Computer Science And Information Technology - CS 2013 GATE Paper (Practice Test) - GATE

Choose the grammatically INCORRECT sentence:

What will be the maximum sum of 44, 42, 40, ... ?

Q. No. 6 – 10 Carry Two Marks Each

Q.

Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at
random. What is the probability that the selected number is not divisible by 7?

A tourist covers half of his journey by train at 60 km/h, half of the remainder by bus at 30
km/h and the rest by cycle at 10 km/h. The average of the tourist in km/h during his entire
journey is

Find the sum of the expression

The current erection cost of a structure is Rs. 13,200. If the labour wages per day increase by
1/5 of the current wages and the working hours decrease by 1/24 of the current period, then
the new cost of erection in Rs. is

After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just
before committing suicide, he came across a spider attempting tirelessly to have its net. Time
and again, the spider failed but that did not deter it to refrain from making attempts. Such
attempts by the spider made Bruce curious. Thus, Bruce started observing the nearimpossible
goal of the spider to have the net. Ultimately, the spider succeeded in having its
net despite several failures. Such act of the spider encouraged Bruce not to commit suicide.
And then, Bruce went back again and won many a battle, and the rest is history.

Which one of the following assertions is best supported by the above information?

Q. No. 11 – 35 Carry One Mark Each

Q.

Consider an undirected random graph of eight vertices. The probability that there is an edge
between a pair of vertices is ½. What is the expected number of unordered cycles of length
three?

Which of the following statements is/are TRUE for undirected graphs?
P: Number of odd degree vertices is even.
Q: Sum of degrees of all vertices is even.

Function f is known at the following points:

Which one of the following functions is continuous at x = 3 ?

Which one of the following expressions does NOT represent exclusive NOR of x and y?

In a k-way set associative cache, the cache is divided into v sets, each of which consists of k
lines. The lines of a set are placed in sequence one after another. The lines in set s are
sequenced before the lines in set (s+1). The main memory blocks are numbered 0 onwards.
The main memory block numbered j must be mapped to any one of the cache lines from

What is the time complexity of Bellman-Ford single-source shortest path algorithm on a
complete graph of n vertices?

Which of the following statements are TRUE?
(1) The problem of determining whether there exists a cycle in an undirected graph is in P.
(2) The problem of determining whether there exists a cycle in an undirected graph is in NP.
(3) If a problem A is NP-Complete, there exists a non-deterministic polynomial time
algorithm to solve A.

Which of the following statements is/are FALSE?
(1) For every non-deterministic Turing machine, there exists an equivalent deterministic
Turing machine.
(2) Turing recognizable languages are closed under union and complementation.
(3) Turing decidable languages are closed under intersection and complementation
(4) Turing recognizable languages are closed under union and intersection.

Three concurrent processes X, Y, and Z execute three different code segments that access and
update certain shared variables. Process X executes the P operation (i.e., wait) on semaphores
a, b and c; process Y executes the P operation on semaphores b, c and d; process Z executes
the P operation on semaphores c, d, and a before entering the respective code segments. After
completing the execution of its code segment, each process invokes the V operation (i.e.,
signal) on its three semaphores. All semaphores are binary semaphores initialized to one.
Which one of the following represents a deadlock-free order of invoking the P operations by
the processes?

An index is clustered, if

Assume that source S and destination D are connected through two intermediate routers
labeled R. Determine how many times each packet has to visit the network layer and the data
link layer during a transmission from S to D.

The transport layer protocols used for real time multimedia, file transfer, DNS and
email, respectively are

Using public key cryptography, X adds a digital signature σ to message M, encrypts <M,
σ >, and sends it to Y, where it is decrypted. Which one of the following sequences of keys is
used for the operations?

Match the problem domains in Group I with the solution technologies in Group II.

A scheduling algorithm assigns priority proportional to the waiting time of a process. Every
process starts with priority zero(the lowest priority). The scheduler re-evaluates the process
priorities every T time units and decides the next process to schedule. Which one of the
following is TRUE if the processes have no I/O operations and all arrive at time zero?

What is the maximum number of reduce moves that can be taken by a bottom-up parser for a
grammar with no epsilon- and unit-production (i.e., of type A → and A→a) to parse a
string with n tokens?

Consider the languages and . Which one of the following represents  ?

Which one of the following is the tightest upper bound that represents the time complexity of
inserting an object into a binary search tree of n nodes?

Which one of the following is the tightest upper bound that represents the number of swaps
required to sort n numbers using selection sort?

In the following truth table, V = 1 if and only if the input is valid.

What function does the truth table represent?

The smallest integer than can be represented by an 8-bit number in 2’s complement form is

Which one of the following does NOT equal

Suppose p is number of cars per minute passing through a certain road junction between 5
PM and 6PM, and p has a Poisson distribution with mean 3. What is the probability of
observing fewer than 3 cars during any given minute in this interval?

A binary operation on a set of integers is defined as . Which one of the
following statements is TRUE about ?

Q. No. 36 – 65 Carry Two Marks Each

Q.

Which one of the following is NOT logically equivalent to

A RAM chip has a capacity of 1024 words of 8 bits each (1K x 8) . The number of 2 x 4
decoders with enable line needed to construct a 16K x 16 RAM from1K x 8 RAM is

Consider an instruction pipeline with five stages without any branch prediction: Fetch
Instruction (FI), Decode Instruction (DI), Fetch Operand (FO), Execute Instruction (EI) and
Write Operand (WO). The stage delays for FI, DI, FO, EI and WO are 5 ns, 7 ns, 10 ns, 8 ns
and 6 ns, respectively. There are intermediate storage buffers after each stage and the delay of
each buffer is 1 ns. A program consisting of I2 instructions  I₁ , I₂ , I₃ ,......I is executed in this
pipelined processor. Instruction  I₄ is the only branch instruction and its branch target is 9 I . If
the branch is taken during the execution of this program, the time (in ns) needed to complete
the program is

Consider the following operation along with Enqueue and Dequeue operations on queues,
where k is a global parameter

MultiDequeue Q {
m k
while Q is not empty and m 0 {
Dequeue Q
m m 1
}
}

What is the worst case time complexity of a sequence of n queue operations on an initially
empty queue?

The preorder traversal sequence of a binary search tree is 30, 20, 10, 15, 25, 23, 39, 35, 42.
Which one of the following is the postorder traversal sequence of the same tree?

What is the return value of  f(p,p) if the value of p is initialized to 5 before the call? Note
that the first parameter is passed by reference, whereas the second parameter is passed by
value.
int f (int &x, int c) {
c= c- 1;
if (c= 0) return 1;
x = x+ 1;
return f (x,c )* x;
}

Which of the following is/are undecidable?

Consider the following two sets of LR(1) items of an LR(1) grammar

Which of the following statements related to merging of the two sets in the corresponding
LALR parser is/are FALSE?

1.  Cannot be merged since look aheads are different
2. Can be merged but will result in S–R conflict
3. Can be merged but will result in R–R conflict
4. Cannot be merged since goto on c will lead to two different sets

A certain computation generates two arrays a and b such that a[i] = f (i) for 0 i < n and
b[i] = g (a [i]) for 0 i < n . Suppose this computation is decomposed into two concurrent
processes X and Y such that X computes the array a and Y computes the array b. The
processes employ two binary semaphores R and S, both initialized to zero. The array a is
shared by the two processes. The structures of the processes are shown below.

Process X:
private i;
for (i=0; i<n; i++) {
a[i] = f(i);
ExitX(R, S);
}

Process Y:
private i;
for (i=0; i<n; i++) {
EntryY(R, S);
b[i] = g(a[i]);
}

Which one of the following represents the CORRECT implementations of ExitX and EntryY?

The following figure represents access graphs of two modules M1 and M2. The filled circles
represent methods and the unfilled circles represent attributes. IF method m is moved to
module M2 keeping the attributes where they are, what can we say about the average
cohesion and coupling between modules in the system of two modules?

In an IPv4 datagram, the M bit is 0, the value of HLEN is 10, the value of total length is 400
and the fragment offset value is 300. The position of the datagram, the sequence numbers of
the first and the last bytes of the payload, respectively are

Determine the maximum length of cable (in km) for transmitting data at a rate of 500 Mbps in
an Ethernet LAN with frames of size 10,000 bits. Assume the signal speed in the cable to be
2,00,000 km/s

Consider the following relational schema.
Students(rollno: integer, sname: string)
Courses(courseno: integer, cname: string)
Registration(rollno: integer, courseno; integer, percent: real)
Which of the following queries are equivalent to this query in English?
“Find the distinct names of all students who score more than 90% in the course numbered
107”
(I) SELECT DISTINCT S.sname
FROM Students as S, Registration as R
WHERE R.rollno=S.rollno AND R.Courseno=107 AND R.percent>90

A shared variable x, initialized to zero, is operated on by four concurrent processes W, X, Y, Z as
follows. Each of the processes W and X reads x from memory, increments by one, stores it to
memory, and then terminates. Each of the processes Y and Z reads x from memory, decrements by
two, stores it to memory, and then terminates. Each process before reading x invokes the P
operation (i.e., wait) on a counting semaphore S and invokes the V operation (i.e., signal) on the
semaphore S after storing x to memory. Semaphore S is initialized to two. What is the maximum
possible value of x after all processes complete execution?

Consider the DFA given below.

Which of the following are FALSE?

1. Complement of L(A) is context–free

2.  L(A) = L((11* 0 + 0)(0 +1)* 0 *1*)
3. For the language accepted by A, A is the minimal DFA
4. A accepts all strings over {0, 1} of length at least 2

Consider the following languages

Which one of the following statements is FALSE?

Consider the following function

int unknown (int n) {
int i, j, k 0;
for (i =n/2; i<= n; i++)
for (j= 2; j<= n; j= j* 2)
k= k+ n / 2;
return k ;
}
The return value of the function is

The number of elements that can be sorted in time using heap sort is

Consider a hard disk with 16 recording surfaces (0 −15) having 16384 cylinders (0 −16383)
and each cylinder contains 64 sectors (0 − 63) . Data storage capacity in each sector is 512
bytes. Data are organized cylinder–wise and the addressing format is <cylinder no., sector
no.>. A file of size 42797 KB is stored in the disk and the starting disk location of the file is
<1200, 9, 40>. What is the cylinder number of the last sector of the file, if it is stored in a
contiguous manner?

Consider the following sequence of micro–operations

Which one of the following is a possible operation performed by this sequence?

The line graph L(G) of a simple graph G is defined as follows:
       • There is exactly one vertex v(e) in L(G) for each edge e in G.
      • For any two edges e and e’ in G, L(G) has an edge between v(e) and v(e’), if and only if e
and e’ are incident with the same vertex in G.
Which of the following statements is/are TRUE?

(P) The line graph of a cycle is a cycle.
(Q) The line graph of a clique is a clique.
(R) The line graph of a planar graph is planar.
(S) The line graph of a tree is a tree.

What is the logical translation of the following statement?
“None of my friends are perfect.”

The procedure given below is required to find and replace certain characters inside an input
character string supplied in array A. The characters to be replaced are supplied in array oldc,
while their respective replacement characters are supplied in array newc. Array A has a fixed
length of five characters, while arrays oldc and newc contain three characters each. However, the
procedure is flawed

void find _ and _ replace (char *A, char *oldc, char * newc ) {
for (int i= 0; i <5; i++)
for (int j =0; j <3; j++)
if (A [i] ==oldc[ j])  A [i]= newc [j] ;
}
The procedure is tested with the following four test cases
(1) oldc = "abc", newc = "dab"            (2) oldc = "cde", newc = "bcd"
(3) oldc = "bca", newc = "cda"            (4) oldc = "abc", newc = "bac"

Q.

The tester now tests the program on all input strings of length five consisting of characters
‘a’, ‘b’, ‘c’, ‘d’ and ‘e’ with duplicates allowed. If the tester carries out this testing with the
four test cases given above, how many test cases will be able to capture the flaw?

The procedure given below is required to find and replace certain characters inside an input
character string supplied in array A. The characters to be replaced are supplied in array oldc,
while their respective replacement characters are supplied in array newc. Array A has a fixed
length of five characters, while arrays oldc and newc contain three characters each. However, the
procedure is flawed

void find _ and _ replace (char *A, char *oldc, char * newc ) {
for (int i= 0; i <5; i++)
for (int j =0; j <3; j++)
if (A [i] ==oldc[ j])  A [i]= newc [j] ;
}
The procedure is tested with the following four test cases
(1) oldc = "abc", newc = "dab"            (2) oldc = "cde", newc = "bcd"
(3) oldc = "bca", newc = "cda"            (4) oldc = "abc", newc = "bac"

Q.

If array A is made to hold the string “abcde”, which of the above four test cases will be
successful in exposing the flaw in this procedure?

The following code segment is executed on a processor which allows only register operands in
its instructions. Each instruction can have almost two source operands and one destination operand.
Assume that all variables are dead after this code segment

c= a+ b;
d = c * a;
e= c+ a;
x =c *c;
if ( x >a) {
y= a * a;
}
else {
d =d * d;
e =e * e;
}
 

Q.

Suppose the instruction set architecture of the processor has only two registers. The only allowed
compiler optimization is code motion, which moves statements from one place to another while
preserving correctness. What is the minimum number of spills to memory in the compiled code?

The following code segment is executed on a processor which allows only register operands in
its instructions. Each instruction can have almost two source operands and one destination operand.
Assume that all variables are dead after this code segment

c= a+ b;
d = c * a;
e= c+ a;
x =c *c;
if ( x >a) {
y= a * a;
}
else {
d =d * d;
e =e * e;
}

Q.

What is the minimum number of registers needed in the instruction set architecture of the
processor to compile this code segment without any spill to memory? Do not apply any
optimization other than optimizing register allocation

Relation R has eight attributes ABCDEFGH. Fields of R contain only atomic values.
F ={CH→G, A→BC, B→CFH, E→A, F→EG} is a set of functional dependencies (FDs) so that F+ is exactly the set of FDs that hold for R

Q.

How many candidate keys does the relation R have?

Relation R has eight attributes ABCDEFGH. Fields of R contain only atomic values.
F ={CH→G, A→BC, B→CFH, E→A, F→EG} is a set of functional dependencies (FDs) so that F+ is exactly the set of FDs that hold for R

Q.

The relation R is

A computer uses 46–bit virtual address, 32–bit physical address, and a three–level paged page
table organization. The page table base register stores the base address of the first–level table
( T₁) ,which occupies exactly one page. Each entry of T1 stores the base address of a page of the
second–level table ( T2) . Each entry of T₂ stores the base address of a page of the third–level table
( T₃)  Each entry of T₃ stores a page table entry (PTE). The PTE is 32 bits in size. The processor
used in the computer has a 1 MB 16 way set associative virtually indexed physically tagged cache.
The cache block size is 64 bytes.

Q.

What is the size of a page in KB in this computer?

A computer uses 46–bit virtual address, 32–bit physical address, and a three–level paged page
table organization. The page table base register stores the base address of the first–level table
( T₁) ,which occupies exactly one page. Each entry of T1 stores the base address of a page of the
second–level table ( T2) . Each entry of T₂ stores the base address of a page of the third–level table
( T₃)  Each entry of T₃ stores a page table entry (PTE). The PTE is 32 bits in size. The processor
used in the computer has a 1 MB 16 way set associative virtually indexed physically tagged cache.
The cache block size is 64 bytes.

Q.

What is the minimum number of page colours needed to guarantee that no two synonyms map to
different sets in the processor cache of this computer?