JT(IT) 2018 PARTB Computer Science
Question 1 
Which of the following numerical values is NOT a valid constant in C language?
12345L  
018CDF
 
9.3e12  
0XBCF

→ 018CDF starts with 0 means octal number but actually we are given decimal and hexa numbers. So it is not a valid constant.
→ 9.3e12 float number
→ 0XBCF is hexa number. Valid constant.
Question 2 
Let P, Q and R be three atomic prepositional assertions, and
 X : (P ∨ Q) → R
Y : (P → R) ∨ (Q → R)
Which one of the following is a tautology?
X → Y
 
Y → X  
X ≣ Y  
~Y → X

Question 3 
Which of the following is NOT a symmetric key algorithm?
Ellipse Curve Cryptography
 
Advanced Encryption standard
 
Data Encryption Standard
 
Blowfish 
Question 4 
Which of the following statements is FALSE?
The long term scheduler controls the degree of multiprogramming
 
Multiple process of a single program cannot exist  
Ready queue of the processes resides in main memory
 
A process can have multiple sub processes

→ Ready queue of the processes resides in main memory.
→ A process can have multiple sub processes.
→ Multiple process of a single program cannot exist because each program can have only one process.
Question 5 
Which of the following Boolean equations is/are correct?
X(X'+ Y) = XY' X + XY = X X + X'Y = X + Y
only (iii)  
only (ii)
 
only (i)  
Both (ii) and (iii)

Question 6 
With respect to compiler design, "recursive descent" is a ____ parsing technique that reads the inputs from ____.
topdown, right to left
 
topdown, left to right
 
bottom up, right to left  
bottom up, left to right

→ Top down parsers reads the input from left to right and bottom up parsers are reads the input from left to right and reverse.
Question 7 
Which of the following statements is/are FALSE?
 (i) XML element names are case sensitive
(ii) In XML, empty element can be represented as
(iii) XML element names can contain spaces
only (iii)  
only (ii) and (iii)
 
only (i) and (iii)
 
only (ii)

1. text
2. attributes
3. other elements or a mix of the above
Note: XML element names cannot contain spaces.
Question 8 
For what values of k, the points(k+1, 2k),(k, 22K) and (4k, 62k) are collinear?
0, 1
 
1, 1  
1, 1/2
 
1/2, 1/2

1/2[X1(Y2  Y3) + X2(Y3  Y1) + X3(Y1  Y2)] = 0
Here, X1 = k + 1, Y1 = 2k, X2 = k, Y2 = 2 – 2k, X3 = 4  k, Y3 = 6 – 2k
1/2[k + 1(2 – 2k  6 + 2k) + k(6 – 2k  2k)  4 k(2k  2 + 2k)] = 0
1/2[k + 1(4) + k(6  4k) 4  k(4k  2)] = 0
1/2[4k  4 + 6k  4k^{2}  16k + 8  4k^{2} + 2k)] = 0
1/2(8k^{2}  4k + 4) = 0
8k^{2}  4k + 4 = 0
8k^{2}  8k + 4k + 4 = 0
8K(k + 1) + 4(k + 1) = 0
(k + 1) (4  8k) = 0
k + 1 = 0
k = 1
4  8k = 0
k = 4/8
k = 1/2
So, the value of k is 1 and 1/2 .
Question 9 
If a connected graph G has planar embedding with 4 faces and 4 vertices, then what will be the number of edges in G?
7  
6  
4  
3 
For any(connected) planar graph with v vertices, e edges and faces, we have
V  E + F = 2
= 4  E + 4 =2
E = 4  2 + 4
E = 6
Question 10 
What is the area bounded by the parabola 2y = x^{2} and the line x = y  4?
18  
36  
72  
6 
and the line x = y – 4  (2)
Then y = x+4
Now, Substitute Y value in Equation(1)
x^{2} = 2 ( x + 4 )  (3)
Solving equation3 we get x = 4,  2.
Place Values of x in equation (1) and (2) we will get y = 8, 2.
Then the points of intersection are (8, 4), (2, –2).
After solving the integration, we will get 18.
Question 11 
The following circuit represents the function of a 2–input __________ logic gate.
ExclusiveOR
 
ExclusiveNOR
 
NAND
 
NOR

Step2:
Step3: We have to apply not operation then we are getting ExNOR.
Question 12 
What is the possible number of reflexive relations on a set of 5 elements?
2^{25}
 
2^{15}  
2^{10}
 
2^{20}

Step2: The possible number of reflexive relations on a set of 5 elements 2^{(n2n)} which is 2^{20} for n=5.
Question 13 
XML documents form a ___ structure.
Binary tree
 
Tree
 
Linear list  
Graph 
→ This specification does not specify how the document entity is to be located by an XML processor; unlike other entities, the document entity has no name and might well appear on a processor input stream without any identification at all.
Question 14 
Banker’s algorithm is used for:
Deadlock avoidance  
Deadlock recovery
 
Deadlock resolution
 
Deadlock prevention

Question 15 
Which one of the following is most affected by the presence of outliers in sample data?
Variance
 
Mean
 
Median
 
Mode

For the sample data set:
1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4
We find the following mean, median, mode, and standard deviation:
Mean = 2.58
Median = 2.5
Mode = 2
Standard Deviation = 1.08
If we add an outlier to the data set:
1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 400
The new values of our statistics are:
Mean = 35.38
Median = 2.5
Mode = 2
Standard Deviation = 114.74
Note: Outliers often has a significant effect on your mean and standard deviation.
Question 16 
Consider the matrix A defined as follows:
What is the eigenvalue of 3A^{3 }+ 5A^{2 } 6A + 21, where I is an identity matrix?
4, 110, 10
 
1, 27, 8
 
1, 9, 4
 
4, 27, 9

Eigenvalues of A^{3} are 1, 27 and –8.
Eigenvalues of A^{2} are 1, 9 and 4.
Eigenvalues of A are 1, 3 and –2.
Eigenvalues of I are 1, 1 and 1.
∴ The eigenvalues of 3A^{3} + 5A^{2} – 6A + 2I.
First eigenvalue = 3(1) + 5(1) – 6(1) + 2(1) = 4
Second eigenvalue = 3(27) + 5(9) – 6(3) + 2(1) = 110
Third eigenvalue = 3(–8) + 5(4) – 6(–2) + 2(1) = 10
∴ The required eigenvalues are 4, 110, and 10.
Question 17 
If A and B are sets and AUB = A∩B, then which of the following is correct?
A=B  
A=∅
 
B=∅  
A⊂B

= x belongs to A intersection B
= x belongs to A and x Belongs to B
= x belongs to B
so A subset of B  (2)
Now we will let y belong to B which implies y belongs to A U B
= y belongs to A intersection B
= y belongs to A and y belongs to B
= y belongs to A
Therefore, B subset of A  (3) from (2) and (3) we get A=B.
Question 18 
What is the total number of spanning trees of a complete graph of 4 vertices (K_{4})?
16  
8  
4  
15 
n^{n2} = 4^{2} = 16
Question 19 
Considering 0address instructions machine, what will be the top of the stack after executing the following sequence of instructions?
PUSH 15, PUSH 4, PUSH 6, MULT, PUSH 30, ADD, ADD
30  
69  
54  
10 
Step1: PUSH 15,PUSH 4 and PUSH 6 from bottom to top. Now top of the stack value is 6.
Step2: Perform MULT operation. 6*4=24. Now present stack values are from bottom is 15 and 24.
Step3: Next again PUSH 30. Now top of the stack is 30.
Step4: Perform ADD operation. 30+24=54
Step5: Now present stack values are from bottom is 15 and 54. Perform ADD operation.
Step6: 15+54=69
Question 20 
The maximum number of boolean functions that can be formed using 3 boolean variable is ____.
512  
256  
128  
1024 
→ For three Boolean variables (n = 3), there are 2^{3} = 8 different cases, giving us a total of 2^{8}
= 256 Boolean functions of 3 variables.
Question 21 
Which of the following statements is/are correct?

(i) If the rank of the matrix of given vectors is equal to the number of vectors, then the vectors are linearly independent.
(ii) If the rank of the matrix of given vectors is less than the number of vectors, then the vectors are linearly dependent.
Both (i) and (ii)
 
Only (ii)
 
Only (i)  
Neither (i) nor (ii) 
→ You can think of an r x c matrix as a set of r row vectors, each having c elements; or you can think of it as a set of c column vectors, each having r elements.
→ The rank of a matrix is defined as (a) the maximum number of linearly independent column vectors in the matrix or (b) the maximum number of linearly independent row vectors in the matrix. Both definitions are equivalent.
For an r x c matrix,
1. If r is less than c, then the maximum rank of the matrix is r.
2. If r is greater than c, then the maximum rank of the matrix is c.
→ The rank of a matrix would be zero only if the matrix had no elements. If a matrix had even one element, its minimum rank would be one.
Question 22 
Which of the following is NOT a bottom up, shift reduce parser?
LR parser
 
LL parser  
SLR parser
 
LALR parser

1. SLR
2. LALR
3. CLR
4. LR(0)
Top Down parser:
1. Recursive descent
2. Non Recursive descent(LL(1))
Question 23 
Which of the following does NOT represent the Exclusive NOR operation over the binary variables A and B?
A’ ⊕ B’
 
A ⊕ B’
 
A’ ⊕ B
 
AB + A’B’ 
Question 24 
Namespaces
 
DTD  
CSS  
DOM

Question 25 
Suppose x and y are floating point variables that have been assigned the values x = 8.8 and y = 3.5. What will be the value of the following arithmetic expression?
2 * x / 3 * y
20.33335
 
24.45453
 
16.35353
 
20.53333 
= 1 (equal priority
Associativity (left to Right)
(((2 * x)/3) * y)
((2 x *) / 3) * y)
(2x * 31) * y
2x * 31) y*
(2x * 31 y*
Put the 2 * 8.8 * 3 / 3.5 *
= 20.53333
Question 26 
State whether TRUE or FALSE
 (i) In NDFA, the transition function δ: Q × Σ → 2^{Q}
(ii) NDFA does not permit empty string transitions
(i) False (ii) False
 
(i) True (ii) False
 
(i) False (ii) True
 
(i) True (ii) True 
An NDFA can be represented by a 5tuple (Q, ∑, δ, q_{0}, F) where
Q is a finite set of states.
∑ is a finite set of symbols called the alphabets.
δ is the transition function where δ: Q × ∑ → 2^{Q}
(Here the power set of Q (2Q) has been taken because in case of NDFA, from a state, transition can occur to any combination of Q states)
q_{0} is the initial state from where any input is processed (q_{0} ∈ Q).
F is a set of final state/states of Q (F ⊆ Q).
DFA: Empty string transitions are not seen in DFA.
NDFA: permits empty string transitions.
Question 27 
Which of the following data structures is used in level order traversal of a binary tree?
Skip list  
Stack  
Array
 
Queue

Example:
Level order traversal of binary tree.
For each node, first the node is visited and then it’s child nodes are put in a FIFO queue.
printLevelorder(tree)
1) Create an empty queue q
2) temp_node = root /*start from root*/
3) Loop while temp_node is not NULL
a) print temp_node>data
b) Enqueue temp_node’s children (first left then right children) to q
c) Dequeue a node from q and assign it’s value to temp_node
Note:
Level order traversal of binary tree is time Complexity is O(n) where n is number of nodes in the binary tree.
Question 28 
The boolean function X’Y’ + XY + X’Y, where X’ represents the complement of X, is equivalent to ____
X + Y’  
X’ + Y’  
X’ + Y
 
X + Y 
Question 29 
Which of the following is a white box testing technique?
Data flow testing
 
Equivalence class testing
 
Cause effect graphing
 
State based testing

White box testing techniques
1. Statement coverage
2. Branch CoverAge
3. Condition Coverage
4. Multiple Condition Coverage
5. Basis Path Testing
6. Flow graph notation
7. Loop Testing
Question 30 
In a BigEndian machine, a 32 bit word is stored at address 0 in a memory that is byte addressable. What byte of the word will be stored at address 0?
Byte 3
 
Byte 2
 
Byte 1
 
Byte 0

→ How is a 32bit pattern held in the four bytes of memory?
There are 32 bits in the four bytes and 32 bits in the pattern, but a choice has to be made about which byte of memory gets what part of the pattern. There are two ways that computers commonly do this:
Big Endian Byte Order: The most significant byte (the "big end") of the data is placed at the byte with the lowest address. The rest of the data is placed in order in the next three bytes in memory.
Little Endian Byte Order: The least significant byte (the "little end") of the data is placed at the byte with the lowest address. The rest of the data is placed in order in the next three bytes in memory.
→ In these definitions, the data, a 32bit pattern, is regarded as a 32bit unsigned integer.
→ The "most significant" byte is the one for the largest powers of two: 231, ..., 224. The "least significant" byte is the one for the smallest powers of two: 27, ..., 20.
→ For example, say that the 32bit pattern 0x12345678 is stored at address 0x00400000. The most significant byte is 0x12; the least significant is 0x78.
Within a byte the order of the bits is the same for all computers (no matter how the bytes themselves are arranged).
Question 31 
Which of the following relation schemas is definitely in BCNF?
R1(A,B)  
R4(A,B,C,D,E)
 
R3(A,B,C,D)
 
R2(A,B,C) 
1. BCNF is free from redundancy.
2. If a relation is in BCNF, then 3NF is also also satisfied.
3. Every Binary Relation ( a Relation with only 2 attributes ) is always in BCNF.
4. Sometimes going for BCNF form may not preserve functional dependency.
Question 32 
Suppose a network using CSMA/CD has a bandwidth of 10 Mbps. If the maximum propagation time is 25 microsec, that what will be the minimum frame size?
500 bits  
50 bits  
500 bytes
 
4*10^{11} bits

→ This means, in the worst case, a station needs to transmit for a period of 50 μs to detect the collision.
→ The minimum size of the frame is 10 Mbps × 50 μs = 500 bits or 62.5 bytes.
→ This is actually the minimum size of the frame for Standard Ethernet.
Question 33 
If 100 users are making 10 request/sec to a slotted ALOHA channel and each slot is of 50 m sec, then what will be the channel load?
10  
20  
2  
50 
→Total user = 100 making 10 request/sec, Then total number of requests are 1000
Each slot time is 50 ms, so the number of slots in one second = 1/(50 X 10^{3}) = 20 slots/sec
Requests per second = 1000
Time slots per second = 20
Channel load = Number of Requests / Number of Slots = 1000 / 20 = 50
Question 34 
Every cut set of a connected euler graph has____
An odd number of edges
 
At least three edges
 
An even number of edges  
A single edge 
Question 35 
A fair coin is tossed 6 times. What is the probability that exactly two heads will occur?
11/32  
1/64  
15/64
 
63/64 
The probability can be calculated as:
n is a total number of experiments
k is an expected number of successes
p is the probability of a success
Step2: The first task can be simply solved by calculating the probability of 2 successes:
A "success" is "tossing heads in a single toss".
A "failure" is "tossing tails in a single toss".
Step3: The probability of a success is ½
The number of all experiments is n=6.
The number of successes is k=2
Question 36 
Which of the following data structures is most suitable for radix sort?
Stack
 
Binary search tree
 
Tree
 
Linked list

→ This concept of a circularly linked trie structure is similar to the concept of a threaded binary tree. This structure will be called a circularly threaded trie.
Question 37 
How many solutions does the equation x + y  z = 11 have, where x, y and z are non negative integers?
120  
78  
156  
130 
Here, n=3 and k=11, giving you
Question 38 
Which of the following is the first module of a language processing system?
Preprocessor
 
Loader
 
Compiler
 
Linker

→ The output is said to be a preprocessed form of the input data, which is often used by some subsequent programs like compilers.
→ The amount and kind of processing done depends on the nature of the preprocessor.
→ Preprocessor is the first module of a language processing system.
Question 39 
Which of the following is the correct syntax to insert an image in HTML documents?
< a href=”flower.jpg”? >
 
< image href=”flower.jpg” width=”500” height=”600” >  
< img src=”flower.jpg” >
 
< img href=”flower.jpg” >

→ The < img > tag is empty, it contains attributes only, and does not have a closing tag.
→ The src attribute specifies the URL (web address) of the image: < img src="url" >
Question 40 
A graph G is dual if and only if G is a ___
Euler graph
 
Regular graph  
Complete graph  
Planar graph

→ The correspondence between edges of G and those of G* is as follows:
if e∈E(G) lies on the boundaries of faces X and Y, then the endpts of the dual edge e*∈(G*) are the vertices x and y that represent faces X and Y of G.
Question 41 
It is the infinite set of all possible strings of all possible lengths over Σ(input set) excluding ʎ(empty string)
 
It is the finite set of all possible strings of all possible lengths over Σ(input set) excluding ʎ(empty string)
 
It is the finite set of all possible strings of all possible lengths over Σ(input set)
 
It is the infinite set of all possible strings of all possible lengths over Σ(input set) 
It is the infinite set of all possible strings of all possible lengths over Σ(input set) excluding ʎ(empty string).
Question 42 
Which of the given options is the logical translation of the following statement, where F(x) and P(x) express the terms friend and perfect, respectively?
“None of my friends are perfect”?
∃x(~F(x)∧P(x))
 
∃x(F(x)∧ ~P(x))
 
~∃x(F(x)∧P(x))  
∃x(~F(x)∧~P(x))

P(x) represents x is perfect.
Given statement is “None of my friends are perfect”.
F(x)∧P(x) > X is both Friend and perfect.
~∃x > There is exist no one.
We can also write the above statement as follows
∀x[F(x) ⟹ ¬P(x)]
≡ ∀x[¬F(x) ∨ ¬P(x)]
≡∀x¬[F(x) ∧ P(x)]
≡¬∃x[F(x) ∧ P(x)]
Question 43 
Consider the following algorithm:
Algorithm Anand(n) { sum=0; For i=1 to n do { For j=1 to i do { sum=sum+i; } } }
What will be the output of this algorithm for n=10?
370  
385
 
380  
55 
Step1: if i=1, j is also will execute 1 time because it is purely dependent to the variable i.
Sep2: The sum variable is perform addition how many time jth loop executes with the difference of i value.
Question 44 
In C language ______ is a process in which a function calls itself repeatedly until some specified condition has been satisfied
Infinite loop
 
Call by value
 
Call by reference
 
Recursion 
Question 45 
The average rate of convergence of the bisection method is ____.
1/2  
3  
2  
1 
Question 46 
What is the return value of the C library function fmod(d1,d2), where d1 and d2 are integer numbers?
It returns the remainder of d2/d1, with the same sign as d1  
It returns the remainder of d2/d1, with the same sign as d2  
It returns the remainder of d1/d2, with the same sign as d1
 
It returns the remainder of d1/d2, with the same sign as d2

Take d1 = 10 and d2 = 20
d1/d2 = 10/20 = 10
So, option C is correct.
Question 47 
What is the chromatic number of an nvertex simple connected graph, which does NOT contain any oddlength cycle?
N  
N1  
2  
3 
→ A bipartite graph has the chromatic number 2.
Eg: Consider a square, which has 4 edges. It can be represented as bipartite ,with chromatic number 2.
Question 48 
Chose the option which matches each element of LIST1 with exactly one element of LIST2:
(i)(d), (ii)(c), (iii)(b), (iv)(a)
 
(i)(b), (ii)(a), (iii)(d), (iv)(c)
 
(i)(a), (ii)(d), (iii)(c), (iv)(b)
 
(i)(d), (ii)(b), (iii)(c), (iv)(a)

2. Gateway→ All seven layers: A gateway, as the name suggests, is a passage to connect two networks together that may work upon different networking models. They basically works as the messenger agents that take data from one system, interpret it, and transfer it to another system. Gateways are also called protocol converters and can operate at any network layer. Gateways are generally more complex than switch or router.
3. Router→ Network layer: A router is a device like a switch that routes data packets based on their IP addresses. Router is mainly a Network Layer device. Routers normally connect LANs and WANs together and have a dynamically updating routing table based on which they make decisions on routing the data packets. Router divide broadcast domains of hosts connected through it.
Bridge→ Data link layer: A bridge is a repeater, with add on functionality of filtering content by reading the MAC addresses of source and destination. It is also used for interconnecting two LANs working on the same protocol. It has a single input and single output port, thus making it a 2 port device.
Question 49 
How many different headings tags are available in HTML?
6  
8  
3  
5 
→ A heading element implies all the font changes, paragraph breaks before and after, and any white space necessary to render the heading.
→ The heading elements are H1, H2, H3, H4, H5, and H6 with H1 being the highest (or most important) level and H6 the least.
Question 50 
Considering an undirected graph, which of the following statements is/are true?
 (i) Number of vertices of odd degree is always even
(ii) Sum of degrees of all the vertices is always even
Neither (i) nor (ii)
 
Both (i) and (ii)  
Only (ii)  
Only (i)

True: Sum of degrees of all the vertices is always even.
Question 51 
In a full binary tree of height 10, the number of nodes with degree 0,1, and 2 will be ____,____ and ____ respectively.
Note: Consider height of a tree as the number of nodes in the longest path from root to any leaf node
512, 0, 511
 
512, 1, 510  
511, 0, 512
 
511, 1, 511 
Full binary tree consists of either 0 or 2 childs . So one child to the node is not possible.
The number of nodes with the degree of 1 is 0.
The nodes with degree 0 are leaf nodes, 2^{h1} = 2^{9} = 512.
The nodes with degree 2 are internal nodes 2^{h1}  1 = 511.
Question 52 
Which of the following greedy strategies gives the optimal solution for the following 01 knapsack problem?
w=30, w1=10, p1=11, w2=15, p2=12, w3=20, p3=24, w4=25, p4=25
Largest profit per unit weight first
 
Largest profit first
 
Lightest item first
 
Heaviest item first

Note: Even though they are asking 0/1 knapsack. We are always takes first profit/weight first.
→ W=30, we can exceed weight and we can’t take fractions of weight.
→ According to profit/weight, W3 having more profit. And W1 having more profit.
→ 0/1 knapsack optimal solution = 24+11 = 35
Question 53 
Select the option that best describes the relationship between the following graphs:
G and H are directed  
G and H are isomorphic
 
G and H are homomorphic  
G and H are not isomorphic 
1. V(G1) = V(G2)
2. E(G1) = E(G2)
3. Degree sequences of G1 and G2 are same.
4. If the vertices {V1, V2, ... Vk} form a cycle of length K in G1, then the vertices {f(V1), f(V2), … f(Vk)} should form a cycle of length K in G2.
→ Graph G and H are having same number of vertices and edges. So, it satisfied first rule.
→ u1 degree 2, u2 degree 3, u3 degree 3, u4 degree 2, u5 degree 3, u6 degree 3.
→ V1 degree 2, V2 degree 3, V3 degree 3, V4 degree 2, V5 degree 3, V6 degree 3.
→ But it violates the property of number of cycles. The number of cycles are not same.
Question 54 
Which of the following is the time complexity to find the determinant of an upper triangular matrix of order n*n?
Θ(n^{2.5})  
Θ(n)  
Θ(n^{2})
 
Θ(n) 
Question 55 
State whether TRUE or FALSE
 (i) Shortest remaining time (SRT) algorithm is the preemptive version of the shortest job next(SJN) CPU scheduling algorithm
(ii) A “context switch” is the mechanism to store and restore the state or context of a CPU in PCB
(i) True, (ii) True  
(i) False, (ii) False
 
(i) False, (ii) True
 
(i) True, (ii) False

TRUE: A “context switch” is the mechanism to store and restore the state or context of a CPU in PCB.
Question 56 
A language is a subset of Σ* for some alphabet Σ. If a language takes all possible strings of length 2 over Σ = {a,b}, then, which of the below is correct?
L = {ab,bb,ba}
 
L = {aa,ab,ba,bb}
 
L = {ab,bb,aa}
 
L = {ab,ba,aa} 
→ We are computing all possible strings using 2^{n} formula. Where n is number of strings.
Question 57 
Which of the following protocols is used to map IP address to MAC address?
ARP  
IP  
DHCP  
RARP

→ MAC address to IP address using Reverse Address resolution protocol(RARP).
Question 58 
Consider the following statements. Which one is/are correct?
 (i) The LU decomposition method fails if any of the diagonal elements of the matrix is zero.
(ii) The LU decomposition is guaranteed when the coefficient matrix is positive definite.
Both (i) and (ii)  
Only (i)
 
Neither (i) nor (ii)  
Only (ii) 
1. The LU decomposition method fails if any of the diagonal elements of the matrix is zero.
2. The LU decomposition is guaranteed when the coefficient matrix is positive definite.
Question 59 
What is the base(radix) of the number system whose numbers 312, 20 and 13.1 satisfy the following equation?
312/20 = 13.18  
4  
5  
6 
(3r^{2} + r + 2) / 2r = (r + 3 + 1/r)
(3r^{2} + r + 2) / 2r = (r^{2} + 3r + 1) / r
(3r^{2} + r + 2) = (2r^{2} + 6r + 2)
r^{2}  5r = 0
Therefore, r = 5
Question 60 
Which of the following DFD levels depicts the entire information system as one diagram concealing all the underlying details?
Level 0  
Level 1  
Level 3  
Level 2 
→ It Highest abstraction level DFD is known as Level 0 DFD, which depicts the entire information system as one diagram concealing all the underlying details.
→ Level 0 DFDs are also known as context level DFDs.
→ It shows a data system as a whole and emphasizes the way it interacts with external entities.
→ This DFD level 0 example shows how such a system might function within a typical retail business.
DFD level 1:
→ DFD depicts basic modules in the system and flow of data among various modules.
→ Level 1 DFD also mentions basic processes and sources of information.
→ It breaks down the main processes in to subprocesses that can then be analyzed and improved on a more intimate level.
DFD level 2:
A level 2 data flow diagram (DFD) offers a more detailed look at the processes that make up an information system than a level 1 DFD does it. Higher level DFDs can be transformed into more specific lower level DFDs with deeper level of understanding unless the desired level of specification is achieved.
Question 61 
Which of the following phases of the compilation process is also known as parsing?
Lexical analysis
 
Code optimization
 
Syntax analysis
 
Semantic analysis

Question 62 
Consider an AVL tree constructed by inserting the elements 18, 10, 5, 3, 27, 7, 35, 43, 32 one by one. Which of the following options give the number of comparisons to search the key value 45 in this AVL tree?
5  
4  
3  
2 
Question 63 
Which of the following Hasse diagrams is are lattice(s)?
Only (a), (b) and (c)  
Only (a) and (b)
 
Only (b) and (c)
 
Only (a) and (c)

Question 64 
The DELETE/FROM/WHERE command is used for removing one or more ___.
Attributes from a table(relation)
 
Tables from a database
 
Databases
 
Tuples from a table(relation)

DROP command is used for dropping entire table.
Question 65 
What is the hexadecimal representation of the decimal number 8537?
(2059)_{16}
 
(2159)_{16}
 
(2195)_{16}
 
(2157)_{16}

Step2: (8537)_{10} = (0010000101011001)_{2}
Step3: Divide binary number into 4 segments (0010 0001 0101 1001)_{2}
Step4: Write equivalent number of hexadecimal (2159)_{16}
Question 66 
Which of the following is a recursive algorithm to convert a positive decimal integers into equivalent binary integers?
Take decimal number is 12.
Step1 → 12%2 which is equal to 0+10*(⌊12/2⌋)%2
Step2 → 6%2 which is equal to 0+10*(⌊6/2⌋)%2
Step3 → 3%2 which is equal to 1+10*(⌊3/2⌋)%2
Step4 → 1%2 which is equal to 1+10*(⌊1/2⌋)%2
Question 67 
Referential integrity constraints works on the concept of:
Secondary key
 
Super key
 
Foreign key
 
Primary key

Referential Integrity Rules
→ A referential integrity rule is a rule defined on a key (a column or set of columns) in one table that guarantees that the values in that key match the values in a key in a related table (the referenced value).
→ Referential integrity also includes the rules that dictate what types of data manipulation are allowed on referenced values and how these actions affect dependent values.
The rules associated with referential integrity are:
1. Restrict: Disallows the update or deletion of referenced data.
2. Set to Null: When referenced data is updated or deleted, all associated dependent data is set to NULL.
3. Set to Default: When referenced data is updated or deleted, all associated dependent data is set to a default value.
4. Cascade: When referenced data is updated, all associated dependent data is correspondingly updated. When a referenced row is deleted, all associated dependent rows are deleted.
5. No Action: Disallows the update or deletion of referenced data. This differs from RESTRICT in that it is checked at the end of the statement, or at the end of the transaction if the constraint is deferred.
Question 68 
Which of the following is NOT a goal of the software testing?
Failure detection
 
Fault detection
 
Size reduction  
Error detection

Question 69 
Choose the option that correctly matches each element of LIST1 with exactly one element of LIST2:
LIST1 LIST2 (i) NewtonRaphson method (a) Solving nonlinear equation (ii) Simpson’s rule (b) Solving ordinary differential equations (iii)RungeKutta method (c) Numerical integration (iv) Gauss elimination (d) Interpolation
(i)(b), (ii)(d), (iii)(a), (iv)(c)  
(i)(a), (ii)(b), (iii)(c), (iv)(d)
 
(i)(a), (ii)(c), (iii)(d), (iv)(b)
 
(i)(d), (ii)(c), (iii)(b), (iv)(a)

Simpson’s rule→ Numerical integration
RungeKutta method→ Solving ordinary differential equations
Gauss elimination→ Solving nonlinear equation
Question 70 
How many ways are there to arrange the nine letters of the word ALLAHABAD?
4560
 
4000
 
7560
 
7500

Step2: Total number of alphabets! / alphabets are repeating using formula (n!) / (r1! r2!..).
Step3: Repeating letters are 4A's and 2L's
= 9! / (4!2!)
= 7560
Question 71 
Consider an array with n elements. Which of the following options gives the maximum number of swap(a_{j}, a_{j+1}) operations to sort the array elements using efficient bubble sort algorithm?
n^{2} /2  
n(n1)/2  
n^{2}
 
n(n+1)/2 
→ This means that in the first iteration it would have to look at n elements, then after that it would look n  1 elements (since the biggest integer is at the end) and so on and so forth till 1 comparison occurs.
→ For n number of numbers, total number of comparisons done will be (n1)+ ... + 2 + 1.
= (n*(n1))/2
= O(n^{2})
Question 72 
A DFA can be expressed as a 5 tuple(Q, Σ, δ, q_{0}, F), where δ is the transition function defined as ___?
δ: Σ → Q
 
δ: Q x Q → Σ  
δ: Q → Q
 
δ: Q x Σ → Q

DFA consists of 5 tuples {Q, ∑, q, F, δ}.
Q : set of all states.
∑ : set of input symbols. (Symbols which machine takes as input)
q : Initial state. (Starting state of a machine)
F : set of final state.
δ : Transition Function, defined as δ: QX∑ → Q.
Question 73 
How many bit strings of length eight (either start with a 1 bit or end with the two bits 00) can be formed?
64  
255  
160  
128 
1. Number of bit strings of length eight that start with a 1 bit: 2^{7} = 128
2. Number of bit strings of length eight that end with bits 00: 2^{6} = 64
3. Number of bit strings of length eight that start with a 1 bit and end with bits 00: 2^{5} = 32
The number is 128+64+32 = 160
Question 74 
Which of the following statements are logically equivalent?
 (i) ∀x(P(x))
(ii) ~∃x(P(x))
(iii) ~∃x(~P(x))
(iv) ∃x(~P(x))
Only (ii) and (iv)  
Only (ii) and (iii)
 
Only (i) and (iv)
 
Only (i) and (ii) 
Question 75 
State whether TRUE or FALSE
 (i) Secondary index cannot be defined on key attribute values
(ii) In B^{+} tree indexing the nonleaf nodes contain the actual data pointers
(i)False, (ii)True  
(i)True, (ii)True
 
(i)False, (ii)False
 
(i)True, (ii)False 
→ Indexing can be of the following types −
1. Primary Index − Primary index is defined on an ordered data file. The data file is ordered on a key field. The key field is generally the primary key of the relation.
2. Secondary Index − Secondary index may be generated from a field which is a candidate key and has a unique value in every record, or a nonkey with duplicate values.
3. Clustering Index − Clustering index is defined on an ordered data file. The data file is ordered on a nonkey field.
→ B^{+} tree
The structure of leaf nodes of a B^{+} tree is quite different from the structure of internal nodes of the B^{+} tree. Since data pointers are present only at the leaf nodes, the leaf nodes must necessarily store all the key values along with their corresponding data pointers to the disk file block, in order to access them. Moreover, the leaf nodes are linked to provide ordered access to the records.
Question 76 
What is the solution of the recurrence relation a_{n} = 6a_{n1}  9a_{n2} with initial conditions a_{0}=1 and a_{1}=6?
a_{n} = 3^{n} + 3n^{2}
 
a_{n} = 3^{n} + n3^{n}
 
a_{n} = 3^{n} + 3n^{n}
 
a_{n} = n^{3} + n3^{n}

→ Suppose that the characteristic equation r^{k} −c_{1}r^{k}−1 −···−c_{k} = 0 has k distinct roots r_{1}, r_{2}, ..., r_{k}.
→ Then, a sequence {a_{n}} is a solution of the recurrence relation: a_{n} = c_{1}a_{n−1} + c_{2}a_{n−2} + ··· + c_{k}a_{n−k}
→ if and only if a_{n} = α_{1}r^{n}_{1} + α_{2}r^{n}_{2} + ··· + α_{k} r^{n}_{k} for n = 0,1,2,..., where α_{1}, α_{2}, ..., α_{k} are constants.
→ r^{2} − 6r + 9 = 0 has only 3 as a root.
→ So the format of the solution is a_{n} = α_{1}3^{n} + α_{2}n3^{n}.
→ Need to determine α_{1} and α_{2} from initial conditions:
a_{0} = 1 = α_{1}
a_{1} = 6 = α_{1}3 + α_{2}3
Solving these equations we get α_{1}=1 and α_{2}=1
Therefore, a_{n} = 3^{n} + n3^{n}.
Question 77 
What is the Cyclomatic Complexity of the following flowgraph of a software code?
10  
4  
8  
2 
Number of regions(R) + 1
Predicates(P) + 1
Edges(E)  Vertex(V) + 2
Step2: We can apply any formula to find cyclomatic complexity.
Step3: 8 vertex and 10 edges.
10  8 + 2 = 4
Question 78 
Which of the following ‘C’ language operators has the right to left associativity?
Relational operators
 
Conditional operators
 
Logical AND and OR operators
 
Arithmetic multiply and divide operators

Question 79 
What is the minimum number of 2 input NOR gates to implement the Boolean function (XY+Z)?
8  
5  
3  
7 
= (X+Z)(Y+Z)( Distribute + over .)
= ((X+Z)' +(Y+Z)' )'
Question 80 
If R(A,B,C,D) is a relation schema, which is decomposed into R1(A,B,C) and R2(C,D), which of the following ensures that the given decomposition is non additive(or lossless)?
R1 → R2
 
R2 → R1
 
R1 ∩ R2 → R1 or R1 ∩ R2 → R2
 
R1 U R2 → R1 R1 U R2 → R2

For lossless decomposition:
R_{1} ∩ R_{2} → R_{1} (OR) R_{1} ∩ R_{2} → R_{1}  R_{2}
R_{1} ∩ R_{2} → R_{2} (OR) R_{1} ∩ R_{2} → R_{2}  R_{1}
Question 81 
If r and s are regular expression representing the languages L(r) and L(s), respectively, then which of the following is FALSE?
(r)(s) is a regular expression representing L(r)UL(s)
 
(r)(s) is a regular expression representing (L(r))* or (L(s))*  
(r)* is a regular expression representing (L(r))*  
(r)(s) is regular expression representing L(r)L(s)

1. Union : (r)(s) is a regular expression denoting L(r) U L(s)
2. Concatenation : (r)(s) is a regular expression denoting L(r)L(s)
3. Kleene closure : (r)* is a regular expression denoting (L(r))*
(r) is a regular expression denoting L(r).
Question 82 
Which of the following statements about the NewtonRaphson method is/are correct?
 (i) It is quadratic convergent
(ii) If f'(x) is zero, it fails
(iii) It is also used to obtain complex root
(i), (ii) and (iii)
 
only (i) and (iii)
 
only (i) and (ii)  
only (i)

Note: NewtonRaphson method is mainly used for Interpolation.
Question 83 
What is the minimum number of students in a class to be sure that three of them are born in the same month?
24  
12  
25  
13 
Question 84 
Considering every instruction and address as one word long, how many memory access are required for the following instruction, where R1, R2 and R3 are registers, and (R3) represents that R3 contains a memory address where some value (operand) is stored?
ADD R1, R2, (R3)
4  
1  
3  
2 