## Gate 2011

 Question 1
 A B C D Digital-Logic-Design       Boolean-Algebra
Question 1 Explanation: Question 2
The minimum number of D flip-flops needed to design a mod-258 counter is
 A 9 B 8 C 512 D 258
Digital-Logic-Design       Sequential-Circuits
Question 2 Explanation:
Let n is the number of flip-flops.
The max Mod values is 2n.
So 2n ≥ 258 ⇒ n = 9
 Question 3
Which one of the following circuits is NOT equivalent to a 2-input XNOR (exclusive NOR) gate?
 A B C D Digital-Logic-Design       Logic-Gates
Question 3 Explanation:
All options except option ‘D’ gives EX-NOR gates
 Question 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 following is TRUE?
 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
Question 4 Explanation:
A) False, because on per thread basis OS maintains register, stack and program counter.
B) False, OS do maintain a separate stack for each thread.
C) True
D) False
 Question 5
K4 and Q3 are graphs with the following structures. which one of the following statement 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
Engineering-Mathematics        Graph-Theory
Question 5 Explanation: Both the above graphs are planar.
 Question 6
If the difference between the expectation of the square of a random variable (E[X2]) and the square of the expectation of the random variable (E[X])2 is denoted by R, then
 A R = 0 B R < 0 C R ≥ 0 D R > 0
Engineering-Mathematics       Probability
Question 6 Explanation:
We know that difference of E(X2) and E(X))2 is nothing but variance or V(X) which is always greater than or equal to zero.
So the answer will be R≥0.
 Question 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 D Turing machine
Compiler-Design       Compilers
Question 7 Explanation:
Lexical Analysis is implemented by finite automata
 Question 8
Let the page fault service time to 10 ms in a computer with average memory access time being 20 ns. If one page fault is generated for every 106 memory accesses, what is the effective access time for the memory?
 A 21 ns B 30 ns C 23 ns D 35 ns
Operating-Systems       Memory-Management
Question 8 Explanation:
P = page fault rate
EA = p × page fault service time + (1 – p) × Memory access time
=1/106×10×106+(1-1/106)×20 ≅29.9 ns
 Question 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 memory?
Computer-Organization       Machine-Instructions
Question 9 Explanation:
Here 20 will act as base and content of R2 will be index.
 Question 10
What does the following fragment of C-program print?
 `char` `c[] = ``"GATE2011"``;` `char` `*p =c;` `printf``(``"%s"``, p + p - p) ;`
 A GATE2011 B E2011 C 2011 D 011
Programming       C-Programming
Question 10 Explanation:
p is the starting address of array.
p - p = 4, and p+4 will be pointing to the fifth position in the array 'c'. So printf starts printing from 2 and prints 2011.
 Question 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 Data-Structures       Binary-Heap
Question 11 Explanation:
Heap is a complete binary tree
Option A: It violates the property of complete binary tree.
Option C: 8 is greater than 5. The root value is always greater than his children. So, the above tree is violating the property of max heap
Option D: 10 is greater than 8. The root value is always greater than his children. So, the above tree is violating the property of max heap
 Question 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 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.
Algorithms        Dynamic-Programming
Question 12 Explanation:
Key Note of Dynamic programming: 1. Dynamic programming is when you use past knowledge to make solving a future problem easier.
2. Dynamic programming is a technique used to avoid computing multiple time the same sub-problem in a recursive algorithm.
Note: It is neither backtracking nor branch and bound because we are not branching anywhere in the solution space. The algorithm is not divide and conquer as we are not dividing the problem and then merging the solution
 Question 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 [pnqn | n N]). Then which of the following is ALWAYS regular?
 A P ∩ Q B P – Q C Σ* – P D Σ* – Q
Theory-of-Computation       Regular-Language
Question 13 Explanation:
Exp: Σ* - P is the complement of P so it is always regular,
since regular languages are closed under complementation
 Question 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
Compiler-Design       Compilers
Question 14 Explanation:
Any identifier is also a token so it is recognized in lexical Analysis
 Question 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
Computer-Networks       Network-Security
Question 15 Explanation:
(A) It is possible to block entire HTTP traffic by blocking port no.80.
(B) Possible because it is network layer protocol.
(C) Possible because SP address is present in Network layer.
(D) Not possible, because to block specific user, we need user id which is present in Application layer.
 Question 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
Engineering-Mathematics        Probability
Question 16 Explanation:
Sample space = {HH, HT, TH} Required probability = 1/3
 Question 17
Consider different activities related to email:
```m1: Send an email from a mail client to a mail server
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
Computer-Networks        Application-Layer-Protocol
Question 17 Explanation:
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 in a web browser is done through HTTP
 Question 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 Ll. 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?
 A 4000 B 5000 C 4333 D 4667
Question 18 Explanation:
Note: Out of syllabus.
 Question 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 (t1) > (t2) B (t1) = (t2) C (t1) < (t2) D Nothing can be said about the relation between t1 and t2
Operating-Systems       Context-Switching
Question 19 Explanation:
Context switch between the processes involves mode switch also.
 Question 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 person-months?
 A 234.25 B 932.5 C 287.8 D 122.4
Question 20 Explanation:
Note: Out of syllabus.
 Question 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 (NFDA) C Deterministic single-tape Turning machine and Non-deterministic single tape Turning machine D Single-tape Turning machine and multi-tape Turning machine
Theory-of-Computation       NFA
Question 21 Explanation:
NPDA is more powerful than DPDA.
 Question 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
Question 22 Explanation:
Note: Out of syllabus.
 Question 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
Question 23 Explanation:
Note: Out of syllabus.
 Question 24
A computer handles several interrupt sources of which 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 when a key is
pressed or released)
. Interrupt from Hard Disk(raises interrupt when a disk
Which one of these will be handled at the HIGHEST priority?```

 A Interrupt from Hard Dist B Interrupt from Mouse C Interrupt from Keyboard D Interrupt from CPU temperature sensor
Computer-Organization       Interrupt
Question 24 Explanation:
The interrupts of higher priority are assigned to requests which, if delayed, can cause serious problems. High speed transfer device such as magnetic disks are given higher priority, and slow devices such as keyboard, mouse receive low priority. Also delaying a CPU temperature sensor can cause serious problems like can damage CPU.
Therefore, we can say that priorities are,
CPU temperature sensor > Hard disk > Mouse > Keyboard.
 Question 25
Consider a relational table with a single record for each registered student with the following attributes.
```1. Registration_Num: Unique registration number
of 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 join accounts. This attribute stores the
primary account number.
4. Name: Name of the student
5. Hostel_Room: Room number of the hostel
Which one of the following option is INCORRECT?```

 A BankAccount_Num is a candidate key B Registration_Num 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
Database-Management-System       Candidate-Keys
Question 25 Explanation:
In case two students hold joint account then Bank Account_Num will not uniquely determine other attributes.
 Question 26
 A f3, f2, f4, f1 B f3, f2, f1, f4 C f2, f3, f1, f4 D f2, f3, f4, f1
Algorithms        Asymptotic-Complexity
Question 26 Explanation:
If they are expecting to find an asymptotic complexity functions means
→ Divide functions into 2 categories
1. Polynomial functions
2. Exponential functions
Above 4 functions we have only one exponential function is f1 (n) = 2n . So, It’s value is higher than to rest of the functions.
Substitute log on both sides then we get an ascending order is f3, f2, f4.
 Question 27
Four matrices M1, M2, M3 and M4 of dimensions pxq, qxr, rxs and sxt respectively can be multiplied is several ways with different number of total scalar multiplications. For example, when multiplied as ((M1 X M2) X (M3 X M4)), the total number of multiplications is pqr + rst + prt. When multiplied as (((M1 X M2) X M3) X M4), the total number of scalar multiplications is pqr + prs + pst. If p = 10, q = 100, r = 20, s = 5 and t = 80, then the number of scalar multiplications needed is:
 A 248000 B 44000 C 19000 D 25000
Algorithms        Dynamic-Programming
Question 27 Explanation:
Given matrices are, p = 10
q = 100
r = 20
s = 5
t = 80
Total no. of matrix multiplication for (n+1) matrices,
2nCn/(n+1)
Here,
n+1 = 4
n = 3
So, total no. of matrix multiplication possible is,
6C3/4 = ∠6/∠3×∠3×4 = 5
So, total 5 cases are possible,
Case 1:
(((M1 × M2) × M3) × M4) ∴ Total no. of scalar multiplications needed is,
20000 + 4000 + 1000 = 25000
Case 2:
((M1 × M2) × (M3 × M4)) ∴ Total no. of scalar multiplications needed is,
20000 + 8000 + 16000 = 44000
Case 3:
(M1 ×(M2 ×(M3 × M4))) ∴ Total scalar multiplications,
160000 + 80000 + 8000 = 248000
Case 4:
((M1 ×(M2 ×M 3)) × M4) ∴ Total scalar multiplications,
10000 + 5000 + 4000 = 19000
Case 5:
(M1 × ((M2 × M3) × M4)) ∴ Total scalar multiplications,
10000 + 40000 + 80000 = 130000
Hence, the minimum number of scalar multiplications is, 19000.
 Question 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. 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.
Database-Management-System       Relational-Algebra
Question 28 Explanation:
Hashing works well on the "equal" queries, while ordered indexing works well better on range queries.
For example, consider B+ tree, once you have searched a key in B+; you can find range of values via the block pointers pointing to another block of values on the leaf node level.
 Question 29
Consider the matrix as given below. 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
Engineering-Mathematics       Linear-Algebra
Question 29 Explanation:
Given matrix is upper triangular matrix and its diagonal elements are its eigen values = 1, 4, 3
 Question 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 B 2.5 C 1.1 D 3
Computer-Organization       Instruction-Pipelining
Question 30 Explanation:
Sppedup = Time without pipelining/Time with pipelining
Clock cycle time of pipelining
= max (5ns, 6ns, 11ns, 8ns) + 1ns
= 11 + 1
= 12ns
Time without pipelining = 5 + 6 + 11 + 8 = 30 ns
∴ Speedup = 30/12 = 2.5
 Question 31
Definition of a language L with alphabet {a} is given as foloowing. What is the minimum number of states needed in a DFA to recognize L?
 A k+1 B n+1 C 2n+1 D 2k+1
Theory-of-Computation       Finite-Automata
Question 31 Explanation:
Given that n is a constant.
So lets check of n = 2,
L = a2k, k>0
Since k>0 than zero.
So L is the language accepting even no. of a's except 'ε'.
So DFA will be, So, no. of states required is 2+1 = 3.
So for ank, (n+1) states will be required.
 Question 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 meta-data (tags) for the cache?
 A 4864 bits B 6144 bits C 6656 bits D 5376 bits
Computer-Organization       Cache
Question 32 Explanation:
No. of cache blocks = cache size/size of a block = 8KB/32B = 256
So we need 8 bits for indexing the 256 blocks in the cache. And since a block is 32 bytes we need 5 word bits to address each byte.
So out of remaining (32 - 8 - 5), 19 bits should be tag bits.
So tag entry size = 19 + 1 (valid bit) + 1 (modified bit) = 21 bits
∴ Total size of metadata = 21 × Number blocks = 21 × 256 = 5376 bits
 Question 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 10 ms. 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 0.50 s B 1.50 s C 1.25 s D 1.00 s
Computer-Organization       Secondary-Storage
Question 33 Explanation:
Transfer Time = Seek Time + Rotational latency/2 + time to read/write
= 10ms + (60/12000)+0
For 100 libraries = 100(10ms + (60/12000)+0) = 1.5seconds
 Question 34
 A B C D Theory of Computation        Finite-Automata
Question 34 Explanation:
(A) True.
(B) False, as it accepts string 'b', which is not accepted by original DFA.
(C) Same reason as (B).
(D) False, as it accepts string 'bba' which is not accepted by the given DFA.
 Question 35
The following is the comment written for a C function
```/* This function computes the roots of a quadratic equation
a.x^2 + b.x + c = . 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 discreminant is positive
(iii) When discriminant is zero
(iv) When discriminant is negative.
Only in case (ii) and (iii) the stored roots are valid.
Otherwise 0 is stored in roots. The function returns
0 when the roots are valid and -1 otherwise.
The function 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. Which one of the following option 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
Question 35 Explanation:
Note: Out of syllabus.
T1 and T2 checking same condition a = 0 hence, any one of T1 and T2 is redundant.
T3, T4: in both case discriminant (D) = b2 – 4ac = 0. Hence any one of it is
T5 : D > 0
T6 : D < 0
 Question 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
Database-Management-System       SQL
Question 36 Explanation: Question 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 (73432)?
 A B C D Compiler-Design       Parsers
Question 37 Explanation:
7 ↓ 3 ↑ 4 ↑ 3 ↓ 2
⇒ 7 ↓ (3 ↑ (4 ↑ 3)) ↓ 2
⇒ 7 ↓ (3 ↑ (4 ↑ 3))) ↓ 2 as ↓ is left associative
 Question 38
Consider the languages L1,L2 and L3 as given below. Which of the following statements is NOT TRUE?
 A Push Down Automate (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
Theory-of-Computation       Identify-Class-Language
Question 38 Explanation:
L1: regular language
L2: context free language
L3: context sensitive language
 Question 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
Decrement the count
If count != 0 go to LOOP```

Assume that each statement in this program is equivalent to 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 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
Computer-Organization       DMA
Question 39 Explanation:
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 = 3502/1020=3.4
 Question 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 Data-Structures       Binary-Trees
Question 40 Explanation:
Corresponding to each set only 1 binary search tree can be formed because in-order is fixed. only 1 tree possible. If Binary trees would be asked n! possible corresponding to each distinct tree set. Here tree structure is fixed and have only 1 possibility for BST as elements are distinct.
 Question 41
Which one of the following options is CORRECT given three positive integers x,y and z, and a predicate A P(x) being true means that x is a prime number 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
Engineering-Mathematics       Propositional-Logic
Question 41 Explanation:
Statement: x is not equal to 1 and if there exists some z for all y such that product of y and z is x, then y is either the no. itselfor 1.
This is the definition of prime nos.
 Question 42
 A 0 B 2 C –i D i
Engineering-Mathematics       Calculus
Question 42 Explanation:
We know that, Question 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=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?
`SELECT Y FROM T WHERE X=7;`
`
 A 127 B 255 C 129 D 257
Database-Management-System       SQL
Question 43 Explanation: Question 44
Consider a finite sequence of random values X = [x1, x2, …, xn]. Let μx be the mean and σx be the standard deviation of X. Let another finite sequence Y of equal length be derived from this as yi = a * xi + b, where a and b are positive constants. Let μy 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 μy = aμx + b D σy = aσx + b
Engineering-Mathematics       Probability-and-Statistics
Question 44 Explanation:
σy is standard deviation then
y)2 is variance so,
yi = a * xi + b
y)2 = a2 x)2
⇒ σy = a σx
Hence option (D) is incorrect.
 Question 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.
 A 1/5 B 4/25 C 1/4 D 2/5
Engineering-Mathematics       Probability
Question 45 Explanation:
The possible events are
(2,1) (3,2) (4,3) (5,4).
So only 4 possibilities are there and sample space will be,
5C1 × 4C1 = 20
So probability = 4/20 = 1/5
 Question 46
Consider the following table of arrival time and burst time for three processes P0, P1 and P2.
` `
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
Operating-Systems       Process-Scheduling
Question 46 Explanation: CT = Completion time
TAT = Turn Around Time
WT = Waiting Time
TAT = CT - AT
WT = TAT - BT
Gantt Chart using pre-emptive shortest job first scheduling algorithm, Avg. WT = 4+0+11/3 = 5ns
 Question 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 initially stored in memory. The binary operators used in this expression tree can be evaluate by the machine only when the operands are in registers. The instructions produce results 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
Compiler-Design       Register-Allocation
Question 47 Explanation:
Load R1, a ; R1 ← M[a]
Load R2, b ; R2 ← M[b]
Sub R1, R2 ; R1 ← R1 – R2
Load R2, c ; R2 ← M[c]
Load R3, d ; R3 ← M[d]
Add R2, R3 ; R2 ← R2 + R3
Load R3, e ; R3 ← M[e]
Sub R3, 3 ; R3 ← R3 – R2
Add R1, R3 ; R1 ← R1 + R3
Total 3 Registers are required minimum
 Question 48
 A 9 B 8 C 5 D 2
Programming       C-Programming
Question 48 Explanation: ∴ 1+0+0+0+0+0+0+0+0+1+0 = 2
 Question 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;` `}`
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
Programming       C-Programming
Question 49 Explanation: ∴ 5+4+3+0 = 12
 Question 50
Consider the following circuit involving three D-type flip-flops used in a certail type of counter configuration. If all the flip-flops were reset to O 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
Digital-Logic-Design       Sequential-Circuits
Question 50 Explanation: So total no. of distinct output (states) are 4.
 Question 51
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?
 A 000 B 001 C 010 D 011
Digital-Logic-Design       Sequential-Circuits
Question 51 Explanation: So, after 010 it moves to 011.
 Question 52
An undirected graph G(V, E) contains n ( n > 2 ) nodes named v1 , v2 ,….vn. Two nodes vi , vj are connected if and only if 0 < |i – j| <= 2. Each edge (vi, vj ) 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?
 A 1/12(11n2-5n) B n2 – n + 1 C 6n – 11 D 2n + 1
Algorithms        Minimum-Spanning-Tree
Question 52 Explanation:
Let take example of 5 vertices, Cost of MST, = 3+4+6+8 = 21
Only option (B) satisfies it.
 Question 53
An undirected graph G(V, E) contains n ( n > 2 ) nodes named v1 , v2 ,….vn. Two nodes vi , vj are connected if and only if 0 < |i – j| <= 2. Each edge (vi, vj ) is assigned a weight i + j. A sample graph with n = 4 is shown below. 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
Algorithms        Minimum-Spanning-Tree
Question 53 Explanation:
Lets first draw graph with 10 vertices, Now MST of above graph is, ∴ The length of path from v5 to v6 in the MST is,
8+4+3+6+10 = 31
 Question 54
Consider a network with five nodes, N1 to N5 as shown below. The network a distance vector protocol. What is the routes Have stabilised, the distance vector a different notes 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) The network 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 distance of the best known path at the 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. 52. 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.
 A (3, 2, 0, 2, 5) B (3, 2, 0, 2, 6) C (7, 2, 0, 2, 5) D (7, 2, 0, 2, 6)
Computer-Networks       Routing
Question 54 Explanation: Question 55
Consider a network with five nodes, N1 to N5m as show below. The network a distance vector protocol. What is the routes Have stabilised, the distance vector a different notes 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)
 A 3 B 9 C 10 D ∞
Computer-Networks       Routing
Question 55 Explanation:
N3 has neighbors N2 and N4
N4 has the distance of 8 to N1
N3 has the distance of 2 to N4
So 2 + 8 = 10
 Question 56
If Log (P) = (1/2) Log (Q) = (1/3) Log (R), then which of the following options is TRUE?
 A P2 = Q3R2 B Q2 = PR C Q2 = R3P D R = P2Q2
Aptitude       Numerical
Question 56 Explanation:
logP = 1/2 logQ = 1/3 log (R) = k
∴ P = bk, Q = b2k, R = b3k
Now, Q2 = b4k = b3k bk = PR
 Question 57
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.
 A to visit B having to visit C visiting D for a visit
Aptitude       Verbal
Question 57 Explanation:
Contemplate is a transitive verb and hence is followed by a gerund Hence the correct usage of contemplate is verb + ing form.
 Question 58
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 og __________
 A hyperbolic B restrained C argumentative D indifferent
Aptitude       Verbal
Question 58 Explanation:
the tone of the sentence clearly indicates a word that is similar to understated is needed for the blank. Alternatively, the word should be antonym of strong (fail to make strong impression). Therefore, the best choice is restrained which means controlled/reserved/timid.
 Question 59
Choose the word from the options given below that is most nearly opposite in meaning to the given word: Amalgamate
 A merge B split C collect D separate
Aptitude       Verbal
Question 59 Explanation:
Amalgamate means combine or unite to form one organization of structure. So the best option here is spilt. Separate on the other hand, although a close synonym, it is too general to be the best antonym in the given question while Merge is the synonym; Collect is not related.
 Question 60
Which of the following options is the closest in the meaning to the word below: Inexplicable
 A Incomprehensible B Indelible C Inextricable D Infallible
Aptitude       Verbal
Question 60 Explanation:
Inexplicable means not explicable; that cannot be explained, understood, or accounted for. So the best synonym here is incomprehensible.
 Question 61
P,Q,R and S are four types of dangerous microbes recently found in a human habit. The area of each circle with it diameter printed in barcakets representl the growth of a single microbe surviving human immunity system with in 24 hours of entering the body. The danger to human begin varies proportionality with the toxicity, potency and growth attributed to a microbe show in the figure below A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. Which microbe should be the  company target in its first attempt?
 A P B Q C R D S
Aptitude       Numerical
Question 61 Explanation:
By observation of the table, we can say S Question 62
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 5 B 4 C 7 D 6
Aptitude       Numerical
Question 62 Explanation:
Checking with all options in formula: (4q+100/q) i.e. (V+F). Option A gives the minimum cost.
 Question 63
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 the 5th day?
 A 4 B 5 C 6 D 7
Aptitude       Numerical
Question 63 Explanation:
Let each truck carry 100 units.
2800 = 4n + e; n = normal
300 = 10n + 2; e = excess/pending
n = 100/3, e = 8000/3
5 days: 500 ×(5⋅100/3)+ 8000/3
Minimum possible = 6
 Question 64
A container originally contains 10 litres of pure spirit. Form this container 1 litre of spirit is 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?
 A 7.58 litres B 7.84 litres C 7 litres D 7.29 litres
Aptitude       Numerical
Question 64 Explanation:
10(729/1000×1=7.29 litres)
 Question 65
Few school curricula include a unit on how to deal with bereavement and grief, and ye all students at some point in their lives suffer from losses through death and parting Based on the aboce passage which topic would not be included in a unit on bereavement?
 A how to write a letter of condolence B what emotional stages are passed through in the healing process C what the leading causes of death are D how to give support to a grieving friend
Aptitude       Verbal
Question 65 Explanation:
The given passage clearly deals with how to deal with bereavement and grief and so after the tragedy occurs and not about precautions. Therefore, irrespective of the causes of death, a school student, rarely gets into details of causes–which is beyond the scope of the context. Rest all the important in dealing with grief.
There are 65 questions to complete.