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QUESTION: 1

**Q. 1 – Q. 5 carry one mark each.**

**Q.**

**Out of the following four sentences, select the most suitable sentence with respect to grammar and usage.**

Solution:

‘until’ itself is negative so it can’t take one more negative i.e., ‘does not’. Hence, Option (D) is the

right answer

QUESTION: 2

**A rewording of something written or spoken is a ______________.**

Solution:

‘paraphrase’ means a restatement of a text, passage or a rewording of something written or spoken.

QUESTION: 3

**Archimedes said, “Give me a lever long enough and a fulcrum on which to place it, and I will move the world.”**

**The sentence above is an example of a ___________ statement**

Solution:

‘figurative’ means representing by a figure or resemblance or expressing one thing in terms normally denoting another with which it may be regarded as analogous.

QUESTION: 4

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

Solution:

From given codes

relftaga carefree

Otaga careful

Fertaga careless

From these codes, clearly known that “care” means “taga,” from given alternatives, option ‘C’ is correct.

QUESTION: 5

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 __________.

Solution:

From given data, 64 cubic blocks of one unit

Sizes are formed No of faces of the

Cube is ‘6’ No of corners of the

Cube is ‘8’ After removing one

Cubic block from Each corner,

The resulting surface area of the body = 6 x (4) = 96 sq. Units.

QUESTION: 6

**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?

Solution:

Total No. of razors Elegance type from all four quarters = 27300 + 25222 + 28976 + 201012

= 10,2510

Total No. of razors of Smooth type from all four quarters = 20009 + 19392 + 22429 + 18229

= 8,0059

Total No. of razors of Soft type from all four Quarters = 17602 + 18445 + 19544 + 16595

= 7,2186

Total No. of razors of Executive type from all four Quarters = 9999 + 8942 + 10234 + 10109

= 3,9286

The revenue of the company in that year of 4 different types of razors

Elegance = 10,2510 x 48 = 49,20,480

Smooth = 8,0059 x 63 = 50,43,717

Soft = 7,2186 x 78 = 56,30,508

Executive = 3,9284 x 193 = 67,96,132

The Executive of razors contributes the greatest revenue of the company in that year.

QUESTION: 7

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?

Solution:

If seventeen languages were not an indication of the nation’s diversity, nothing else is. If nothing else is so the best inference is option ‘D’.

QUESTION: 8

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

Solution:

From the given data

Player P > Player Q

Player R > Player S

Player S < Player P (sometimes only)

Player R < Player Q

Player ‘P’ > Player ‘Q’ > Player ‘R’ > Player ‘S’

Logically, the statement (i) is definitely true, but statement (ii) is not

Option ‘A’ is true

QUESTION: 9

If f(x) = 2x^{7}+3x−5, which of the following is a factor of f(x)?

Solution:

**f (x) = 2x ^{7} + 3x - 5 for x = 1 the equation is satisfied. The factor is (x–1).**

QUESTION: 10

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 ________.

Solution:

**Option (A)**

Load = 40units, it says that, the load is halved, it takes 10,000 cycles for failure. 80/2 =(100)^{2 }

40 units = 10,000 cycles, it is not

**Option (D)**

Load = 92.02 units means it is more than 80 units, so it is not.

**Option (C)**

Load = 60.01 units

3/4(80 units) = 60.01 units

From the given relation

3/4(80 units) = (10)^{4/3} = (100)^{1} x (100)^{1/3} = 100 x 4.64 = 464

It is not

Option (B) only possible

At the load of 46.02 units, the failure will happen in 5000 cycles.

*Answer can only contain numeric values

QUESTION: 11

**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

Solution:

QUESTION: 12

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}?

Solution:

Let a_{n} denote the number of n-bit strings that do not contain two consecutive 1’s

By observing above analysis, we can write a_{n} = a_{n–1}+ a_{n–2}

(OR)

Case 1: If the first bit is zero, then the remaining bits we can choose in an–1 ways.

Case 2: If the first bit is one, then the second bit is 0 and the remaining bits we can choose in an–2

ways.

The recurrence relation is a_{n} = a_{n–1}+ a_{n–2}

*Answer can only contain numeric values

QUESTION: 13

Solution:

(OR)

The given limit is in 0/0 form. Applying L. Hospital’s rule, we get

The limiting value = 1

*Answer can only contain numeric values

QUESTION: 14

A probabilitydensity function on the interval [a,1] is given by1/x^{2} and outside this interval the value of the function is zero.The value of a is _____________.

Solution:

*Answer can only contain numeric values

QUESTION: 15

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

Solution:

(OR)

Complex roots of a polynomial equation always occur in pairs.

If (2 + i) is an eigen value then (2 – i) is also an eigen value of P.

Determinant of P = (2 + i) (2 – i) 3 = 15

QUESTION: 16

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

Solution:

Since there are more than one outputs and number of outputs is less than inputs, it is a Priority encoder V=1 when input is valid and for priority encoder it checks first high bit encountered. Except all are having at least one bit high and ‘x’ represents the “don’t care” as we have found a high bit already. So answer is (A).

*Answer can only contain numeric values

QUESTION: 17

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

Solution:

Integer size is 16 bit, already it is given in it’s 2’s complement notation; So, when it is 2’s

complemented once again it gives value. So answer is –11.

*Answer can only contain numeric values

QUESTION: 18

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 ____________.

Solution:

In the given first loop of states, zero has repeated 3 times. So, minimum 4 number of Flip-flops are needed.

*Answer can only contain numeric values

QUESTION: 19

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.

Solution:

Word size = 16 bit,

so memory size = 2^{31} words.

31 address bits are needed.

QUESTION: 20

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)?

Solution:

*Answer can only contain numeric values

QUESTION: 21

Consider the following directed graph:

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

Solution:

QUESTION: 22

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?

Solution:

i is integer and *p is value of a pointer to short.

1) Option 1 is wrong because we are passing “*S” as second argument check that S is not a pointer variable .So error

2) Second option is we are trying to store the value of f(i,s) into i but look at the function definition outside main it has no return type. It is simply void so that assignment is wrong. So error

3) Option 3 is wrong because of the same reason why option 1 is wrong

4) So option d is correct.

QUESTION: 23

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

Solution:

QUESTION: 24

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

Solution:

*Answer can only contain numeric values

QUESTION: 25

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 _____________ .

Solution:

Whatever modifications are performed in mystery ( ) function, those modifications are not reflected

in main ( ) function so it will print 2016.

QUESTION: 26

Solution:

S → aS |bS |

S → (a + b)*

{a, b}* = (a + b)*

QUESTION: 27

Which of the following decision problems are undecidable?

Solution:

III. Equality of CFG is undecidable

IV. Emptiness of TM is undecidable

QUESTION: 28

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

Solution:

*Answer can only contain numeric values

QUESTION: 29

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 ______________ .

Solution:

QUESTION: 30

What type of memory is volatile ?

Solution:

QUESTION: 31

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

Solution:

A superkey is one which contains a candidate key.

QUESTION: 32

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

Solution:

A: Atomicity

C: Consistency

I: Isolation

D: Durability

QUESTION: 33

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?

Solution:

(Volume, Number) → Year is a partial functional dependency. So, the given relation is in 1 NF but

not in 2 NF.

QUESTION: 34

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

Solution:

DHCP is dynamic host configuration protocol: allocates one of the unused IP address

QUESTION: 35

Which of the following is/are example(s) of stateful application layer protocols?

(i) HTTP

(ii) FTP

(iii) TCP

(iv) POP3

Solution:

POP3 and FTP are stateful application layer protocols

*Answer can only contain numeric values

QUESTION: 36

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

**Q.**

The coefficient of x^{12} in (x^{3}+x^{4}+x^{5}+x^{6}+... )^{3} is ____________ .

Solution:

**(OR)**

*Answer can only contain numeric values

QUESTION: 37

Consider the recurrence relation a_{1} = 8, a_{n} = 6n^{2}+2n+a_{n-1}. Let a_{99} = K x10^{4}. The value

of K is ___________.

Solution:

The recurrence relation is a_{n} – a_{n}-1 = 6n^{2} + 2n

Complementary function = C1

Let particular solution = (An^{2} + Bn C)n

Substituting in the recurrence relation, and solving we get A = 2, B = 4 and C = 2.

The solution is a_{n} = C_{1} + 2n^{3} + 4n^{2} + 2^{n}

a1 = 8 8 = C1 + 8

C1 = 0

a_{99} = 2{(99^{3}) + 2(99^{2}) + 99}

= 2{(100 – 1)^{3} + 2(100 – 1)^{2} + (100 – 1)}

= 10^{4} (198)

k = 198

*Answer can only contain numeric values

QUESTION: 38

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

Solution:

Using the definition of the function we can show that

f(1) = f(2) = f(3) = f(4) = f(6) = f(7) = f(8) = f(9) …

and f(5) = f(10) = f(15) = f(20) = …..

The range of f(n) contain two distinct elements.

*Answer can only contain numeric values

QUESTION: 39

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) ____________.

Solution:

QUESTION: 40

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

Solution:

*Answer can only contain numeric values

QUESTION: 41

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

Solution:

Size of data count register of the DMA controller = 16 bits

Data that can be transferred in one go = 2^{16} bytes = 64 kilobytes

File size to be transferred = 29154 kilobytes

So, number of times the DMA controller needs to get the control of the system bus from the processor to transfer the file from the disk to main memory = ceil(29154/64) = 456

*Answer can only contain numeric values

QUESTION: 42

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.

Solution:

Old pipeline maximum delay = 800 ns

New pipeline maximum delay = 600 ns

800 : 600 = 4:3

Increasing throughput= (4-3)/3= 33.3%

QUESTION: 43

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

Solution:

Size of the integer = n bit and maximum number of inputs to the gate is two. So, time is

depending on size.

QUESTION: 44

**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**

Solution:

If b! = a we get maximum element of an integer

QUESTION: 45

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);

}

Solution:

Output = 3, 1, 2, 2, 1, 3, 4, 4, 4

QUESTION: 46

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);}

Solution:

QUESTION: 47

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?

Solution:

*Answer can only contain numeric values

QUESTION: 48

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 .

Solution:

*Answer can only contain numeric values

QUESTION: 49

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 _________.

Solution:

QUESTION: 50

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

Solution:

I. TRUE

Suppose ‘e’ does not belong to T*

Adding ‘e’ to T* creates a(unique) cycle ‘C’ in T*

Some other edge in cycle ‘C’, say ‘f’ has exactly one end point in ‘s’

T = T* ?{e}–f is also spanning Tree and since Ce < Cf

So,cost(T) < cost(T*)

Which is contridicts minimality of T*.

II. TRUE

Suppose ‘f’ belongs to T*

Deleting ‘f’ from T* disconnects T* and let ‘s’ be one side of cut.

Some other edge in cycle ‘C’ say ‘e’ has exactly one end point in S

T = T* {e} – {f} is also a spanning Tree.

Since Ce < Cf so cost(T) < cost(T*)

Which is contradictory to minimality of T*

*Answer can only contain numeric values

QUESTION: 51

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 ________.

.

Solution:

Trying with queue elements, say n = 1, 2, 3, then maximum number of iterations are noticed as n2.

Here n = 16, So answer will be 256.

QUESTION: 52

Consider the following context - free grammars:

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

Solution:

QUESTION: 53

Which one of the following is TRUE?

Solution:

L = {a^{n} | n 0} {a^{n} b^{n} | n 0} and

L is DCFL

QUESTION: 54

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?

Solution:

*Answer can only contain numeric values

QUESTION: 55

Solution:

2–5+1–7*3

2-6–7*3

2-(–1)*3

3*3

9

QUESTION: 56

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:

Solution:

S → aA {print 1}

S → a {print 2}

S → Sb {print 3}

Input: aab

*Answer can only contain numeric values

QUESTION: 57

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.

Solution:

*Answer can only contain numeric values

QUESTION: 58

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 .

Solution:

QUESTION: 59

Consider a computer system with ten physical page frames.The system is provided with an access sequence (a_{1};a_{2}; :::;a_{20};a_{1};a_{2}; :::;a_{20}), 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 .

Solution:

QUESTION: 60

Consider the following proposed solution for the critical section problem.There are n

processes: P_{0} ...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?

Solution:

QUESTION: 61

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

Solution:

QUESTION: 62

Solution:

*Answer can only contain numeric values

QUESTION: 63

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___________.

Solution:

L =1000 bytes

MTU = 100 bytes

IP header = 20 bytes

So MTU payload is 100–20 = 80 bytes

Number of fragments = 1000/80 = 13

*Answer can only contain numeric values

QUESTION: 64

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.

Solution:

Given

Maximum burst rate, M = 20 MB

Token arrival rate, P = 10 MB

Constant rate(bucket o/p), P = 10 MB

Bucket capacity, C = 1 MB

Time for 1 MB, S = C/(M-P)

=1/(20-10) = 0.1 sec

For the total message of 12 MB is 1.2 sec

*Answer can only contain numeric values

QUESTION: 65

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.

Solution:

*B = 80 kbps
L = 1000 bytes
Tp = 100 ms
Tx = L/B = 100 ms
Tax = ack size/ bandwidth = 100 ms
Efficiency = tx/(tx +2tp+tax)
Throughput = efficiency * bandwidth = .25 *104 bytes
= 2500 bytes*

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