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Q. No. 1 – 25 Carry One Mark Each

1. The simplified SOP (Sum of Product) form of the Boolean expression

( ) ( + + + + + + P Q R . P Q R . P Q R ) ( ) is

(A) (PQ R + ) (B) ( + P QR) (C) (PQ R + ) (D) (PQ R + )

Answer: – (B)

Exp: –

( = + + f P R P Q ) ( )

= + P QR

Alternate method

( ) ( ) ( ) + + + + + + = + + + + + + P Q R . P Q R . P Q R P Q R . P Q R . P Q R ( ) ( ) ( )

( ) ( )

( )

P Q R P Q R P Q R P Q R R P Q R P Q P Q R P Q Q R

P Q R P Q R

+ = + = + + = + + =

+ = + =

2. Which one of the following circuits is NOT equivalent to a 2-input XNOR

(exclusive NOR) gate?

(A) (B)

(C) (D)

Answer: – (D)

Exp: – All options except option ‘D’ gives EX-NOR gates

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

(A) 9 (B) 8 (C) 512 (D) 258

Answer: – (A)

Exp: –

n

≥ 2 258 n 9 ⇒ =

4. A thread is usually defined as a ‘light weight process’ because an operating

system (OS) maintains smaller data structures for a thread than for a process. In

relation to this, which of the followings is TRUE?

QR

P

1

0 1 1 1

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(A) On per-thread basis, the OS maintains only CPU register state

(B) The OS does not maintain a separate stack for each thread

(C) On per-thread basis, the OS does not maintain virtual memory state

(D) On per thread basis, the OS maintains only scheduling and accounting

information

Answer: – (A)

5. K4 and Q3 are graphs with the following structures

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

(A) K4 is planar while Q3 is not (B) Both K4 and Q3 are planar

(C) Q3 is planar while K4 is not (D) Neither K4 not Q3 is planar

Answer: – (B)

Exp: –

∴ Both K4 and Q3 are planar

6. If the difference between the expectation of the square of random variable

( )

2

E X

and the square of the expectation of the random variable ( )

2

E X

is

denoted by R then

(A) R 0 = (B) R<0 (C) R 0 ≥ (D) R>0

Answer: – (C)

7. 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?

(A) Finite state automata

(B) Deterministic pushdown automata

(C) Non-Deterministic pushdown automata

K4 Q3

K4

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(D) Turing machine

Answer: – (A)

Exp: – Lexical Analysis is implemented by finite automata

8. Let the page fault service time be 10ms in a computer with average memory

access time being 20ns. If one page fault is generated for every 10

6

memory

accesses, what is the effective access time for the memory?

(A) 21ns (B) 30ns (C) 23ns (D) 35ns

Answer: – (B)

Exp: – P = page fault rate

EA = p × page fault service time

( )

6

6 6

1 p Memory access time

1 1

10 10 1 20 29.9ns

10 10

× − +

≅ × − + × × =

9. 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 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?

(A) Immediate Addressing (B) Register Addressing

(C) Register Indirect Scaled Addressing (D) Base Indexed Addressing

Answer: – (D)

Exp: – Here 20 will act as base and content of R2 will be index

10. What does the following fragment of C-program print?

( )

char c “GATE2011”;

char *p =c;

printf “%s”, p+p 3 p 1 ;

=

−

(A) GATE2011 (B) E2011 (C) 2011 (D) 011

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11. 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?

(A) (B)

(C) (D)

Answer: – (B)

Exp: – Heap is a complete binary tree

12. 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 Li denote the length of the longest monotonically increasing sequence starting

at index i in the array

Initialize Ln-1 =1

For all i such that 0 i n 2 ≤ ≤ −

[ ] [ ]

{ i 1

i

1 L if A i A i 1

L

1 Otherwise

+

+ > +

=

Finally the length of the longest monotonically increasing sequence is

( Max L ,L ,…, L

0 1 n 1− ) . Which of the following statements is TRUE?

(A) The algorithm uses dynamic programming paradigm

(B) The algorithm has a linear complexity and uses branch and bound paradigm

(C) The algorithm has a non-linear polynomial complexity and uses branch and

bound paradigm

(D) The algorithm uses divide and conquer paradigm.

Answer: – (A)

13. Let P be a regular language and Q be a context free language such that ⊆ Q P.

(For example, let P be the language represented by the regular expression p*q*

and Q be { ∈ }

n n

p q | n N ). Then which of the following is ALWAYS regular?

(A) ∩ P Q (B) − P Q (C) ∑ − * P (D) ∑ − * Q

10

8 6

4 5 2

1

10

8 6

4 5 1 2

10

5 6

4 8 2 1

5

2 8

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Answer: – (C)

Exp: –

*

Σ − P is the complement of P so it is always regular,

since regular languages are closed under complementation

14. In a compiler, keywords of a language are recognized during

(A) parsing of the program (B) the code generation

(C) the lexical analysis of the program (D) dataflow analysis

Answer: – (C)

Exp: – Any identifier is also a token so it is recognized in lexical Analysis

15. A layer-4 firewall (a device that can look at all protocol headers up to the

transport layer) CANNOT

(A) block entire HTTP traffic during 9:00PM and 5:00AM

(B) block all ICMP traffic

(C) stop incoming traffic from a specific IP address but allow outgoing traffic to

the same IP address

(D) block TCP traffic from a specific user on a multi-user system during 9:00PM

and 5:00AM

Answer: – (A)

Exp: – Since it is a layer 4 firewall it cannot block application layer protocol like HTTP.

16. 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?

(A) 1/3 (B) 1/4 (C) 1/2 (D) 2/3

Answer: – (A)

Exp: – Sample space = {HH, HT, TH}

Required probability

1

3

=

17. 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) m1:HTTP m2:SMTP m3:POP (B) m1:SMTP m2:FTP m3:HTTP

(C) m1: SMTP m2: POP m3: HTTP (D) m1: POP m2: SMTP m3:IMAP

Answer: – (C)

Exp: – Sending an email will be done through user agent and message transfer agent by

SMTP, downloading an email from mail box is done through POP, checking email

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18. 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.

Parameter Language L1 Language L2

Man years needed for development LOC / 10000 LOC / 10000

Development Cost per year Rs. 10,00,000 Rs. 7,50,000

Maintenance time 5 years 5 years

Cost of maintenance per year Rs. 1,00,000 Rs. 50,000

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?

(A) 4000 (B) 5000 (C) 4333 (D) 4667

Answer: – (B)

Exp: –

1

LOC L x =

2

= L 2x

Total cost of project

× + × = × + ×

+ = +

− = ⇒

= ⇒ = ∴

x 2x

1000000 5 100000 750000 50000 5

10000 10000

100x 500000 150x 250000

50x 500000 250000

250000

x x 5000

50

19. Let the time taken to switch between user and kernel modes of execution be t1

while the time taken to switch between two processes be t2. Which of the

following is TRUE?

(A)

1 2

t t >

(B)

1 2

t t =

(C)

1 2

t t <

(D) Nothing can be said about the relation between t1 and t2

Answer: – (C)

Exp: – Process switching also involves mode changing.

20. A company needs to develop digital signal processing software for one of its

newest inventions. The software is expected to have 40000 lines of code. The

company needs to determine the effort in person-months needed to develop this

software using the basic COCOMO model. The multiplicative factor for this model

is given as 2.8 for the software development on embedded systems, while the

exponentiation factor is given as 1.20. What is the estimated effort in personmonths? CS-Paper Code-B GATE 2011 www.gateforum.com

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(A) 234.25 (B) 932.50 (C) 287.80 (D) 122.40

Answer: – (A)

Exp: – Effort person per month

( )

( )

B

1.20

kDSI .

KDSI Kilo LOC

2.8 40

2.8 83.6511

234.22 person per month

= α

=

× =

× =

=

21. Which of the following pairs have DIFFERENT expressive power?

(A) Deterministic finite automata (DFA) and Non-deterministic finite automata

(NFA)

(B) Deterministic push down automata (DPDA) and Non-deterministic push down

automata (NPDA)

(C) Deterministic single-tape Turing machine and Non-deterministic single tape

Turing machine

(D) Single-tape Turing machine and multi-tape Turing machine

Answer: – (B)

Exp: – NPDA is more powerful than DPDA.

Hence answer is (B)

22. HTML (Hyper Text Markup Language) has language elements which permit

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?

(A) Embed web objects from different sites into the same page

(B) Refresh the page automatically after a specified interval

(C) Automatically redirect to another page upon download

(D) Display the client time as part of the page

Answer: – (D)

23. Which of the following is NOT desired in a good Software Requirement

Specifications (SRS) document?

(A) Functional Requirements

(B) Non Functional Requirements

(C) Goals of Implementation

(D) Algorithms for Software Implementation

Answer: – (D)

24. A computer handles several interrupt sources of which the following are relevant

for this question.

Interrupt from CPU temperature sensor

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Interrupt from Keyboard

Interrupt from Hard Disk

(A) Interrupt from Hard Disk (B) Interrupt from Mouse

(C) Interrupt from Keyboard (D) Interrupt from CPU temp sensor

Answer: – (D)

25. Consider a relational table with a single record for each registered student with

the following attributes.

1. Registration_Number: Unique registration number for each registered student

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

3. BankAccount_Number: Unique account number at the bank. A student can

have multiple accounts or joint accounts. This attributes 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?

(A) BankAccount_Number is a candidate key

(B) Registration_Number can be a primary key

(C) UID is a candidate key if all students are from the same country

(D) If S is a superkey such that ∩ ∪ S UID is NULL then S UID is also a superkey

Answer: – (A)

Exp: – In case two students hold joint account then BankAccount_Num will not uniquely

determine other attributes.

Q. No. 26 – 51 Carry Two Marks Each

26. Which of the given options provides the increasing order of asymptotic

complexityoffunctionsf1,f2,f3andf4?

( ) ( ) ( ) ( )

2 n 3 / 2 log n

1 2 3 2 4

f n 2 ; f n n ; f n nlog n; f n n = = = =

(A) f3, f2, f4,f1 (B) f3, f2, f1,f4 (C) f2, f3, f1,f4 (D) f2, f3, f4,f1

Answer: – (A)

Let n 1024 =

( )

( )

( )

( )

1024

1

15

2

10

3

10 100

4

3 2 4 1

f n 2

f n 2

f n 10 2

f n 1024 2

f , f , f , f is the rquired increasin g order

=

=

× =

= =

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27. Four matrices M1, M2, M3 and M4 are dimensions p q, q r, r s and s t × × × ×

respectively can be multiplied in several ways with different number of total

scalar multiplications. For example When multiplied as (( ) M M M M × × × ( 1 2 3 4 )) the

total number of scalar multiplications is pqr+rst+prt. When multiplied as

((( ) M M M M × × × 1 2 3 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

(A) 248000 (B) 44000 (C) 19000 (D) 25000

Answer: – (C)

Exp: – Multiply as ( ( M M M M × × × 1 2 3 4 ))

The total number of scalar multiplication is

qrs pqs pst

10000 5000 4000 19000

+ + =

= + + =

28. Consider a relational table r with sufficient number of records, having attributes

A1, A2,…, An and let ≤ ≤ 1 p n. Two queries Q1 and Q2 are given below.

(( ) )

( ) ( )

n P

n 1 P 2

A1…A A c

A1…A c A c 1 2

Q1 : r where c is a const

Q2: r where c and c are constants

=

≥ ≥

π σ

π σ

The database can be configured to do ordered indexing on Ap or hashing on Ap.

Which of the following statements is TRUE?

(A) Ordered indexing will always outperform hashing for both queries

(B) Hashing will always outperform ordered indexing for both queries

(C) Hashing will outperform ordered indexing on Q1, but not on Q2

(D) Hashing will outperform ordered indexing on Q2, but not on Q1.

Answer: – (C)

29. Consider the matrix as given below.

1 2 3

0 4 7

0 0 3

Which one of the following provides the CORRECT values of eigenvalues of the

matrix?

(A) 1,4,3 (B) 3,7,3 (C) 7,3,2 (D) 1,2,3

Answer: – (A)

Exp: – Given matrix is upper triangular matrix and its diagonal elements are its eigen

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30. 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?

(A) 4.0 (B) 2.5 (C) 1.1 (D) 3.0

Answer: – (B)

Exp: –

( )

( )

5 6 11 8 30

2.5

11 1 12

+ + +

= =

+

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

{ }

nk

= > L a | k 0, and n is a positive integer constant

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

(A) k+1 (B) n+1 (C) 2

n+1

(D) 2

k+1

Answer: – (B)

Exp: – Let n = 3 and k=1

(n 1 + ) states

32. An 8KB direct mapped write-back cache is organized as multiple blocks, each of

size 32-bytes. The processor generates 32-bit addresses. The cache controller

maintains 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 metadata (tags) for the cache?

(A) 4864 bits (B) 6144bits (C) 6656bits (D) 5376bits

Answer: – (D)

State S1

Delay

5ns

Pipeline

Reg

Delay

1ns

State

S2

Delay

6ns

State

S3

Delay

11ns

Pipeline

Reg

Delay

1ns

State

S4

Delay

8ns

Pipeline

Reg

Delay

1ns

Pipeline

Reg

Delay

1ns

a a a

a

q0 q1 q2

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Exp: –

Required answer ( = × + = 256 19 2 5376 bits )

33. An application loads 100 libraries at startup. Loading each library requires exactly

one disk access. The seek time of the disk to a random location is given as 10ms.

Rotational speed of disk is 6000rpm. 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) 0.50s (B) 1.50s (C) 1.25s (D) 1.00s

Answer: – (B)

Exp: – 6000 rotations ________ 60 sec

1 rotation ________ 10 ms

∴ Rotational latency = 5ms

Time for one disk access = 15 ms

Time to load all libraries = × = = 15 100 1500ms 1.5sec

34. A deterministic finite automation (DFA D) with alphabet ∑ = {a,b} is given below

Which of the following finite state machines is a valid minimal DFA which accepts

the same language as D?

(A) (B)

a,b

a,b

a

b

a,b

s

p q r

p q r

s

a

b b

a,b

a

a,b

p q r

s t

a

b b a,b

a,b

a

a,b

19 2 + 8 5

TAG

= =

13

8

5

block

offset

2

2

2

5

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(C) (D)

Answer: – (A)

Exp: – Options B and C will accept the string b

Option – D will accept the string “bba”

Both are invalid strings.

So the minimized DFA is option A

35. The following is comment written for a C function

/* This function computes the roots of a quadratic equation

a.x^2+b.x+c=0. The function stores two real roots

in *root1 and *root2 and returns the status of validity of

roots. It handles four different

( )

( )

( )

( )

( ) ( )

kinds of cases.

i When coefficient a is zero irrespective of discriminant

ii When discriminant is positive

iii When discrimanant is zero

iv When discrimanant is negative

Only in cases ii and iii , the stored roots are valid.

Otherwise 0 is stored in the roots. the function returns 0 when

the roots are valid and -1 otherwise.

The functin also ensures root1>=root2.

( int get_QuadRoots float a, float b, float c, float *root1, float *root2 😉

/ *

A software test engineer is assigned the job of doing black box testing. He comes

up with the following test cases, many of which are redundant.

Test Case

Input set Expected Output set

a b C Root1 Root2

Return

Value

T1 0.0 0.0 7.0 0.0 0.0 -1

T2 0.0 1.0 3.0 0.0 0.0 -1

T3 1.0 2.0 1.0 -1.0 -1.0 0

T4 4.0 -12.0 9.0 1.5 1.5 0

T5 1.0 -2.0 -3.0 3.0 -1.0 0

T6 1.0 1.0 4.0 0.0 0.0 -1

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?

(A) T1,T2,T3,T6 (B) T1,T3,T4,T5 (C) T2,T4,T5,T6 (D) T2,T3,T4,T5

Answer: – (C)

p r

b

a, b

a, b

a, b

q

p q

s

a

b

a

a, b

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Exp: – T1 and T2 checking same condition a = 0 hence, any one of T1 and T2 is

redundant.

T3, T4: in both case discriminant (D)=

2

b 4ac 0 − = . Hence any one of it is

redundant.

T5 : D>0

T6 : D<0

36. Database table by name Loan_Records is given below.

Borrower Bank_Manager Loan_ Amount

Ramesh Sunderajan 10000.00

Suresh Ramgopal 5000.00

Mahesh Sunderajan 7000.00

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

;(

(A) 3 (B) 9 (C) 5 (D) 6

Answer: – (C)

Exp: –

After executing the given query, the output would be

Borrower Bank_Manager Load_Amount

Ramesh Sunderajan 10000.00

Ramesh Sunderajan 7000.00

Suresh Ramgopal 5000.00

Mahesh Sunderajan 10000.00

Mahesh Sunderajan 7000.00

Borrower Bank _ Manager

Ramesh Sunderajan

Suresh Ramgqpal

Mahesh Sunderjan

S

Bank _ Manager Loan _ Amount

Sunderajan 10000.00

Ramgopal 5000.00

Sunderjan 7000.00

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37. Consider two binary operators ‘ ‘ and ‘ ‘ ↑ ↓ with the precedence of operator ↓

being lower than that of the operator ↑ . Operator ↑ is right associative while

operator ↓, is left associative. Which one of the following represents the parse

tree for expression ( ↓ ↑ ↑ ↓ 7 3 4 3 2 ?)

(A) (B)

(C) (D)

Answer: – (B)

Exp: – 7 3 4 3 2 ↓ ↑ ↑ ↓

⇒ ( 7 3 4 3 2 ↓ ↑ ↑ ↓ ) as ↑ is right associative

⇒ ( ( 7 3 4 3 2 ↓ ↑ ↑ ↓ ))

⇒ ( ( ( 7 3 4 3 2 ↓ ↑ ↑ ↓ ))) as ↓ is left associative

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

{ }

{ }

{ }

p q

p q

p q r

L1 0 1 | p, q N

L2 0 1 | p, q N and p q and

L3 0 1 0 | p, q, r N and p q r

∋ =

= ∋ =

= = ∋ =

Which of the following statements is NOT TRUE?

(A) Push Down Automata (PDA) can be used to recognize L1 and L2

(B) L1 is a regular language

(C) All the three languages are context free

(D) Turing machines can be used to recognize all the languages

7

3

4

3 2

7

4 3

2

3

7

3 4

2

3

7

3

4

2

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Answer: – (C)

Exp: – L1: regular language

L2: context free language

L3: context sensitive language

39. On a non-pipelined sequential processor, a program segment, which is a 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 speedup when the DMA controller based design is used

in place of the interrupt driven program based input-output?

(A) 3.4 (B) 4.4 (C) 5.1 (D) 6.7

Answer: – (A)

Exp: – No. of clock cycles required by using load-store approach = 2 + 500 × 7 = 3502

and that of by using DMA = 20 + 500 × 2 = 1020

Required speed up

3502

3.4

1020

= =

40. 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?

(A) 0 (B) 1 (C) n! (D)

2n

n

1

C .

n 1 +

Answer: – (D)

41. Which one of the following options is CORRECT given three positive integers x, y

and z, and a predicate

( ) ( ) = ¬ = ∧ ∀ ∃ = ( ( P x x 1 y z x y * z y x y 1 ) ⇒ ( ) = ∨ = ( ))

(A) P(x) being true means that x is a prime numberCS-Paper Code-B GATE 2011 www.gateforum.com

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(B) P(x) being true means that x is a number other than 1

(C) P(x) is always true irrespective of the value of x

(D) P(x) being true means that x has exactly two factors other than 1 and x

Answer: – (A)

42. Given = − i 1, what will be the evaluation of the definite integral

/ 2

0

cos x isin x

dx ?

cos x isin x

π

+

−

∫

(A) 0 (B) 2 (C) –i (D) i

Answer: – (D)

Exp: –

ix

2 2 2ix

ix 0 0

e

dx e dx

e

π π

−

=

∫ ∫

=

2ix 2

0

e

2i

π

1 i

e 1

2i

π

= −

1

cos isin 1

2i

= π + π −

1

1 0 1

2i

= − + −

2 1 i

2i i i

− −

× = =

i

i

1

−

= =

−

43. 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=l) 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?

SELECT Y FROM T WHERE X=7;

(A) 127 (B) 255 (C) 129 (D) 257

Answer: – (A)

Exp: –

X Y

1 1

2 3

3 7

4 15

5 31

6 63

7 127 CS-Paper Code-B GATE 2011 www.gateforum.com

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44. Consider a finite sequence of random values X x , x ,…x . Let

1 2 n x

= µ

be the mean

and σx

be the standard deviation of X .Let another finite sequence Y of equal

length be derived from this as

i i y a * x b, = + where a and b are positive

constants. Let

y

µ be the mean and σy be the standard deviation of this

sequence. Which one of the following statements is INCORRECT?

(A) Index position of mode of X in X is the same as the index position of mode of Y

in Y.

(B) Index position of median of X in X is the same as the index position of median

of Y in Y.

(C) µ = µ +

y x a b

(D) σ = σ +

y x a b

Answer: – (D)

45. 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?

(A) 1/5 (B) 4/25 (C) 1/4 (D) 2/5

Answer: – (A)

Exp: – (2,1), (3,2), (4,3), (5,4)

Required probability =

4 4 1

5 4 20 5

= =

×

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

P1 and P2.

Process Arrival time Burst Time

P0 0 ms 9 ms

P1 1 ms 4ms

P2 2 ms 9ms

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?

(A) 5.0 ms (B) 4.33 ms (C) 6.33 ms (D) 7.33 ms

Answer: – (A) CS-Paper Code-B GATE 2011 www.gateforum.com

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Exp: –

4 11

Average waiting time 5 ms

3

+

= =

47. 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 the 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?

(A) 2 (B) 9 (C) 5 (D) 3

Answer: – (D)

Exp: –

1 1

Load R , a ; R M a ←

2 2

Load R ,b ; R M b ←

Sub R ,R ; R R R 1 2 1 1 2 ← −

2 2

Load R , c ; R M c ←

3 3

Load R , d ; R M d ←

Add R , R ; R R R 2 3 2 2 3 ← +

3 3

Load R , e ; R M e ←

Sub R ,R : R R R 3 2 3 3 2 ← −

Add R ,R ; R R R 1 3 1 1 3 ← +

Total 3 Registers are required minimum

+

− −

a b e +

c d

P0

P1 P0 P2

0 1 5 13 22CS-Paper Code-B GATE 2011 www.gateforum.com

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Common Data Questions: 48 & 49

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;

{

+ <

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

(A) 9 (B) 8 (C) 5 (D) 2

Answer: – (D)

Exp: –

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

(A) 345 (B) 12 (C) 5 (D) 3

Answer: – (B)

Exp: –

( f 513, 2)

( f 256,2)

( f 128,2)

( f 64,2)

( f 32,2)

( f 16,2)

( f 8,2)

( f 4,2)

( f 2, 2)

( f 1, 2)

( f 0,2)

1 +

0 +

0 +

0 +

0 +

0 +

0 +

0 +

0 +

1 +

+ = 1 1 2

( f 345,10)

( f 34,10)

( f 3,10)

( f 0,10)

+

+

+

5

4

3

+ + = 5 4 3 12CS-Paper Code-B GATE 2011 www.gateforum.com

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Common Data Questions: 50 & 51

Consider the following circuit involving three D-type flip-flops used in a certain

type of counter configuration.

50. 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?

(A) 3 (B) 4 (C) 5 (D) 6

Answer: – (B)

Exp: –

CLOCK Inputs Outputs

=

1 D R

2 D P R ( = + ) =

3 D Q R P Q R

1 0 1 0 0 1 0

2 0 1 1 0 1 1

3 1 0 0 1 0 0

4 0 0 0 0 0 0

So Total number of distinct outputs is 4

51. 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?

(A) 000 (B) 001 (C) 010 (D) 011

P

D Q

Q

Clock

D Q

Q

D Q

Q

Q

R

Clock

ClockCS-Paper Code-B GATE 2011 www.gateforum.com

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Answer: – (D)

Exp: -From the Table Shown in the explanation of question 50, if first state is 010 next

State is 011

Linked Answer Questions: Q.52 to Q.55 Carry Two Marks Each

Statement for Linked Answer Questions: 52 & 53

An undirected graph G(V,E) contains n ( n > 2 ) nodes named v , v ,….v .

1 2 n

Two

nodes v , v i j

are connected if and only if < − ≤ 0 i j 2. Each edge ( v , v i j ) is

assigned a weight i + j. A sample graph with n = 4 is shown below

52. What will be the cost of the minimum spanning tree (MST) of such a graph with n

nodes?

(A) ( )

1 2

11n 5n

12

− (B)

2

n n 1 − +

(C) 6n 11 − (D) 2n 1 +

Answer: – (B)

53. The length of the path from v5 to v6 in the MST of previous question with n = 10

is

(A) 11 (B) 25 (C) 31 (D) 41

Answer: – (C)

Exp: –

+ + + + + = 12 8 4 3 6 10 31

7

5 6

3

4

V1 V2

V3 V4

12

4

8

3

6

10

v7

v5

v3

v1 v2

v4

v6CS-Paper Code-B GATE 2011 www.gateforum.com

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Statement for Linked Answer Questions: 54 & 55

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

The net work uses a Distance Vector Routing protocol. Once the routes have

stabilized, the distance vectors at different nodes are as following

( )

( )

( )

( )

( )

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 distan

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