GATE 2011
Question 1 
The simplified SOP (sum of product) form of the boolean expression
Question 2 
The minimum number of D flipflops needed to design a mod258 counter is
9  
8  
512  
258 
The max Mod values is 2n.
So 2^{n} ≥ 258 ⇒ n = 9
Question 3 
Which one of the following circuits is NOT equivalent to a 2input XNOR (exclusive NOR) gate?
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?
On perthread basis, the OS maintains only CPU register state  
The OS does not maintain a separate stack for each thread  
On perthread basis, the OS does not maintain virtual memory state  
On per thread basis, the OS maintains only scheduling and accounting information 
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?
K4 is planar while Q3 is not  
Both K4 and Q3 are planar  
Q3 is planar while K4 is not  
Neither K4 not Q3 is planar 
Both the above graphs are planar.
Question 6 
If the difference between the expectation of the square of a random variable (E[X^{2}]) and the square of the expectation of the random variable (E[X])^{2} is denoted by R, then
R = 0  
R < 0  
R ≥ 0  
R > 0 
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?
Finite state automata  
Deterministic pushdown automata  
NonDeterministic pushdown automata  
Turing machine 
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 10^{6} memory accesses, what is the effective access time for the memory?
21 ns  
30 ns  
23 ns  
35 ns 
EA = p × page fault service time + (1 – p) × Memory access time
= 1/10^{6}×10×106+(11/106)×20 ≅ 29.9 ns
Question 9 
Consider a hypothetical processor with an instruction of type LW R1, 20 (R2), which during execution reads a 32bit word from memory and stores it in a 32bit 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?
Immediate Addressing  
Register Addressing  
Register Indirect Scaled Addressing  
Base Indexed Addressing 
Question 10 
What does the following fragment of Cprogram print?
char c[] = "GATE2011"; char *p =c; printf("%s", p + p[3]  p[1]) ;
GATE2011  
E2011  
2011  
011 
p[3]  p[1] = 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 maxheap 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 maxheap?
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:n1] is given below. Let L_{i} denote the length of the longest monotonically increasing sequence starting at index i in the array
Initialize L_{n1}=1. For all i such that 0≤i≤n2
Finally the length of the longest monotonically increasing sequence is Max(L_{0}, L_{1}, ..., L_{n1}).
Which of the following statements is TRUE?
The algorithm uses dynamic programming paradigm  
The algorithm has a linear complexity and uses branch and bound paradigm  
The algorithm has a nonlinear polynomial complexity and uses branch and bound paradigm  
The algorithm uses divide and conquer paradigm 
2. Dynamic programming is a technique used to avoid computing multiple time the same subproblem 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 contextfree language such that Q ⊆ P. (For example, let P be the language represented by the regular expression p*q* and Q be [p^{n}q^{n}  n ∈ N]). Then which of the following is ALWAYS regular?
P ∩ Q  
P – Q  
Σ* – P  
Σ* – Q 
since regular languages are closed under complementation.
Question 14 
In a compiler, keywords of a language are recognized during
parsing of the program  
the code generation  
the lexical analysis of the program  
dataflow analysis 
Question 15 
A layer4 firewall (a device that can look at all protocol headers up to the transport layer) CANNOT
block entire HTTP traffic during 9:00PM and 5:00AM  
block all ICMP traffic  
stop incoming traffic from a specific IP address but allow outgoing traffic to the same IP address  
block TCP traffic from a specific user on a multiuser system during 9:00PM and 5:00AM 
(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?
1/3  
1/4  
1/2  
2/3 
Required probability = 1/3
Question 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?
m1: HTTP m2: SMTP m3: POP  
m1: SMTP m2: FTP m3: HTTP  
m1: SMTP m2: POP m3: HTTP  
m1: POP m2: SMTP m3: IMAP 
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?
4000  
5000  
4333  
4667 
Question 19 
Let the time taken to switch between user and kernel modes of execution be t_{1} while the time taken to switch between two processes be t_{2}. Which of the following is TRUE?
(t_{1}) > (t_{2})  
(t_{1}) = (t_{2})  
(t_{1}) < (t_{2})  
Nothing can be said about the relation between t_{1} and t_{2} 
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 personmonths 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?
234.25  
932.50  
287.80  
122.40 
Question 21 
Which of the following pairs have DIFFERENT expressive power?
Deterministic finite automata (DFA) and Nondeterministic finite automata (NFA)  
Deterministic push down automata (DPDA) and Nondeterministic push down automata (NFDA)  
Deterministic singletape Turning machine and Nondeterministic single tape Turning machine  
Singletape Turning machine and multitape Turning machine 
Hence answer is (B).
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?
Embed web objects from different sites into the same page  
Refresh the page automatically after a specified interval  
Automatically redirect to another page upon download  
Display the client time as part of the page 
Question 23 
Which of the following is NOT desired in a good Software Requirement Specifications (SRS) document?
Functional Requirements  
NonFunctional Requirements  
Goals of Implementation  
Algorithms for Software Implementation 
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 read is completed)
Which one of these will be handled at the HIGHEST priority?
Interrupt from Hard Dist  
Interrupt from Mouse  
Interrupt from Keyboard  
Interrupt from CPU temperature sensor 
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?
BankAccount_Num is a candidate key  
Registration_Num can be a primary key  
UID is a candidate key if all students are from the same country  
If S is a superkey such that S∩UID is NULL then S∪UID is also a superkey 
Question 26 
Which of the given options provides the increasing order of asymptotic complexity of functions f_{1}, f_{2}, f_{3} and f_{4}?
f_{1}(n)=2^{n} f_{2}(n)=n^{3/2} f_{3}(n)=n log_{2} n f_{4}(n)=n^{log2n}
f_{3}, f_{2}, f_{4}, f_{1}  
f_{3}, f_{2}, f_{1}, f_{4}  
f_{2}, f_{3}, f_{1}, f_{4}  
f_{2}, f_{3}, f_{4}, f_{1} 
→ Divide functions into 2 categories
1. Polynomial functions
2. Exponential functions
Above 4 functions we have only one exponential function is f_{1} (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 f_{3}, f_{2}, f_{4}.
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:
248000  
44000  
19000  
25000 
p = 10
q = 100
r = 20
s = 5
t = 80
Total no. of matrix multiplication for (n+1) matrices,
^{2n}C_{n}/(n+1)
Here,
n+1 = 4
n = 3
So, total no. of matrix multiplication possible is,
^{6}C_{3}/4 = ∠6/∠3×∠3×4 = 5
So, total 5 cases are possible,
Case 1:
(((M_{1} × M_{2}) × M_{3}) × M_{4})
∴ Total no. of scalar multiplications needed is,
20000 + 4000 + 1000 = 25000
Case 2:
((M_{1} × M_{2}) × (M_{3} × M_{4}))
∴ Total no. of scalar multiplications needed is,
20000 + 8000 + 16000 = 44000
Case 3:
(M_{1} ×(M_{2} ×(M_{3} × M_{4})))
∴ Total scalar multiplications,
160000 + 80000 + 8000 = 248000
Case 4:
((M_{1} ×(M_{2} ×M _{3})) × M_{4})
∴ Total scalar multiplications,
10000 + 5000 + 4000 = 19000
Case 5:
(M_{1} × ((M_{2} × M_{3}) × M_{4}))
∴ 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 A_{1}, A_{2},…, A_{n} and let 1≤p≤n. Two queries Q1 and Q2 are given below.
 Q1: π_{A1},...,A_{p}(σ_{Ap=c}(r)) where c is a constant
Q2: π_{A1},...,A_{p}(σ_{c1≤Ap≤c2}(r)) where c_{1} and c_{2} is a constants
The database can be configured to do ordered indexing on A_{p} or hashing on A_{p}. Which of the following statements is TRUE?
Ordered indexing will always outperform hashing for both queries  
Hashing will always outperform ordered indexing for both queries  
Hashing will outperform ordered indexing on Q1, but not on Q2  
Hashing will outperform ordered indexing on Q2, but not on Q1. 
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?
1, 4, 3  
3, 7, 3  
7, 3, 2  
1, 2, 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 nonpipeline implementation?
4.0  
2.5  
1.1  
3.0 
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 following.
L = {a^{nk} k>0, and n is a positive integer constant}
What is the minimum number of states needed in a DFA to recognize L?
k+1  
n+1  
2^{n+1}  
2^{k+1} 
So lets check of n = 2,
L = a_{2k}, 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 a^{nk}, (n+1) states will be required.
Question 32 
An 8KB directmapped writeback cache is organized as multiple blocks, each of size 32bytes. The processor generates 32bit 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?
4864 bits  
6144 bits  
6656 bits  
5376 bits 
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).
0.50 s  
1.50 s  
1.25 s  
1.00 s 
= 10ms + (60/12000)+0
For 100 libraries = 100(10ms + (60/12000)+0) = 1.5seconds
Question 34 
A deterministic finite automation (DFA) D with alphabet Σ={a,b} is given below.
Which of the following finite state machines is a valid minimal DFA which accepts the same language as D?
(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 nonredundant tests using equivalence class partitioning approach from input perspective for black box testing?
T1, T2, T3, T6  
T1, T3, T4, T5  
T2, T4, T5, T6  
T2, T3, T4, T5 
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 7000.00What 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 );
3  
9  
5  
6 
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 (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.
 L1 = {0^{p}1^{q}p,q∈N},
L2 = {0^{p}1^{q}p,q∈N and p=q} and
L3 = {0^{p}1^{q}0^{r}p,q,r∈N and p=q=r}.
Which of the following statements is NOT TRUE?
Push Down Automate (PDA) can be used to recognize L1 and L2  
L1 is a regular language  
All the three languages are context free  
Turing machines can be used to recognize all the languages 
L2: context free language
L3: context sensitive language
Question 39 
On a nonpipelined 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 machine instruction which takes one clock cycle to execute if it is a nonload/store instruction. The loadstore 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 inputoutput?
3.4  
4.4  
5.1  
6.7 
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?
0  
1  
n!  
Question 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))P(x) being true means that x is a prime number  
P(x) being true means that x is a number other than 1  
P(x) is always true irrespective of the value of x
 
P(x) being true means that x has exactly two factors other than 1 and x 
This is the definition of prime numbers.
Question 42 
Given i=√1, what will be the evaluation of the definite integral
0  
2  
i  
i 
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;
127  
255  
129  
257 
Question 44 
Consider a finite sequence of random values X = [x_{1}, x_{2}, …, x_{n}]. 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 y_{i} = a * x_{i} + b, where a and b are positive constants. Let μ_{y} be the mean and σ_{y} be the standard deviation of this sequence. Which one of the following statements is INCORRECT?
Index position of mode of X in X is the same as the index position of mode of Y in Y.  
Index position of median of X in X is the same as the index position of median of Y in Y.  
μ_{y} = aμ_{x} + b  
σ_{y} = aσ_{x} + b 
(σ_{y})^{2} is variance so,
y_{i} = a * x_{i} + b
(σ_{y})^{2} = a^{2 }(σ_{x})^{2}
⇒ σ_{y} = a σ_{x}
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.
1/5  
4/25  
1/4  
2/5 
(2,1) (3,2) (4,3) (5,4).
So only 4 possibilities are there and sample space will be,
^{5}C_{1} × ^{4}C_{1} = 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 preemptive 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?
5.0 ms  
4.33 ms  
6.33 ms  
7.33 ms 
CT = Completion time
TAT = Turn Around Time
WT = Waiting Time
TAT = CT  AT
WT = TAT  BT
Gantt Chart using preemptive shortest job first scheduling algorithm,
Avg. WT = 4+0+11/3 = 5ns
Question 47 
Consider evaluating the following expression tree on a machine with loadstore 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?
2  
9  
5  
3 
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 
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(513,2)?
9  
8  
5  
2 
∴ 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) ?
345  
12  
5  
3 
∴ 5+4+3+0 = 12
Question 50 
Consider the following circuit involving three Dtype flipflops used in a certain type of counter configuration.
If all the flipflops were reset to O at power on, what is the total number of distinct outputs *states) represented by PQR generated by the counter?
3  
4  
5  
6 
So total no. of distinct output (states) are 4.
Question 51 
Consider the following circuit involving three Dtype flipflops 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?
000  
001  
010  
011 
So, after 010 it moves to 011.
Question 52 
An undirected graph G(V, E) contains n (n > 2) nodes named v_{1}, v_{2}, ….v_{n}. Two nodes v_{i} , v_{j} are connected if and only if 0 < i – j ≤ 2. Each edge (v_{i}, v_{j}) 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?
1/12(11n^{2}5n)  
n^{2} – n + 1  
6n – 11  
2n + 1 
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 v_{1}, v_{2}, ….v_{n}. Two nodes v_{i} , v_{j} are connected if and only if 0 < i – j ≤ 2. Each edge (v_{i}, v_{j}) is assigned a weight i + j. A sample graph with n = 4 is shown below.
The length of the path from v_{5} to v_{6} in the MST of previous question with n =10 is
11  
25  
31  
41 
Now MST of above graph is,
∴ The length of path from v_{5} to v_{6} 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 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.
The cost of link N2N3 reduces to 2(in both directions). After the next round of updates, what will be the new distance vector at node, N3.
(3, 2, 0, 2, 5)  
(3, 2, 0, 2, 6)  
(7, 2, 0, 2, 5)  
(7, 2, 0, 2, 6) 
Question 55 
Consider a network with five nodes, N1 to N5 as shown below.
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.
After the update in the previous question, the link N1N2 goes down. N2 will reflect this change immediately in its distance vector as cost, infinite. After the NEXT ROUND of update, what will be cost to N1 in the distance vector of N3?
3  
9  
10  
∞ 
N2 has made entry ∞
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?
P^{2} = Q^{3}R^{2}  
Q^{2} = PR  
Q^{2} = R^{3}P  
R = P^{2}Q^{2} 
∴ P = b^{k}, Q = b^{2k}, R = b^{3k}
Now, Q^{2} = b^{4k} = b^{3k} b^{k} = 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.
to visit  
having to visit  
visiting  
for a visit 
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 or __________.
hyperbolic  
restrained  
argumentative  
indifferent 
Question 59 
Choose the word from the options given below that is most nearly opposite in meaning to the given word:
Amalgamatemerge  
split  
collect  
separate 
Question 60 
Which of the following options is the closest in the meaning to the word below:
InexplicableIncomprehensible  
Indelible  
Inextricable  
Infallible 
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 brackets represents 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?
P  
Q  
R  
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)?
5  
4  
7  
6 
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?
4  
5  
6  
7 
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?
7.58 litres  
7.84 litres  
7 litres  
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 above passage which topic would not be included in a unit on bereavement?
how to write a letter of condolence  
what emotional stages are passed through in the healing process  
what the leading causes of death are  
how to give support to a grieving friend 