles for initialization and other overheads. Each DMA transfer cycle takes two clock cycles to transfer one byte of data from the device to the memory.

What is the approximate speed up when the DMA controller based design is used in a place of the interrupt driven program based input-output?

We are given a set of $n$ distinct elements and an unlabeled binary tree with $n$ nodes. In how many ways can we populate the tree with the given set so that it becomes a binary search tree?

Which one of the following options is CORRECT given three positive integers $x,y$ and $z$, and a predicate

$P\left(x\right) = \neg \left(x=1\right)\wedge \forall y \left(\exists z\left(x=y*z\right) \Rightarrow \left(y=x\right) \vee \left(y=1\right) \right)$

Given $i = \sqrt{-1}$, what will be the evaluation of the definite integral $\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx$?

Consider a database table T containing two columns X and Y each of type integer. After the creation of the table, one record (X=1, Y=1) is inserted in the table.

Let MX and MY denote the respective maximum values of X and Y among all records in the table at any point in time. Using MX and MY, new records are inserted in the table 128 times with X and Y values being MX+1, 2*MY+1 respectively. It may be noted that each time after the insertion, values of MX and MY change.

What will be the output of the following SQL query after the steps mentioned above are carried out?

Consider a finite sequence of random values $X=[x_1,x_2,\dots x_n]$. Let $\mu_x$ be the mean and $\sigma_x$ be the standard deviation of $X$. Let another finite sequence $Y$ of equal length be derived from this as $y_i=a*x_i+b$, where $a$ and $b$ are positive constants. Let $\mu_y$ be the mean and $\sigma_y$ be the standard deviation of this sequence.

Which one of the following statements is INCORRECT?

A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card?

Consider the following table of arrival time and burst time for three processes P0,P1 and P2.

$\small \begin{array}{|c|c|c|} \hline \textbf{Process} & \textbf{Arrival Time} & \textbf{Burst Time}\\\hline \text{P0} & \text{0 ms} & 9 \\\hline \text{P1} & \text{1 ms} & 4 \\\hline \text{P2} & \text{2 ms} & 9 \\\hline \end{array}$

The pre-emptive shortest job first scheduling algorithm is used. Scheduling is carried out only at arrival or completion of processes. What is the average waiting time for the three processes?

Consider evaluating the following expression tree on a machine with load-store architecture in which memory can be accessed only through load and store instructions. The variables $a, b, c, d,$ and $e$ are initially stored in memory. The binary operators used in this expression tree can be evaluated by the machine only when operands are in registers. The instructions produce result only in a register. If no intermediate results can be stored in memory, what is the minimum number of registers needed to evaluate this expression?

Which of the given options provides the increasing order of asymptotic complexity of functions f₁, f₂, f₃ and f₄?

$f_1(n)=2^n$

$f_2(n)=n^{3/2}$

$f_3(n)=n\log_2 n$

$f_4(n)=n^{\log_2 n}$

Four Matrices $M_1 , M_2, M_3$ and $M_4$ of dimensions $p \times q, \ q \times r , \ r \times s$ and $s \times t$ respectively can be multiplied in several ways with different number of total scalar multiplications. For example when multiplied as $((M_1 \times M_2) \times (M_3 \times M_4))$  the total number of scalar multiplications is $pqr + rst + prt$. When multiplied as $(((M_1 \times M_2) \times M_3) \times M_4)$, the total number of scalar multiplications is $pqr + prs + pst$.

If $p=10, q=100, r=20, s=5$ and $t=80$, then the minimum number of scalar multiplications needed is

Consider a relational table $r$ with sufficient number of records, having attributes $A_1, A_2, \dots ,A_n$ and let $1 \leq p \leq n$. Two queries $Q1$ and $Q2$ are given below.

$Q1: \pi_{A_1, \dots ,A_p} \left(\sigma_{A_p=c}\left(r\right)\right)$ where $c$ is a constant

$Q2: \pi_{A_1, \dots ,A_p} \left(\sigma_{c_1 \leq A_p \leq c_2}\left(r\right)\right)$ where $c_1$ and $c_2$ are constants.

The database can be configured to do ordered indexing on $A_p$ or hashing on $A_p$. Which of the following statements is TRUE?

Consider the matrix as given below.

$\begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 7 \\ 0 & 0 & 3\end{bmatrix}$

Which one of the following options provides the CORRECT values of the eigenvalues of the matrix?

Consider an instruction pipeline with four stages (S1, S2, S3 and S4) each with combinational circuit only. The pipeline registers are required between each stage and at the end of the last stage. Delays for the stages and for the pipeline registers are as given in the figure.

What is the approximate speed up of the pipeline in steady state under ideal conditions when compared to the corresponding non-pipeline implementation?

Definition of a language $L$ with alphabet $\{a\}$ is given as following.

$L = \left\{a^{nk} \mid k > 0, \:\: and \:\: n \text{ is a positive integer constant} \right\}$

What is the minimum number of states needed in a DFA to recognize$L$?

An 8KB direct-mapped write-back cache is organized as multiple blocks, each size of 32-bytes. The processor generates 32-bit addresses. The cache controller contains the tag information for each cache block comprising of the following.

1 valid bit

1 modified bit

As many bits as the minimum needed to identify the memory block mapped in the cache.

What is the total size of memory needed at the cache controller to store meta-data (tags) for the cache?

An application loads 100 libraries at start-up. Loading each library requires exactly one disk access. The seek time of the disk to a random location is given as 10 milliseconds. Rotational speed of disk is 6000 rpm. If all 100 libraries are loaded from random locations on the disk, how long does it take to load all libraries? (The time to transfer data from the disk block once the head has been positioned at the start of the block may be neglected)

A deterministic finite automaton (DFA) $D$ with alphabet $Σ=\{a,b\}$ is given below.

Which of the following finite state machines is a valid minimal DFA which accepts the same languages as $D$?

Database table by name Loan_Records is given below.

What is the output of the following SQL query?

SELECT count(*) FROM ( SELECT Borrower, Bank_Manager FROM Loan_Records) AS S NATURAL JOIN (SELECT Bank_Manager, Loan_Amount FROM Loan_Records) AS T );

The following is the comment written for a C function.

A software engineer is assigned the job of doing black box testing. He comes up with the following test cases, many of which are redundant.

Which one of the following options provide the set of non-redundant tests using equivalence class partitioning approach from input perspective for black box testing?

Consider the following recursive C function that takes two arguments.

unsigned int foo(unsigned int n, unsigned int r) { if (n>0) return ((n%r) + foo(n/r, r)); else return 0; }

What is the return value of the function foo when it is called as foo(345, 10)?

Consider the following recursive C function that takes two arguments

unsigned int rer (unsigned int n, unsigned int r) {
  if (n > 0) return (n% r + rer(n/r, r));
  else return 0;
 } 

What is the return value of the function rer when it is called as rer (513, 2) ?

Consider the following circuit involving three D-type flip-flops used in a certain type of counter configuration.

If at some instance prior to the occurrence of the clock edge, P,Q and R have a value 0, 1 and 0 respectively, what shall be the value of PQR after the clock edge?

 Consider the following circuit involving three D-type flip-flops used in a certain type of counter configuration.

If all the flip-flops were reset to 0 at power on, what is the total number of distinct outputs (states) represented by $PQR$ generated by the counter?

Consider a network with five nodes, N1 to N5, as shown as below.

The network uses a Distance Vector Routing protocol. Once the routes have been stabilized, the distance vectors at different nodes are as follows.

N1: (0,1,7,8,4)

N2: (1,0,6,7,3)

N3: (7,6,0,2,6)

N4: (8,7,2,0,4)

N5: (4,3,6,4,0)

Each distance vector is the distance of the best known path at that instance to nodes, N1 to N5, where the distance to itself is 0. Also, all links are symmetric and the cost is identical in both directions. In each round, all nodes exchange their distance vectors with their respective neighbors. Then all nodes update their distance vectors. In between two rounds, any change in cost of a link will cause the two incident nodes to change only that entry in their distance vectors.

The cost of link N2−N3 reduces to 2 (in both directions). After the next round of updates, what will be the new distance vector at node, N3?

Consider a network with five nodes, N1 to N5, as shown as below.

The network uses a Distance Vector Routing protocol. Once the routes have been stabilized, the distance vectors at different nodes are as follows.

N1: (0,1,7,8,4)

N2: (1,0,6,7,3)

N3: (7,6,0,2,6)

N4: (8,7,2,0,4)

N5: (4,3,6,4,0)

Each distance vector is the distance of the best known path at that instance to nodes, N1 to N5, where the distance to itself is 0. Also, all links are symmetric and the cost is identical in both directions. In each round, all nodes exchange their distance vectors with their respective neighbors. Then all nodes update their distance vectors. In between two rounds, any change in cost of a link will cause the two incident nodes to change only that entry in their distance vectors.

In Q52, the cost of link N2−N3 reduces to 2 (in both directions). After the update in the previous question, the link N1−N2 goes down. N2 will reflect this change immediately in its distance vector as cost, ∞. After the NEXT ROUND of update, what will be the cost to N1 in the distance vector of N3 ?

An undirected graph $G(V,E)$ contains $n \: (n>2)$ nodes named $v_1,v_2, \dots, v_n$. Two nodes $v_i, v_j$  are connected if and only if $0 < \mid i-j\mid \leq 2$. Each edge $(v_i,v_j)$ is assigned a weight $i+j$. A sample graph with $n=4$ is shown below.

What will be the cost of the minimum spanning tree (MST) of such a graph with $n$ nodes?

An undirected graph $G(V,E)$ contains $n \: (n>2)$ nodes named $v_1,v_2, \dots, v_n$. Two nodes $v_i, v_j$  are connected if and only if $0 < \mid i-j\mid \leq 2$. Each edge $(v_i,v_j)$ is assigned a weight $i+j$. A sample graph with $n=4$ is shown below.

The length of the path from $v_5$ to $v_6$ in the MST of previous question with $n = 10$ is

Which of the following options is the closest in the meaning to the word below:

Inexplicable

If $Log⁡(P)=(1/2)Log⁡(Q)=(1/3)Log⁡(R)$, then which of the following options is TRUE?

Choose the most appropriate word(s) from the options given below to complete the following sentence.

I contemplated _________ Singapore for my vacation but decided against it.

Choose the most appropriate word from the options given below to complete the following sentence.

If you are trying to make a strong impression on your audience, you cannot do so by being understated, tentative or ________.

Choose the word from the options given below that is most nearly opposite in the meaning to the given word

Amalgamate

Few school curriculum include a unit on how to deal with bereavement and grief, and yet all students at some point in their lives suffer from losses through death and parting.

Based on the above passage which topic would not be included in a unit on bereavement?

P,Q,R and S are four types of dangerous microbes recently found in a human habitat. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within 24 hours of entering the body. The danger to human beings varies proportionately with the toxicity, potency and growth attributed to a microbe shown in the figure below:

A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. Which microbe should the company target in its first attempt?

The variable cost (V) of manufacturing a product varies according to the equation V=4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to the equation F=100/q. How many units should be produced to minimize the total cost (V+F)?

A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of 5th day?

A container originally contains 10 litres of pure spirit. From this container, 1 litre of spirit replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of water and this process is repeated one more time. How much spirit is now left in the container?