Computer Science And Information Technology - CS 2016 GATE Paper (Practice Test) - GATE

If ‘relftaga’ means carefree, ‘otaga’ means careful and ‘fertaga’ means careless, which of the following could mean ‘aftercare’?

A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in square units) after the removal is __________.

Q. 6 – Q. 10 carry two marks each.

Q.

A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive. Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The table below shows the numbers of each razor sold in each quarter of a year.

Which product contributes the greatest fraction to the revenue of the company in that year?

Indian currency notes show the denomination indicated in at least seventeen languages. If this is not an indication of the nation’s diversity, nothing else is.

Which of the following can be logically inferred from the above sentences?

Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q

Which of the following can be logically inferred from the above statements?

(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set

If f(x) = 2x⁷+3x−5, which of the following is a factor of f(x)?

In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for failure. The load for which the failure will happen in 5000 cycles is ________.

Q.11-Q.35carryonemarkeach.

Q.

Let p,q, r; s represent thefollowing propositions.
p: x {8,9,10,11,12}
q: x is acompositenumber
r: x is aperfectsquare
s: x is aprimenumber

Let a_n be thenumberof n-bit strings that do NOT contain two consecutive 1s.Which one of
the following is the recurrence relation for a_n?

A probabilitydensity function on the interval [a,1] is given by1/x² and outside this interval the value of the function is zero.The value of a is _____________.

Two eigenvalues of a 3 x 3 real matrix P are   and 3 .The determinant of P is ______________.

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

The 16-bit 2’s complement representation of an integer is1111 1111 1111 0101; its decimal representation is  ______________.

We want to design asynchronous counter that counts the sequence 0-1-0-2-0-3 and then repeats. The minimum number of J-K flip-flops required to implement this counter is ____________.

A processor can support a maximum memory of 4GB,where the memory is word - addressable
(a word consists of two bytes).The size of the address bus of the processor is at least _________ bits.

A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are
performed efficiently. Which one of the following statements is CORRECT (n refers to the
number of items in the queue)?

Consider the following directed graph:

The number of different topological orderings of the vertices of the graph is _____________ .

Consider the following C program.

void f(int,short);
void main()
{
int i=100;
short s=12;
short *p=&s;
__________ ;//calltof()
}

Which one of the following expressions,when placed in the blank above, will NOT result in
a type checking error?

The worst case running times of Insertion sort, Merge sort and Quick sort, respectively,are:

Let G be aweighted connected undirected graph with distinct positive edge weights.If every edge weight is increased by the same value,then which of the following statements is/are TRUE?

P: Minimum spanning tree of G does notchange
Q: Shortest path between any pair of vertices does not change

Consider the follwing  C Program.

#include<stdio.h>
void mystery(int*ptra,int*ptrb){
int *temp;
temp =ptrb;
ptrb =ptra;
ptra =temp;
}
int main(){
int a=2016,b=0,c=4,d=42;
mystery(&a, &b);
if (a<c)
mystery(&c, &a);
mystery(&a, &d);
printf("%d ", a);
}

The output of the program is _____________ .

Which of the following decision problems are undecidable?

Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive 0s and two consecutive 1s?

Consider the following code segment.
x =u-t;
y =x*v;
x =y+w;
y =t-z;
y =x*y;
The minimum number of total variables required to convert the above code segment to static single assignment form is ______________ .

What type of memory is volatile ?

Which of the following is NOT a super key in a relational schema with attributes V,W, X, Y, Z and primarykey V Y?

Which one of the following is NOT a part of the ACID properties of database transactions?

A database of research articles in a journal uses the following schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE)
The primary key is(VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following functional dependenciesexist in the schema.

(VOLUME, NUMBER, STARTPAGE, ENDPAGE) → TITLE
(VOLUME, NUMBER)                                        → YEAR
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) → PRICE
The database is redesigned to use the following schemas.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE)
(VOLUME, NUMBER, YEAR)
Which is the weakest normal form that the new database satisfies,but the old one does not?

Which one of the following protocols is NOT used to resolve one form of address to another one?

Which of the following is/are example(s) of stateful application layer protocols?
(i) HTTP
(ii) FTP
(iii) TCP
(iv) POP3

Q.36-Q.65 carry two marks each.

Q.

The coefficient of x¹² in (x³+x⁴+x⁵+x⁶+... )³ is ____________ .

Consider the recurrence relation a₁ = 8, a_n = 6n²+2n+a_n-1. Let a₉₉ = K x10⁴. The value
of K is  ___________.

A function f : N⁺ → N⁺, defined on the set of positive integers N⁺, satisfies the following
properties:
f (n) = f (n=2) if n is even
f (n) = f (n+5) if n is odd

Consider the following experiment.
Step 1. Flip a fair coin twice.
Step 2. If the outcomes are(TAILS, HEADS) then output Y and stop.
Step 3. If the outcomes are either(HEADS, HEADS) or (HEADS, TAILS), then output N and
stop.
Step 4. If the outcomes are(TAILS, TAILS), then go to Step1.
The probability that the output of the experimentis Y is (up to two decimal places) ____________.

Consider the two cascaded 2 - to - 1 multiplexers as shown in the figure.

The size of the data count register of a DMA controller is 16 bits. The processor needs to transfer a file of 29,154 kilobytes from disk to main memory. The memory is byte addressable. The minimum number of times the DMA controller needs to get the c

The stage delays in a 4 - stage pipeline are 800,500,400 and 300 picoseconds.The first stage (with delay 800 picoseconds) is replaced with a functionally equivalent design involving two stages with respective delays 600 and 350 picoseconds.The through put increase of the pipeline is  ____________percent.

Consider a carrylookahead adder for adding two n-bit integers,built using gates of fan-in at most two. The time to perform addition using this adder is

The following function computes the maximum value contained in an integer array p[ ] of size

n (n>=1).
int max(int*p,intn){
int a=0,b=n-1;
while (__________){
if (p[a]<=p[b]){a=a+1;}
else {b=b-1;}
}
return p[a];
}
The missing loop condition is

What will be the output of the following C program ?

void count(intn){
static intd=1;
printf("%d ",n);
printf("%d ",d);
d++;
if(n>1) count(n-1);
printf("%d ",d);
}
void main(){
count(3);
}

What will be the output of the following pseudo-code when parameters are passed by reference
and dynamic scoping is assumed?
a=3;
void n(x){x=x*a;print(x);}
void m(y){a=1;a=y-a;n(a);print(a);}
void main(){m(a);}

An operator delete(i)delete(i) for a binary heap data structure is to be designed to delete the item in the ii-th  node. Assume that the heap is implemented in an array and ii refers to the ii-th index of the array. If the heap tree has depth dd (number of edges on the path from the root to the farthest leaf ), then what is the time complexity to re-fix the heap efficiently after the removal of the element?

Consider the weighted undirected graph with 4 vertices,where the weight of edge {i; j} is
given by the entry W_{i j} in the matrix W.

The largest possible integer value of x, for which at least one shortest path between some pair
of vertices will contain the edge with weight x is .

Let G be acomplete undirected graph on 4 vertices,having 6 edges with weights being1,2, 3, 4,5,and 6.The maximum possible weight that a minimum weight spanning treeof G can have is  _________.

G = (V;E) is an undirected simple graph in which each edge has a distinct weight,and e is a particular edgeof G. Which of the following statements about the minimum spanning trees (MSTs) of G is/are TRUE?

I. If e is the lightest edge of some cycle in G, then every MST of G includes e
II. If e is the heaviest edge of some cycle in G, then everyMST of G excludes e

Let Q denote a queue containing sixteen numbers and S be an empty stack. Head (Q) returns the element at the head of the queue Q without removingitfrom Q. Similarly Top(S) returns the element at the top of S without removing it from S. Consider the algorithm given below.

The maximum possible number of iterations of the while loop in the algorithm is ________.
.

Consider the following context - free grammars:

Which one of the following pairs of languages is generated by G1 and G2, respectively?

Which one of the following is TRUE?

Let X be are cursive language and Y be are cursively enumerable but not recursive language.
Let W and Z be two languages such that Y reduces to W, and Z reduces to X (reduction means
the standard many-one reduction).Which one of the following statements is TRUE?

Consider the following Syntax Directed Translation Scheme (SDTS), with non-terminals {S, A} and terminals {a, b}.

Using the above SDTS, the output printed by a bottom-up parser,for the input aab is:

Consider a computer system with 40-bit virtual addressing and page size of sixteen kilobytes. If the computer system has a one-level page table perprocess and each page table entry requires48 bits,then the size of the per-process page table is megabytes.

Consider a disk queue with requests for I/O to blocks on cylinders 47,38,121,191,87,11, 92, 10.The C-LOOK scheduling algorithm is used.The head is initially at cylinder number 63, moving towards larger cylinder numbers on its servicing pass.The cylinders are numbered from 0 to199.The total head movement (in number of cylinders) incurred while servicing these requestsis .

Consider a computer system with ten physical page frames.The system is provided with an access sequence (a₁;a₂; :::;a₂₀;a₁;a₂; :::;a₂₀), where each a_i is a distinct virtual page number.The difference in the number of page faults between the last-in-first-outpage replacement policy and the optimal page replacement policyis .

Consider the following proposed solution for the critical section problem.There are n
processes: P₀ ...P_n^-1. In the code, function pmax returns an integer not smaller than any
of its arguments.For all i, t[i] is initialized to zero.
Code for P_i:

do {
c[i]=1; t[i]=pmax(t[0],: ::,t[n-1])+1; c[i]=0;
for every j 6= i in{0,: ::,n-1} {
while (c[j]);
while (t[j]!=0 && t[j]<=t[i]);
}
Critical Section;
t[i]=0;
Remainder Section;
} while(true);

Which one of the following is TRUE about the above solution?

Consider the following two phase locking protocol. Suppose a transaction T accesses (for read or write operations), a certain set of objects {O1,…,Ok}. This is done in the following manner:

Step 1. T acquires exclusive locks to O1, . . . , Ok in increasing order of their addresses.
Step 2. The required operations are performed.
Step 3. All locks are released.

This protocol will

An IP data gram of size 1000 bytes arrives at a router.The router has to forward this packet on
a link whose MTU(maximum transmission unit) is100bytes. Assume that the size of the IP
header is 20 bytes.
The number of fragments that the IP data gram will be divided into for transmissionis___________.

For a host machine that uses the token bucket algorithm for congestion control,the token
bucket has a capacity of 1 megabyte and the maximum output rate is 20 megabytes persecond.
Tokens arrive at a rate to sustain output at a rate of 10 megabytes persecond.The token bucket
is currently full and the machine needs to send 12 megabytes of data.The minimum time
required to transmit the data is ______________ seconds.

A sender uses the Stop - and - Wait ARQ protocol for reliable transmission of frames.Frames are of size 1000 bytes and the transmission rate at the sender is 80 Kbps (1Kbps=1000 bits/second). Size of an acknowledgement is100 bytes and the transmission rate at the receiver is 8 Kbps.The one-waypropagation delayis100milliseconds.
Assuming no frame islost,the sender through put is ___________ bytes/second.