## UGC-NET DEC-2019 Part-2

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Question 1 |

Consider the following statements:

(a) The running time of dynamic programming algorithm is always θ(ρ) where ρ is number of subproblems.

(b) When a recurrence relation has cyclic dependency, it is impossible to use that recurrence relation (unmodified) in a correct dynamic program.

(c) For a dynamic programming algorithm, computing all values in a bottom-up fashion is asymptotically faster than using recursion and memorization.

(d) If a problem X can be reduced to a known NP-hard problem, then X must be NP-hard.

Which of the statement(s) is (are) true?

(a) The running time of dynamic programming algorithm is always θ(ρ) where ρ is number of subproblems.

(b) When a recurrence relation has cyclic dependency, it is impossible to use that recurrence relation (unmodified) in a correct dynamic program.

(c) For a dynamic programming algorithm, computing all values in a bottom-up fashion is asymptotically faster than using recursion and memorization.

(d) If a problem X can be reduced to a known NP-hard problem, then X must be NP-hard.

Which of the statement(s) is (are) true?

Only (b) and (a) | |

Only (b) | |

Only (b) and (c) | |

Only (b) and (d) |

Question 1 Explanation:

(i). FALSE: The running time of a dynamic program is the number of subproblems times the time per subproblem. This would only be true if the time per subproblem is O(1).

(ii). TRUE: Cyclic dependency is a relation between two or more modules which either directly or indirectly depend on each other to function properly. Such modules are also known as mutually recursive. So, we can’t get correct solution when we are using dynamic programming.

(iii). FALSE: A bottom up implementation must go through all of the sub-problems and spend the time per subproblem for each. Using recursion and memoization only spends time on the subproblems that it needs. In fact, the reverse may be true: using recursion and memoization may be asymptotically faster then a bottom-up implementation.

(iv). FALSE: If a problem X can be reduced to a known NP-hard problem, then X must be NP-Complete.

(ii). TRUE: Cyclic dependency is a relation between two or more modules which either directly or indirectly depend on each other to function properly. Such modules are also known as mutually recursive. So, we can’t get correct solution when we are using dynamic programming.

(iii). FALSE: A bottom up implementation must go through all of the sub-problems and spend the time per subproblem for each. Using recursion and memoization only spends time on the subproblems that it needs. In fact, the reverse may be true: using recursion and memoization may be asymptotically faster then a bottom-up implementation.

(iv). FALSE: If a problem X can be reduced to a known NP-hard problem, then X must be NP-Complete.

Question 2 |

Let G = (V, T, S, P) be any context-free grammar without any λ-productions or unit productions. Let K be the maximum number of symbols on the right of any production P. The maximum number of production rules for any equivalent grammar in Chomsky normal form is given by:

(K – 1) |P| + |T| - 1 | |

(K – 1) |P| +| T| | |

K |P| + |T| - 1 | |

K |P| + |T| |

Question 2 Explanation:

Let G = (V, T, S, P) be any context-free grammar without any λ-productions or unit productions. Let K be the maximum number of symbols on the right of any production P. The maximum number of production rules for any equivalent grammar in Chomsky normal form is given by (K – 1) |P| + |T|

Question 3 |

Which of the following is not needed by an encryption algorithm used in Cryptography?

KEY | |

Message | |

Ciphertext | |

User details | |

Option-C and Option-D |

Question 3 Explanation:

To Encrypt or decrypt an algorithm it requires Plain Text(or Message) and Key(either public or private).

But it does not require User details.

Not relevant option-"cipher text". Note: According to final answer key, given marks to option-C and Option-D

But it does not require User details.

Not relevant option-"cipher text". Note: According to final answer key, given marks to option-C and Option-D

Question 4 |

A Non-pipelined system takes 30ns to process a task. The same task can be processed in a four-segment pipeline with a clock cycle of 10ns. Determine the speed up of the pipeline for 100 tasks

3 | |

4 | |

3.91 | |

2.91 |

Question 4 Explanation:

S=nt

= 100*30/(100+4-1)*10

= 3000 / 1030

= 2.91

_{n}/ (n+k-1)t_{p}= 100*30/(100+4-1)*10

= 3000 / 1030

= 2.91

Question 5 |

Which tag is used to enclose any number of javascript statements in HTML document?

< code > | |

< script > | |

< title > | |

< body > |

Question 5 Explanation:

The < script > tag is used to define a client-side script (JavaScript).

The < script > element either contains scripting statements, or it points to an external script file through the src attribute.

Common uses for JavaScript are image manipulation, form validation, and dynamic changes of content.

The < script > element either contains scripting statements, or it points to an external script file through the src attribute.

Common uses for JavaScript are image manipulation, form validation, and dynamic changes of content.

Question 6 |

Consider the following languages:
L

_{1}= {a^{n}b^{n}c^{m}} ∪ {a^{n}b^{m}c^{m}}, n. m ≥ o L_{2}= {ωω^{R}|ω ∈ {a, b}*} Where R represents reversible operation. Which one of the following is (are) inherently ambiguous language(s)?only L _{1} | |

only L _{2} | |

both L _{1} and L_{2} | |

neither L _{1} nor L_{2} |

Question 6 Explanation:

A language is inherently ambiguous:

If for a language every existing grammar is ambiguous then that language is called inherently ambiguous language. By this definition of inherently ambiguous, we can conclude that for an inherently ambiguous language an equivalent unambiguous grammar can't be found.

There are several languages (special types ) which are inherently ambiguous.

For example : L= {a

The reason is : It is union of two languages {a

So it will have grammar

S-> A | B

A-> PQ

P->aPb | ab

Q-> cQ | c

B-> UV

U-> aU | a

V-> bVc | bc

Grammar A generates equal number of a's and b's and any number of c's

Grammar B generates equal number of b's and c's and any number of a's

So the strings which have equal numbers of a's, b's and c's can be generated by A or B

So for these strings we always have two parse trees.

Hence this language is ambiguous as we cannot make an unambiguous grammar for it.

If for a language every existing grammar is ambiguous then that language is called inherently ambiguous language. By this definition of inherently ambiguous, we can conclude that for an inherently ambiguous language an equivalent unambiguous grammar can't be found.

There are several languages (special types ) which are inherently ambiguous.

For example : L= {a

^{i}b^{j}c^{k}| i=j or c=k} is inherently ambiguousThe reason is : It is union of two languages {a

^{n}b^{n}c^{m}} U {a^{n}b^{m}c^{m}}So it will have grammar

S-> A | B

A-> PQ

P->aPb | ab

Q-> cQ | c

B-> UV

U-> aU | a

V-> bVc | bc

Grammar A generates equal number of a's and b's and any number of c's

Grammar B generates equal number of b's and c's and any number of a's

So the strings which have equal numbers of a's, b's and c's can be generated by A or B

So for these strings we always have two parse trees.

Hence this language is ambiguous as we cannot make an unambiguous grammar for it.

Question 7 |

Match List-I with List-II:

Choose the correct option from those given below:

Choose the correct option from those given below:

(a).(i), (b).(ii), (c).(iii), (d).(iv) | |

(a).(ii), (b).(i), (c).(iii), (d).(iv) | |

(a).(iv), (b).(iii), (c).(ii), (d).(i) | |

(a).(iii), (b).(iv), (c).(ii), (d).(i) |

Question 7 Explanation:

**Frame attribute**→ To specify the side of the table frame that display border

The < frame > tag defines one particular window (frame) within a < frameset >.

Each < frame > in a < frameset > can have different attributes, such as border, scrolling, the ability to resize, etc.

**< tr > tag**→ To enclose each row in a table.

The < tr > tag defines a row in an HTML table.

A < tr > element contains one or more or elements

**Valign attribute**→ for vertical alignment of content in cell

**< a > tag**→ To create link in HTML

Question 8 |

A network with a bandwidth of 10 Mbps can pass only an average of 12,000 frames per minute with each frame carrying an average of 10,000 bits. What is the throughput of this network?

1,000,000 bps | |

2,000,000 bps | |

12,000,000 bps | |

1,200,00,000 bps |

Question 8 Explanation:

Given data,

Bandwidth= 10 Mbps

Frames per minute=12000

Each frame per bits=10000

Throughput=?

Step-1: Here, they given each frame per minute. So, convert into seconds is

(12000*10000) / 60

Step-2: 120000000 / 60

= 2000000

It is nothing but 2Mbps

Bandwidth= 10 Mbps

Frames per minute=12000

Each frame per bits=10000

Throughput=?

Step-1: Here, they given each frame per minute. So, convert into seconds is

(12000*10000) / 60

Step-2: 120000000 / 60

= 2000000

It is nothing but 2Mbps

Question 9 |

If L is the regular language denoted by T= (w + x*)(ww)*, then the regular language h(L) is given by

(z x yy + xy) (z x yy) | |

(zxyy + (xzy)*) (zxyy zxyy)* | |

(zxyy + xyz) (zxyy)* | |

(zxyy + (xzy)* (zxyy zxyy) |

Question 10 |

A tree has 2n vertices of degree 1, 3n vertices of degree 2, n vertices of degree 3. Determine the number of vertices and edges in tree.

12.11 | |

11.12 | |

10.11 | |

9.10 |

Question 11 |

Given CPU time slice of 2ms and following list of processes.

Find average turnaround time and average waiting time using round robin CPU scheduling?

4.0 | |

5.66, 1.66 | |

5.66, 0 | |

7, 2 |

Question 11 Explanation:

Average Turnaround Time= (5+5+7)/3

= 5.66

Average Waiting Time= (2+1+2)/3

= 1.66

Question 12 |

Consider the following statements:

S

S

Which of the statements is (are) correct?

S

_{1}: If a group (G,*) is of order n, and a ∈ G is such that a^{m}= e for some integer m ≤ n, then m must divide n.S

_{2}: If a group (G,*) is of even order , then there must be an element and a ∈ G is such that a ≠ e and a * a = e.Which of the statements is (are) correct?

Only S _{1} | |

Only S _{2} | |

Both S _{1} and S_{2} | |

Neither S _{1} nor S_{2} |

Question 13 |

What is the worst case running time of Insert and Extract-min, in an implementation of a priority queue using an unsorted array? Assume that all insertions can be accommodated.

θ(1) , θ(n) | |

θ(n) , θ(1) | |

θ(1) , θ(1) | |

θ(n) , θ(n) |

Question 13 Explanation:

Insertion will remain the same for best,average and worst case time complexities. It will take a constant amount of time only.

Extract-Min will take θ(n) time for above conditions. The array is unsorted there is naturally no better algorithm than just linear search. Worst case performance for linear search is Θ(n)

Extract-Min will take θ(n) time for above conditions. The array is unsorted there is naturally no better algorithm than just linear search. Worst case performance for linear search is Θ(n)

Question 14 |

Consider the following statements:
S

_{1}: These exists no algorithm for deciding if any two Turning machine M_{1}and M_{2}accept the same language. S_{2}: Let M_{1}and M_{2}be arbitrary Turing machines. The problem to determine L(M_{1})⊆ L(M_{2})is undecidable. Which of the statements is (are) correct?Only S _{1} | |

Only S _{2} | |

Both S _{1} and S_{2} | |

Neither S _{1} nor S_{1} |

Question 14 Explanation:

Statement S1 is correct because equality problem of recursively enumerable languages is undecidable.

Statement S2 is correct because subset problem of recursively enumerable languages is undecidable.

Statement S2 is correct because subset problem of recursively enumerable languages is undecidable.

Question 15 |

Suppose a system has 12 magnetic tape drives and at time t

_{o}, three processes are allotted tape drives out of their need as given below: At time t_{o}, the system is in safe state. Which of the following is safe sequence so that deadlock is avoided?(p _{0}, p_{1}, p_{2}) | |

(p _{1}, p_{0}, p_{2}) | |

(p _{2}, p_{1}, p_{0}) | |

(p _{0}, p_{2}, p_{1}) |

Question 15 Explanation:

Out of Total 12 resources, 9 resources are allocated. So the remaining resources are 3. With 3 resources process P1 requirements can be fulfilled. So after that total resources will be 3+ resources allocated to P1(i.e. 3+2= 5)

Now process P0 requirement will be fulfilled. So after that total resources will be 5+ resources allocated to P0(i.e. 5+5=10)

Now process P2 requirement will be fulfilled. So after that total resources will be 10+ resources allocated to P2(i.e. 10+2=12)

Question 16 |

Let W

_{o}represents weight between node i at layer k and node j at layer (k – 1) of a given multilayer perceptron. The weight updation using gradient descent method is given by

Where α and E represents learning rate and Error in the output respectively?

Question 17 |

The reduced Instruction Set Computer (RISC) characteristics are:

(a) Single cycle instruction execution

(b) Variable length instruction formats

(c) Instructions that manipulates operands in memory

(d) Efficient instruction pipeline

Choose the correct characteristics from the options given below:

(a) Single cycle instruction execution

(b) Variable length instruction formats

(c) Instructions that manipulates operands in memory

(d) Efficient instruction pipeline

Choose the correct characteristics from the options given below:

(a) and (b) | |

(b) and (c) | |

(a) and (d) | |

(c) and (d) |

Question 17 Explanation:

__Common RISC characteristics__

→ Load/store architecture (also called register-register or RR architecture) which fetches operands and results indirectly from main memory through a lot of scalar registers. Other architecture is storage-storage or SS in which source operands and final results are retrieved directly from memory.

→ Fixed length instructions which (a) are easier to decode than variable length instructions, and (b) use fast, inexpensive memory to execute a larger piece of code. → Hardwired controller instructions (as opposed to microcoded instructions). This is where RISC really shines as hardware implementation of instructions is much faster and uses less silicon real estate than a microstore area.

→ Fused or compound instructions which are heavily optimized for the most commonly used functions.

→ Pipelined implementations with the goal of executing one instruction (or more) per machine cycle.

→ Large uniform register set

→ Minimal number of addressing modes

→ no/minimal support for misaligned accesses

__Characteristic of CISC__:

→ Complex instruction, hence complex instruction decoding.

→ Instruction are larger than one word size.

→ Instruction may take more than a single clock cycle to get executed.

→ Less number of general purpose register as operation get performed in memory itself.

→ Complex Addressing Modes.

→ More Data types.

Question 18 |

A microinstruction format has microoperation field which is divided into 2 subfields F1 and F2. Each having 15 distinct micro operations condition field CD for four status bits. Branch field BR having four options used in conjunction with address field AD. The address space is of 128 memory words. The size of micro instruction is

19 | |

18 | |

17 | |

20 |

Question 19 |

B-Tree, each node represents a disk block. Suppose one block holds 8192 bytes. Each key uses 32 bytes. In a B-tree of order M there are M – 1 keys. Since each branch is on another disk block, we assume a branch is of 4 bytes. The total memory requirement for a non-leaf node is

32 M – 32 | |

36 M – 32 | |

36 M – 36 | |

32 M – 36 |

Question 19 Explanation:

The size of non-leaf node in B-tree = m(P

Where P

In question,P

Hence size of non-leaf node in B-tree = m(4) + (m-1)(32)

= 36M - 32

_{b}) + (m-1)(key+ P_{r})Where P

_{b}is Block pointer and P_{r}is record pointer.In question,P

_{b}= 4 and key size = 32 and since the size of P_{r}is not given in question consider it as zero.Hence size of non-leaf node in B-tree = m(4) + (m-1)(32)

= 36M - 32

Question 20 |

Which of the component module of DBMS does rearrangement and possible ordering of operations, eliminate redundancy in query and use efficient algorithms and indexes during the execution of a query?

query compiler | |

query optimizer | |

Stored data manager | |

Database processor |

Question 20 Explanation:

The

It rearrange and does the possible ordering of operations, eliminate redundancy in query and use efficient algorithms and indexes during the execution of a query

**query optimizer**(called simply the**optimizer**) is built-in database software that determines the most efficient method for a SQL statement to access requested data. The optimizer choose the plan with the lowest cost among all considered candidate plans(the cost computation accounts for factors of query execution such as I/O, CPU, and communication).It rearrange and does the possible ordering of operations, eliminate redundancy in query and use efficient algorithms and indexes during the execution of a query

Question 21 |

Consider the following grammar :

S→0A|0BB

A→00A| λ

B→1B|11C

C→B

Which language does this grammar generate?

S→0A|0BB

A→00A| λ

B→1B|11C

C→B

Which language does this grammar generate?

L(00) * 0+(11)*1) | |

L(0(11)* + 1(00)*) | |

L((00)*0) | |

L(0(11) *1) |

Question 21 Explanation:

Option 1 is incorrect because every string generated by given grammar will contain only 0's and given option is generating string containing 1's also.
Option 2 is incorrect because it can't generate "000".
Option 3 is correct because it generates string same as given grammar do.
Option 4 is incorrect because every string generated by given grammar will contain only 0's and given option is generating string containing 1's also.

Question 22 |

Consider the following Linear programming problem (LPP) :

Maximize z = x

Subject to the constraints:

The solution of the above LPP is:

Maximize z = x

_{1}+ x_{2}Subject to the constraints:

The solution of the above LPP is:

x _{1}=750, x_{2}=750, z=1500 | |

x _{1}=500, x_{2}=100, z=1500 | |

x _{1}=1000, x_{2}=500, z=1500 | |

x _{1}=900, x_{2}=600, z=1500 |

Question 23 |

Let A be the base class in C++ and B be the derived class from A with protected inheritance.

Which of the following statement is false for class B?

Which of the following statement is false for class B?

Member function of class B can access protected data of class A | |

Member function of class access public data of class A | |

Member function of class B cannot access private data of class A | |

Object of derived class B can access public base class data |

Question 23 Explanation:

A→ Base class

B→ Derived class from A with protected inheritance.

The friend functions and the member functions of a friend class can have direct access to both the PRIVATE and PROTECTED data, the member functions of a derived class can directly access only the PROTECTED data.

However, they can access the PRIVATE data through the member functions of the base class TRUE: Member function of class B can access protected data of class A

TRUE: Member function of class access public data of class A

FALSE: Member function of class B cannot access private data of class A

TRUE: Object of derived class B can access public base class data

B→ Derived class from A with protected inheritance.

The friend functions and the member functions of a friend class can have direct access to both the PRIVATE and PROTECTED data, the member functions of a derived class can directly access only the PROTECTED data.

However, they can access the PRIVATE data through the member functions of the base class TRUE: Member function of class B can access protected data of class A

TRUE: Member function of class access public data of class A

FALSE: Member function of class B cannot access private data of class A

TRUE: Object of derived class B can access public base class data

Question 24 |

Given two tables EMPLOYEE (

DEPARTMENT (

Find the most appropriate statement of the given query:

Select count (*) ‘total’

from EMPLOYEE

where DEPTNO IN (D1, D2)

group by DEPTNO

having count (*) > 5

__EID__, ENAME, DEPTNO)DEPARTMENT (

__DEPTNO__. DEPTNAME)Find the most appropriate statement of the given query:

Select count (*) ‘total’

from EMPLOYEE

where DEPTNO IN (D1, D2)

group by DEPTNO

having count (*) > 5

Total number of employees in each department D1 and D2 | |

Total number of employees of department D1 and D2 if their total is >5 | |

Display total number of employees in both departments D1 and D2 | |

The output of the query must have atleast two rows |

Question 25 |

Which of the following are legal statements in C programming language?

(a) int *P = &44;

(b) int *P = &r;

(c) int P = &a;

(d) int P = a:

Choose the correct option:

(a) int *P = &44;

(b) int *P = &r;

(c) int P = &a;

(d) int P = a:

Choose the correct option:

(a) and (b) | |

(b) and (c) | |

(b) and (d) | |

(a) and (d) |

Question 25 Explanation:

__Legal Statements:__

int *P = &r;

int P = a:

__Illegal Statements__:

int *P = &44;

int P= &a;

Question 26 |

Which of the following binary codes for decimal digits are self complementing?

(a) 8421 code

(b) 2421 code

(c) excess-3 code

(d) excess-3 gray code

Choose the correct option:

(a) 8421 code

(b) 2421 code

(c) excess-3 code

(d) excess-3 gray code

Choose the correct option:

(a) and (b) | |

(b) and (c) | |

(c) and (d) | |

(d) and (a) |

Question 26 Explanation:

Note: 8421 is not self complementing. Self complementing is nothing but reverse order from starting and last number.

Ex: 0 value is 0000

9 value is 1111

So, it is self complementing.

Note: Excess-3 and Gray code is different. So, it is not relevant.

Question 27 |

Consider the following statements:

Which of the following statements is/are correct?

Only S _{1} | |

Only S _{2} | |

Both S _{1 } and S_{2} | |

Neither S _{1} nor S_{2} |

Question 28 |

Consider a paging system where translation lookaside buffer (TLB) a special type of associative memory is used with hit ratio of 80%.

Assume that memory reference takes 80 nanoseconds and reference time to TLB is 20 nanoseconds. What will be the effective memory access time given 80% hit ratio?

Assume that memory reference takes 80 nanoseconds and reference time to TLB is 20 nanoseconds. What will be the effective memory access time given 80% hit ratio?

110 nanoseconds | |

116 nanoseconds | |

200 nanoseconds | |

100 nanoseconds |

Question 28 Explanation:

T

= 20 + 0.2 × 80 + 80

= 20 + 16 + 80

= 116 ms

_{avg}= TLB access time + miss ratio of TLB × memory access time + memory access time= 20 + 0.2 × 80 + 80

= 20 + 16 + 80

= 116 ms

Question 29 |

According to the ISO-9126 Standard Quality Model, match the attributes given in List-I with their definitions in Lit-II:

Choose the correct option from the ones given below:

(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv) | |

(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii) | |

(a)-(ii), (b)-(iv), (c)-(i), (d)-(iii) | |

(a)-(i), (b)-(ii), (c)-(iv), (d)-(iii) |

Question 29 Explanation:

6 main quality characteristics for ISO-9126 Standard Quality Model:

1. Functionality→ Characteristics related with achievement of purpose

2. Reliability → Capability of software to maintain performance of software

3. Efficiency → Relationship between level of performance and amount of resources

4. Maintainability → Effort needed to make for improvement

5. Usability → Usability only exists with regard to functionality and refers to the ease of use for a given function.

6. Portability → This characteristic refers to how well the software can adapt to changes in its environment or with its requirements.

1. Functionality→ Characteristics related with achievement of purpose

2. Reliability → Capability of software to maintain performance of software

3. Efficiency → Relationship between level of performance and amount of resources

4. Maintainability → Effort needed to make for improvement

5. Usability → Usability only exists with regard to functionality and refers to the ease of use for a given function.

6. Portability → This characteristic refers to how well the software can adapt to changes in its environment or with its requirements.

Question 30 |

Identify the circumstances under which preemptive CPU scheduling is used :

(a) A process switches from Running state to Ready state

(b) A process switches from Waiting state to Ready state

(c) A process completes its execution

(d) A process switches from Ready to Waiting state

Choose the correct option:

(a) and (b) only | |

(a) and (d) only | |

(c) and (d) only | |

(a), (b), (c) only |

Question 30 Explanation:

**CPU scheduling decisions take place under one of four conditions:**

1. When a process switches from the running state to the waiting state, such as for an I/O request or invocation of the wait( ) system call.

2. When a process switches from the running state to the ready state, for example in response to an interrupt.

3. When a process switches from the waiting state to the ready state, say at completion of I/O or a return from wait( ).

4. When a process terminates.

For conditions 1 and 4 there is no choice - A new process must be selected.

For conditions 2 and 3 there is a choice - To either continue running the current process, or select a different one.

Note: If scheduling takes place only under conditions 1 and 4, the system is said to be non-preemptive, or cooperative. Under these conditions, once a process starts running it keeps running, until it either voluntarily blocks or until it finishes. Otherwise the system is said to be preemptive.

Question 31 |

Which of the following interprocess communication model is used to exchange messages among co-operative processes?

Shared memory model | |

Message passing model | |

Shared memory and message passing model. | |

Queues |

Question 31 Explanation:

A process can be of two types:

1. Independent process: It is not affected by the execution of other processes

2. Co-operating process: It can be affected by other executing processes.

Interprocess communication (IPC) method which will allow them to exchange data along with various information among co-operative processes. There are two primary models of interprocess communication:

1. Shared memory.

2. Message passing.

1. Independent process: It is not affected by the execution of other processes

2. Co-operating process: It can be affected by other executing processes.

Interprocess communication (IPC) method which will allow them to exchange data along with various information among co-operative processes. There are two primary models of interprocess communication:

1. Shared memory.

2. Message passing.

Question 32 |

Consider the following statements with respect to network security:

(a) Message confidentiality means that the sender and the receiver expect privacy.

(b) Message integrity means that the data must arrive at the receiver exactly as they were sent.

(c) Message authentication means the receiver is ensured that the message is coming from the intended sender.

Which of the statements is (are) correct?

Only (a) and (b) | |

Only (a) and (c) | |

Only (b) and (c) | |

(a), (b) and (c) |

Question 32 Explanation:

TRUE: Message confidentiality means that the sender and the receiver expect privacy.

TRUE: Message integrity means that the data must arrive at the receiver exactly as they were sent.

TRUE: Message authentication means the receiver is ensured that the message is coming from the intended sender.

TRUE: Message integrity means that the data must arrive at the receiver exactly as they were sent.

TRUE: Message authentication means the receiver is ensured that the message is coming from the intended sender.

Question 33 |

If we want to resize a 1024 × 768 pixels image to one that is 640 pixels wide with the same aspect ratio, what would be the height of the resized image?

420 Pixels | |

460 Pixels | |

480 Pixels | |

540 Pixels |

Question 33 Explanation:

Aspect Ratio= Width / Height

Aspect ration of 1024 × 768 pixels image = 1024/768

= 4/3

Aspect ration of modified pixels image = 640/height

4/3 = 640/height

Height = (3*640)/4

Height = 480 Pixels

Aspect ration of 1024 × 768 pixels image = 1024/768

= 4/3

Aspect ration of modified pixels image = 640/height

4/3 = 640/height

Height = (3*640)/4

Height = 480 Pixels

Question 34 |

The time complexity to multiply two polynomials of degree n using Fast Fourier transform method is:

θ(n lg n) | |

θ(n ^{2}) | |

θ(n) | |

θ(lg lg n ) |

Question 34 Explanation:

To multiply two polynomials time complexity is O(n

^{2}) but the time complexity to multiply two polynomials of degree n using Fast Fourier transform method is θ(n lg n)Question 35 |

Consider the following learning algorithms:

(a) Logistic regression

(b) Back propagation

(c) Linear repression

Which of the following option represents classification algorithms?

(a) and (b) only | |

(a) and (c) only | |

(b) and (c) only | |

(a), (b) and (c) |

Question 35 Explanation:

The classification learning algorithms are

1. Logistic regression

2. Back propagation

Note: They given spelling mistake in Logistic regression instead of “Logistic repression”.

According to final key, given marks to all.

1. Logistic regression

2. Back propagation

Note: They given spelling mistake in Logistic regression instead of “Logistic repression”.

According to final key, given marks to all.

Question 36 |

The following multithreaded algorithm computes transpose of a matrix in parallel:

p Trans (X, Y, N)

if N = 1

then Y[1, 1] ← X[1, 1]

else partition X into four (N/2) × (N/2) submatrices X

_{11}, X

_{12},

X

_{21}, X

_{22}

partition Y into four (N/2) × (N/2) submatrices X

_{11}, X

_{12},

X

_{21}, X

_{22}

spawn p Trans (X

_{11}, Y

_{11}, N/2)

spawn p Trans (X

_{12}, Y

_{12}, N/2)

spawn p Trans (X

_{21}, Y

_{21}, N/2)

spawn p Trans (X

_{22}, Y

_{22}, N/2)

What is the asymptotic parallelism of the algorithm?

Question 37 |

Two concurrent executing transactions T

_{1}and T

_{2}are allowed to update same stock item say ‘A’ in an uncontrolled manner. In such a scenario, following problems may occur:

(a) Dirty read problem

(b) Lost update problem

(c) Transaction failure

(d) Inconsistent database state

Which of the following option is correct if database system has no concurrency module and allow concurrent execution of above two transactions?

(a), (b) and (c) only | |

(c) and (d) only | |

(a) and (b) only | |

(a), (b) and (d) only |

Question 37 Explanation:

Following problems can occur when concurrent transactions execute in an uncontrolled manner:

**The Lost Update Problem**. This problem occurs when two transactions that access the same database items have their operations interleaved in a way that makes the value of some database items incorrect.**The Temporary Update (or Dirty Read) Problem**. This problem occurs when one transaction updates a database item and then the transaction fails for some reason**The Incorrect Summary Problem**. If one transaction is calculating an aggregate summary function on a number of database items while other transactions are updating some of these items, the aggregate function may calculate some values before they are updated and others after they are updated.**The Unrepeatable Read Problem**. Another problem that may occur is called unrepeatable read, where a transaction T reads the same item twice and the item is changed by another transaction T between the two reads. Hence, T receives different values for its two reads of the same item.Question 38 |

Which of the following statements are true regarding C++?

(a) Overloading gives the capacity to an existing operator to operate on other data types.

(b) Inheritance in object oriented programming provides support to reusability.

(c) When object of a derived class is defined, first the constructor of derived class in executed then constructor of a base class is executed.

(d) Overloading is a type of polymorphism.

Choose the correct option from those given below:

(a) and (b) only | |

(a), (b) and (c) only | |

(a), (b) and (d) only | |

(b), (c) and (d) only |

Question 38 Explanation:

TRUE: Overloading gives the capacity to an existing operator to operate on other data types.

TRUE: Inheritance in object oriented programming provides support to reusability.

FALSE: When object of a derived class is defined, first the constructor of derived class in executed then constructor of a base class is executed.

1. Whether derived class's default constructor is called or parameterised is called, base class's default constructor is always called inside them.

2. To call base class's parameterised constructor inside derived class's parameterised constructor, we must mention it explicitly while declaring derived class's parameterized constructor.

TRUE: Overloading is a type of polymorphism.

TRUE: Inheritance in object oriented programming provides support to reusability.

FALSE: When object of a derived class is defined, first the constructor of derived class in executed then constructor of a base class is executed.

**2 important points Order of Constructor Call with Inheritance in C++**1. Whether derived class's default constructor is called or parameterised is called, base class's default constructor is always called inside them.

2. To call base class's parameterised constructor inside derived class's parameterised constructor, we must mention it explicitly while declaring derived class's parameterized constructor.

TRUE: Overloading is a type of polymorphism.

Question 39 |

Match the Agile Process models with the task performed during the model:

Choose the correct option from those given below:

(a)-(ii), (b)-(iv), (c)-(i), (d)-(iii) | |

(a)-(i), (b)-(iii), (c)-(ii), (d)-(iv) | |

(a)-(i), (b)-(iv), (c)-(ii), (d)-(iii) | |

(a)-(i), (b)-(iv), (c)-(ii), (d)-(iii) |

Question 39 Explanation:

Scrum → Sprint backlog

Adaptive software development → Time box release plan

Extreme programming → CRC cards

Feature-driven development → < action > the < result > < by / for / of / to > a(n) < object >

Adaptive software development → Time box release plan

Extreme programming → CRC cards

Feature-driven development → < action > the < result > < by / for / of / to > a(n) < object >

Question 40 |

A counting semaphore is initialized to 8. 3 wait() operations and 4 signal() operations are applied. Find the current value of semaphore variable

9 | |

5 | |

1 | |

4 |

Question 40 Explanation:

In counting semaphore, wait() is nothing but down (or) subtract (or) P.

Signal is nothing but up (or) add (or) V

Initial size is 8.

And 3 wait() operations

4 signal() operations

= 8 - 3 + 4

= 5 + 4

= 9

Signal is nothing but up (or) add (or) V

Initial size is 8.

And 3 wait() operations

4 signal() operations

= 8 - 3 + 4

= 5 + 4

= 9

Question 41 |

Consider the following statement with respect to approaches to fill area on raster systems:

(P) To determine the overlap intervals for scan lines that cross the area.

(Q) To start from a given interior position and paint outward from this point until we encounter the specified boundary conditions.

Select the correct answer from the options given below:

(P) To determine the overlap intervals for scan lines that cross the area.

(Q) To start from a given interior position and paint outward from this point until we encounter the specified boundary conditions.

Select the correct answer from the options given below:

P only | |

Q only | |

Both P and Q | |

Neither P nor Q |

Question 41 Explanation:

Fill area on raster systems:

TRUE: To determine the overlap intervals for scan lines that cross the area.

TRUE: To start from a given interior position and paint outward from this point until we encounter the specified boundary conditions.

TRUE: To determine the overlap intervals for scan lines that cross the area.

TRUE: To start from a given interior position and paint outward from this point until we encounter the specified boundary conditions.

Question 42 |

Piconet is a basic unit of a Bluetooth system consisting of __________ master node and up to _________ active salve nodes

one, five | |

one, seven | |

two, eight | |

one, eight |

Question 42 Explanation:

→ Bluetooth is a packet-based protocol and Bluetooth networks are referred to as piconets.

→ A piconet consists of a one master and up to seven slaves.

→ In the context of connecting a Bluetooth keyboard, the host (SoC or application processor) will be the master and the keyboard the slave.

“M” indicates a master and “S” indicates a slave. The one on the right depicts the maximum of seven slaves connected to a master.

→ A piconet consists of a one master and up to seven slaves.

→ In the context of connecting a Bluetooth keyboard, the host (SoC or application processor) will be the master and the keyboard the slave.

“M” indicates a master and “S” indicates a slave. The one on the right depicts the maximum of seven slaves connected to a master.

Question 43 |

Consider the following:

(a) Trapping at local maxima

(b) Reaching a plateau

(c) Traversal along the ridge.

Which of the following option represents shortcomings of the hill climbing algorithm?

(a) Trapping at local maxima

(b) Reaching a plateau

(c) Traversal along the ridge.

Which of the following option represents shortcomings of the hill climbing algorithm?

(a) and (b) only | |

(a) and (c) only | |

(b) and (c) only | |

(a), (b) and (c) |

Question 43 Explanation:

__Hill climbing limitations__:

1. Local Maxima: Hill-climbing algorithm reaching the vicinity a local maximum value, gets drawn towards the peak and gets stuck there, having no other place to go.

2. Ridges: These are sequences of local maxima, making it difficult for the algorithm to navigate.

3. Plateaux: This is a flat state-space region. As there is no uphill to go, algorithm often gets lost in the plateau.

To avoid above problems using 3 standard types of hill climbing algorithm is

1. Stochastic Hill Climbing selects at random from the uphill moves. The probability of selection varies with the steepness of the uphill move.

2. First-Choice Climbing implements the above one by generating successors randomly until a better one is found.

3. Random-restart hill climbing searches from randomly generated initial moves until the goal state is reached.

Question 44 |

According to Dempster-Shafer theory for uncertainty management,

Where Bel(A) denotes Belief of event A.

Question 45 |

Find minimum number of tables required for converting the following entity relationship diagram into relational database?

2 | |

4 | |

3 | |

5 |

Question 45 Explanation:

There is one to many relationship between R1 and R2. So there will be two tables representing R1 and R2 respectively. And there is a table to represent multivalued attribute B.
So total number of tables required to represent given ER diagram is 3.

Question 46 |

Consider the following statements with respect to duality in LPP:

(a) The final simplex table giving optimal solution of the primal also contains optimal solution of its dual in itself.

(b) If either the primal or the dual problem has a finite optimal solution, then the other problem also has a finite optimal solution.

(c) If either problem has an unbounded optimal solution, then the other problem has no feasible solution at all. Which of the statements is (are) correct?

only (a) and (b) | |

only (a) and (c) | |

only (b) and (c) | |

(a), (b) and (c) |

Question 46 Explanation:

Duality in LPP:

TRUE: The final simplex table giving optimal solution of the primal also contains optimal solution of its dual in itself.

TRUE: If either the primal or the dual problem has a finite optimal solution, then the other problem also has a finite optimal solution.

TRUE: If either problem has an unbounded optimal solution, then the other problem has no feasible solution at all.

TRUE: The final simplex table giving optimal solution of the primal also contains optimal solution of its dual in itself.

TRUE: If either the primal or the dual problem has a finite optimal solution, then the other problem also has a finite optimal solution.

TRUE: If either problem has an unbounded optimal solution, then the other problem has no feasible solution at all.

Question 47 |

The Data Encryption Standard (DES) has a function consists of four steps. Which of the following is correct order of these four steps?

an expansion permutation, S-boxes, an XOR operation, a straight permutation | |

an expansion permutation, an XOR operation, S-boxes, a straight permutation | |

an straight permutation, S-boxes, an XOR operation, an expansion permutation | |

a straight permutation, an XOR operation, S-boxes, an expansion permutation |

Question 47 Explanation:

Question 48 |

Give asymptotic upper and lower bound for T(n) given below. Assume T(n) is constant for n≤2.

T(n)= 4T(√n)+lg^2 n

T(n)= θ(lg*(lg^2 n)lg n) | |

T(n)= θ(lg^2n lg n) | |

T(n)= θ(lg^2 n (lg lg n)) | |

T(n)= θ(lg (lg n)lg n) |

Question 48 Explanation:

Cosider m=log^2 n

T(2^m)=4T(2^(m/2))+m

Then S(m)=4(2^m) produces the recurrence:

S(m)=4S(m/2)+m

T(n)=T(2^m)

= S(m)=O(mlogm)

T(n)=O(lg^2 n (lg lgn))

Note: lg is nothing but log. Both are correct.

T(2^m)=4T(2^(m/2))+m

Then S(m)=4(2^m) produces the recurrence:

S(m)=4S(m/2)+m

T(n)=T(2^m)

= S(m)=O(mlogm)

T(n)=O(lg^2 n (lg lgn))

Note: lg is nothing but log. Both are correct.

Question 49 |

The full form of ICANN is

Internet Corporation for Assigned Names and Numbers | |

Internet Corporation for Assigned Names and Names | |

Institute of Corporation for Assigned Names and Numbers | |

Internet connection for Assigned Names and Numbers |

Question 49 Explanation:

The Internet Corporation for Assigned Names and Numbers is a nonprofit organization responsible for coordinating the maintenance and procedures of several databases related to the namespaces and numerical spaces of the Internet, ensuring the network's stable and secure operation.

ICANN performs the actual technical maintenance work of the Central Internet Address pools and DNS root zone registries pursuant to the Internet Assigned Numbers Authority (IANA) functions contract.

ICANN performs the actual technical maintenance work of the Central Internet Address pools and DNS root zone registries pursuant to the Internet Assigned Numbers Authority (IANA) functions contract.

Question 50 |

Consider a subnet with 720 routers. If a three-level hierarchy is chosen, with eight clusters, each containing 9 regions of 10 routers, then the total number of entries in hierarchical table of each router is

25 | |

27 | |

53 | |

72 |

Question 50 Explanation:

→ Consider a subnet with 720 routers. If there is no hierarchy, each router needs 720 routing table entries.

→ If the subnet is partitioned into 24 regions of 30 routers each, each router needs 30 local entries plus 23 remote entries for a total of 53 entries.

→ If a three-level hierarchy is chosen, with eight clusters, each containing 9 regions of 10 routers, each router needs 10 entries for local routers, 8 entries for routing to other regions within its own cluster, and 7 entries for distant clusters, for a total of 25 entries

→ If the subnet is partitioned into 24 regions of 30 routers each, each router needs 30 local entries plus 23 remote entries for a total of 53 entries.

→ If a three-level hierarchy is chosen, with eight clusters, each containing 9 regions of 10 routers, each router needs 10 entries for local routers, 8 entries for routing to other regions within its own cluster, and 7 entries for distant clusters, for a total of 25 entries

Question 51 |

In a system for a restaurant, the main scenario for placing order is given below:

(a) Customer reads menu

(b) Customer places an order

(c) Order is sent to kitchen for preparation

(d) Ordered items are served

(e) Customer requests for a bill for the order

(f) Bill is prepared for this order

(g) Customer is given the bill

(h) Customer pays the bill

A sequence diagram for the scenario will have at least how many objects among whom the messages will be exchanged.

3 | |

4 | |

5 | |

6 |

Question 52 |

Given two tables R1(x, y) and R2(y, z) with 50 and 30 number of tuples respectively. Find maximum number of tuples in the output of natural join between tables R1 and R2 i.e. R1 * R2? (*. Natural Join)

30 | |

20 | |

50 | |

1500 |

Question 52 Explanation:

For this question one should understand the meaning of natural join.

NATURAL JOIN requires that the two join attributes (or each pair of join attributes) have the same name in both relations.

Let us take a small example where we are having two relations named Employee(EID, Ename) and Department(EID, DID)

Since relation R2 is having 30 tuples, so in best case natural join of R1 and R2 will 30 tuples.

NATURAL JOIN requires that the two join attributes (or each pair of join attributes) have the same name in both relations.

Let us take a small example where we are having two relations named Employee(EID, Ename) and Department(EID, DID)

Since relation R2 is having 30 tuples, so in best case natural join of R1 and R2 will 30 tuples.

Question 53 |

Consider the following statements :

(a) Windows Azure is a cloud-based operating system.

(b) Google App Engine is an integrated set of online services for consumers to communicate and share with others.

(c) Amazon Cloud Front is a web service for content delivery.

Which of the statements is (are) correct?

Only (a) and (b) | |

Only (a) and (c) | |

Only (b) and (c) | |

(a), (b) and (c) |

Question 53 Explanation:

TRUE: Windows Azure is a cloud-based operating system.

FALSE: Google App Engine is an integrated set of online services for consumers to communicate and share with others.

TRUE: Amazon Cloud Front is a web service for content delivery.

FALSE: Google App Engine is an integrated set of online services for consumers to communicate and share with others.

TRUE: Amazon Cloud Front is a web service for content delivery.

Question 54 |

Let A = (001, 0011, 11, 101} and B = (01, 111, 111, 010}. Similarly, let C = {00, 001, 1000} and D = {0, 11,011}.

Which of the following pairs have a post-correspondence solution?

Only pair (A, B) | |

Only pair (C, D) | |

Both (A, B) and (C, D) | |

Neither (A, B) nor (C, D) |

Question 54 Explanation:

Before solving this question you should know what is PCP problem.

The Post Correspondence Problem (PCP), introduced by Emil Post in 1946, is an undecidable decision problem. The PCP problem over an alphabet ∑ is stated as follows −

Given the following two lists, M and N of non-empty strings over ∑ −

M = (x

N = (y

We can say that there is a Post Correspondence Solution, if for some i

The Post Correspondence Problem (PCP), introduced by Emil Post in 1946, is an undecidable decision problem. The PCP problem over an alphabet ∑ is stated as follows −

Given the following two lists, M and N of non-empty strings over ∑ −

M = (x

_{1}, x_{2}, x_{3},………, x_{n})N = (y

_{1}, y_{2}, y_{3},………, y_{n})We can say that there is a Post Correspondence Solution, if for some i

_{1},i_{2},………… i_{k}, where 1 ≤ i_{j}≤ n, the condition x_{i1}…….x_{ik}= y_{i1}…….y_{ik}satisfies.Question 55 |

An __________ chart is a project schedule representation that presents project plan as a directed graph. The critical path is the __________ sequence of ______________ tasks and it defines project _______________

Activity, Shortest, Independent, Cost | |

Activity, Longest, Dependent, Duration | |

Activity, Longest, Independent, Duration | |

Activity, Shortest, Dependent, Duration |

Question 55 Explanation:

The critical path method (CPM), or critical path analysis (CPA), is an algorithm for scheduling a set of project activities. It is commonly used in conjunction with the program evaluation and review technique (PERT). A critical path is determined by identifying the longest stretch of dependent activities and measuring the time required to complete them from start to finish

Question 56 |

Consider a weighted directed graph. The current shortest distance from source S to node x is represented by d[x]. Let d[u] = 15, w[u, v] = 12. What is the updated value of d[u] based on current information

29 | |

27 | |

25 | |

17 |

Question 57 |

Let a

^{2e}mod n = (a^{e})^{2}mod n and a^{2e+1}mod n = a (a^{c})^{2 }mod n. For a = 7, b = 17 and n = 561, what is the value of a^{b}(mod n)?160 | |

166 | |

157 | |

67 |

Question 58 |

Consider the following statements :

(a) Fiber optic cable is much lighter than copper cable.

(b) Fiber optic cable is not affected by power surges or electromagnetic interference.

(c) Optical transmission is inherently bidirectional. Which of the statements is (are) correct?

(a) Fiber optic cable is much lighter than copper cable.

(b) Fiber optic cable is not affected by power surges or electromagnetic interference.

(c) Optical transmission is inherently bidirectional. Which of the statements is (are) correct?

Only (a) and (b) | |

Only (a) and (c) | |

Only (b) and (c) | |

(a), (b) and (c) |

Question 58 Explanation:

TRUE: Fiber optic cable is much lighter than copper cable.

TRUE: Fiber optic cable is not affected by power surges or electromagnetic interference.

FALSE: Optical transmission is inherently bidirectional.

TRUE: Fiber optic cable is not affected by power surges or electromagnetic interference.

FALSE: Optical transmission is inherently bidirectional.

Question 59 |

Which of the following class of IP address has the last address as 223.255.255.255?

Class A | |

Class B | |

Class C | |

Class D |

Question 59 Explanation:

Class A → 0.0.0.0 to 127.255.255.255

Class B → 128.0.0.0 to 191.255.255.255

Class C → 192.0.0.0 to 223.255.255.255

Class D → 224.0.0.0 to 239.255.255.255

Class E → 240.0.0.0 to 254.255.255.254

Class B → 128.0.0.0 to 191.255.255.255

Class C → 192.0.0.0 to 223.255.255.255

Class D → 224.0.0.0 to 239.255.255.255

Class E → 240.0.0.0 to 254.255.255.254

Question 60 |

A computer uses a memory unit of 512 K words of 32 bits each. A binary instruction code is stored in one word of the memory. The instruction has four parts: an addressing mode field to specify one of the two-addressing mode (direct and indirect), an operation code, a register code part to specify one of the 256 registers and an address part. How many bits are there in addressing mode part, opcode part, register code part and the address part?

1, 3, 9, 19 | |

1, 4, 9, 18 | |

1, 4, 8, 19 | |

1, 8, 8, 20 |

Question 60 Explanation:

Given data,

Memory unit= 512K words

512K words of 32 bits each.

Binary instruction code stored in 1 word of memory.

Instruction divided into 4 parts.

1. Operation code= ?

2. Register code= ?

3. Addressing mode (Direct and indirect)

4. Address port= ?

Addressing Mode part = 1 (Direct and indirect)

Operation Code = 32 - 1 - 18 - 8 bits = 5 bits

Register Code = 256 = 2

Address port = 2

final Answer is (1,5,8,18)

Note: None of the options given correct answer. We are given answer according to key given by NTA.

Memory unit= 512K words

512K words of 32 bits each.

Binary instruction code stored in 1 word of memory.

Instruction divided into 4 parts.

1. Operation code= ?

2. Register code= ?

3. Addressing mode (Direct and indirect)

4. Address port= ?

Addressing Mode part = 1 (Direct and indirect)

Operation Code = 32 - 1 - 18 - 8 bits = 5 bits

Register Code = 256 = 2

^{8}= 8 bitsAddress port = 2

^{8}(256kB) * 2^{10}(1024 bytes/kB) = 2^{18}⇒ 18 bitsfinal Answer is (1,5,8,18)

Note: None of the options given correct answer. We are given answer according to key given by NTA.

Question 61 |

Consider the following grammars :

Which of the following is correct w.r.t. the above grammars?

G _{1} and G_{3} are equivalent | |

G _{2} and G_{3} are equivalent | |

G _{2} and G_{4 }are equivalent | |

G _{3 } and G_{4} are equivalent |

Question 62 |

The sequence diagram given in Figure 1 for the Weather Information System takes place when an external system requests the summarized data from the weather station. The increasing order of lifeline for the objects in the system are:

Sat comms → Weather station → Commslink → Weather data | |

Sat comms → Comms link → Weather station → Weather data | |

Weather data → Comms link → Weather station → Sat Comms | |

Weather data → Weather station → Comms link → Sat Comms | |

Given options are wrong |

Question 62 Explanation:

A connection is established in order to send and receive data between sender and receiver. And a link is disconnect after completion of data transfer.

Given diagram, Sat Comms requests data to whether station, whether station requests data to Comms link and comm link requests data from whether data.

Comm link gets data first from whether data then the link between comm link and whether data is smallest. Similarly lifetime if connection between Sat comms and whether station is largest. Hence the increasing order of lifeline for the objects in the system are Weather data → Comms link → Weather station → Sat Comms.

Note: Most appropriate answer is option-C. According to given final key, given marks to all.

Given diagram, Sat Comms requests data to whether station, whether station requests data to Comms link and comm link requests data from whether data.

Comm link gets data first from whether data then the link between comm link and whether data is smallest. Similarly lifetime if connection between Sat comms and whether station is largest. Hence the increasing order of lifeline for the objects in the system are Weather data → Comms link → Weather station → Sat Comms.

Note: Most appropriate answer is option-C. According to given final key, given marks to all.

Question 63 |

Consider the following language families :

L1 = The context – free language

L2 = The context – sensitive language

L3 = The recursively enumerable language

L4 = The recursive language

Which one of the following options is correct?

L _{1} ⊆ L_{2} ⊆ L_{3} ⊆ L_{4} | |

L _{2} ⊆ L_{1} ⊆ L_{3} ⊆ L_{4} | |

L _{1} ⊆ L_{2} ⊆ L_{4} ⊆ L_{3} | |

L _{2 ⊆ L1 ⊆ L4 ⊆ L3} |

Question 63 Explanation:

Question 64 |

When using Dijkstra’s algorithm to find shortest path in a graph, which of the following statement is not true?

It can find shortest path within the same graph data structure | |

Every time a new node is visited, we choose the node with smallest known distance/cost (weight) to visit first | |

Shortest path always passes through least number of vertices | |

The graph needs to have a non-negative weight on every edge |

Question 64 Explanation:

TRUE: Dijkstra’s algorithm always find shortest path with in the same graph data structure. It uses a greedy technique to identify shortest path.

TRUE: Every time a new node is visited, we choose the node with the smallest known distance/cost (weight) to visit first

FALSE: It is false because this algorithm applicable any number of vertices.

TRUE: Dijkstra’s algorithm will support only positive weight edges.

TRUE: Every time a new node is visited, we choose the node with the smallest known distance/cost (weight) to visit first

FALSE: It is false because this algorithm applicable any number of vertices.

TRUE: Dijkstra’s algorithm will support only positive weight edges.

Question 65 |

Let the population of chromosomes in genetic algorithm is represented in terms of binary number. The strength of fitness of a chromosome in decimal form, x, is given by

The population is given by P where:

P = {(01101, (11000), (01000), (10011)}

The strength of fitness of chromosome (11000) is ___________

24 | |

576 | |

14.4 | |

49.2 |

Question 66 |

Match List-I and List-II:

Choose the correct option from those given below:

(a)-(ii), (b)-(iii), (c)-(iv), (d)-(i) | |

(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv) | |

(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii) | |

(a)-(i), (b)-(ii), (c)-(iv), (d)-(iii) |

Question 66 Explanation:

Isolated I/O → Separate instructions for I/O and memory communication

Memory mapped I/O → Same set of control signal for I/O and memory communication

I/O interface → Resolve the differences in central computer and peripherals

Asynchronous data transfer → Requires control signals to be transmitted between the communicating units

Question 67 |

Let P be the set of all people. Let R be a binary relation on P such that (a, b) is in R if a is a brother of b. Is R symmetric, transitive, an equivalence relation, a partial order relation?

NO.NO.NO.NO | |

NO.NO.YES.NO | |

NO.YES.NO.NO | |

NO.YES.YES.NO |

Question 67 Explanation:

In the question there is a conflict.

If

Note: As per our team, question is wrong.

If

**‘a’**is**a**brother of**‘b’**.**‘a’**-- Not from relation**a**-- This is from relation**‘a’**and**a**-- How can we match these two ‘a’ and aNote: As per our team, question is wrong.

Question 68 |

Consider the language L={n>2} on Σ={a,b}. Which ch one of the following generates the language L?

S →aA |a,A → aAb |b | |

S → aaA |λ, A → aAb|λ | |

S → aaaA |a, A → aAb|λ | |

S → aaaA |λ, A → aAb|λ |

Question 68 Explanation:

Option1 is incorrect because it can generate “a” where n=1. so given condition(n>2) is violated.
Option 2 is incorrect because it can generate “null string”. so given condition(n>2) is violated.
Option3 is incorrect because it can generate “a” where n=1. so given condition(n>2) is violated.
Option4 is correct because it can generate strings “ab,aaa, aaaab…...” where nn>2. so it is the correct option.

Question 69 |

The order of schema?10?101? and ???0??1 are ___________ and ______________ respectively.

5.3 | |

5.2 | |

7.5 | |

8.7 |

Question 70 |

(a).(ii), (b).(iv), (c).(iii). (d).(i) | |

(a).(iv). (b).(iii). (c).(ii). (d).(i) | |

(a).(ii), (b).(iv), (c).(i), (d).(iii) | |

(a).(iv), (b).(ii), (c).(i), (d).(iii) |

Question 70 Explanation:

Physical layer → Concerned with transmitting raw bits over a communication channel

Transport layer → True end-to-end layer from source to destination

Session layer → Provide token management service

Presentation layer → Concerned with the syntax and semantics of the information transmitted

Transport layer → True end-to-end layer from source to destination

Session layer → Provide token management service

Presentation layer → Concerned with the syntax and semantics of the information transmitted

Question 71 |

An instruction is stored at location 500 with it address field at location 501. The address field has the value 400. A processor register R1 contains the number 200. Match the addressing mode (List-I) given below with effective address (List-II) for the given instruction:

Choose the correct option from those given below:

(a)-(iii), (b)-(i), (c)-(iv), (d)-(ii) | |

(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv) | |

(a)-(iv), (b)-(ii), (c)-(iii), (d)-(i) | |

(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i) |

Question 71 Explanation:

Direct Address = 400

Relative Address = Next Instruction memory location + Direct Address value

= 502 + 400

= 902

Register indirect Address= 200

Indexed Address = Register Indirect Address + Direct Address

= 200 + 400

= 600

Question 72 |

A rectangle is bounded by the lines x = 0; y=0, x = 5 and y = 3. The line segment joining (–1, 0) and (4, 5), if clipped against this window will connect the points _____________.

(0, 1) and (3, 3) | |

(0, 1) and (2, 3) | |

(0, 1) and (4, 5) | |

(0, 1) and (3, 5) |

Question 72 Explanation:

We have to use Cohen Sutherland line clipping algorithm.

The line segment joining (-1,0) and (4,5)

y-0 = ((5-0) / 4-(-1))*(x-(-1))

y=x+1

Clipped against this window will connect the points are (0, 1) and (2, 3) based on given data. Rest of the options are not correct.

The line segment joining (-1,0) and (4,5)

y-0 = ((5-0) / 4-(-1))*(x-(-1))

y=x+1

Clipped against this window will connect the points are (0, 1) and (2, 3) based on given data. Rest of the options are not correct.

Question 73 |

Consider the following statements with respect to the language L = {a

^{n}b

^{n}| n ≥ 0}

Which one of the following is correct?

only S _{1} and S_{2} | |

only S _{1} and S_{3} | |

only S _{2} and S_{3} | |

S _{1}, S_{2} and S_{3} |

Question 73 Explanation:

S1 is correct because L

Since context free languages are closed under kleen closure so L

Complement of given language L will be a language accepting all strings other than {a

^{2}means L.L i.e resulting language will be L^{2}= {a^{n}b^{n}a^{n}b^{n }| n ≥ 0} which is a context free language.Since context free languages are closed under kleen closure so L

^{k}is context-free language for any given k ≥ 1. Hence S2 is correct.Complement of given language L will be a language accepting all strings other than {a

^{n}b^{n}| n ≥ 0}. And we can easily design a pushdown automata which rejects {a^{n}b^{n}| n ≥ 0} and accepts all string other than this. And as we know, context free languages are closed under kleen closure. Hence S3 is correct.Question 74 |

What are the greatest lower bound (GLB) and the least upper bound (LUB) of the sets A = {3, 9, 12} and B = {1, 2, 4, 5, 10} if they exist in poset (z*,/)?

A (GLB – 3, LUB – 36); B (GLB – 1, LUB – 20) | |

A(GLB – 3, LUB – 12); B (GLB -1, LUB – 10) | |

A (GLB -1, LUB – 36); B (GLB – 2, LUB – 20) | |

A (GLB – 1, LUB – 12); B (GLB – 2, LUB – 10) |

Question 75 |

(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i) | |

(a)-(iv), (b).(iii), (c)-(i), (d)-(ii) | |

(a)-(iii), (b)-(iv), (c)-(i), (d)-(i) | |

(a)-(iii), (b)-(iv), (c)-(ii), (d)-(i) |

Question 75 Explanation:

Micro operation → Elementary operation performed on data stored in registers

Micro programmed control unit → Control Memory

Interrupts → Improve CPU utilization

Micro instruction→ Specify micro operations

Micro programmed control unit → Control Memory

Interrupts → Improve CPU utilization

Micro instruction→ Specify micro operations

Question 76 |

A clique in an undirected graph G = (V, E) is a subset V’ ⊆ V of vertices, such that

If (u, v) ∈ E then u ∈ V’ and v ∈ V’ | |

If (u, v) ∈ E then u ∈ V’ or v ∈ V’ | |

Each pair of vertices in V’ is connected by an edge | |

All pairs of vertices in V’ are not connected by an edge |

Question 76 Explanation:

A clique in an undirected graph G = (V, E) is a subset V’ ⊆ V of vertices, such that each pair of vertices in V’ is connected by an edge

Question 78 |

The weight of minimum spanning tree in graph G, calculated using Kruskal’s algorithm is :

14 | |

15 | |

17 | |

18 |

Question 78 Explanation:

= 2+3+4+6

= 15

Question 79 |

Which of the following CPU scheduling algorithms is/are supported by LINUX operating system?

Non-preemptive priority scheduling | |

Preemptive priority scheduling and time sharing CPU scheduling | |

Time sharing scheduling only | |

Priority scheduling only |

Question 79 Explanation:

Preemptive priority scheduling and time sharing CPU scheduling algorithms is/are supported by LINUX operating system.

Question 80 |

What is the output of following C program?

# include

main( )

{

int i, j, x = 0;

for (i = 0; i <5; ++i)

for (j = 0; j

{

x + = (i + j – 1);

break;

}

printf (“%d”,x) ;

}

{

x + = (i + j – 1);

break;

}

printf (“%d”,x) ;

}

6 | |

5 | |

4 | |

3 |

Question 80 Explanation:

Question 81 |

Which of the following methods are used to pass any number of parameters to the operating system through system calls?

Registers | |

Block or table in main memory | |

Stack | |

Block in main memory and stack |

Question 82 |

The following program is stored in the memory unit of the basic computer. Give the content of accumulator register in hexadecimal after the execution of the program.

A1B4 | |

81B4 | |

A184 | |

8184 |

Question 82 Explanation:

Question 83 |

Java Virtual Machine (JVM) is used to execute architectural neutral byte code. Which of the following is needed by the JVM for execution of Java Code?

Class loader only | |

Class loader and Java Interpreter | |

Class loader, Java Interpreter and API | |

Java Interpreter only |

Question 84 |

Consider the game tree given below

Here Ο and • represent MIN and MAX nodes respectively. The value of the root node of the game tree is

14 | |

17 | |

111 | |

112 |

Question 84 Explanation:

Question 85 |

A basic feasible solution of an mXn Transportation-Problem is said to be non-degenerate, if basic feasible solution contains exactly____number of individual allocation in ___positions

m+n+1, independent | |

m+n-1, independent | |

m+n-1, appropriate | |

m-n+1, independent |

Question 85 Explanation:

The initial solution of a transportation problem is said to be non-degenerate basic feasible solution if it satisfies:

→The solution must be feasible, i.e. it must satisfy all the supply and demand constraints.

→The number of positive allocations must be equal to m+n-1, where m is the number of rows and n is the number of columns.

→All the positive allocations must be in independent positions

A few terms used in connection with transportation models are defined below.

Note: It is very standard and regular question and asked in UGC-NET Dec-2015 paper-3

Ref-https://solutionsadda.in/ugc-net-cs-2015-dec-paper-3/

→The solution must be feasible, i.e. it must satisfy all the supply and demand constraints.

→The number of positive allocations must be equal to m+n-1, where m is the number of rows and n is the number of columns.

→All the positive allocations must be in independent positions

A few terms used in connection with transportation models are defined below.

**1. Feasible solution**: A feasible solution to a transportation problem is a set of non-negative allocations, xij that satisfies the rim (row and column) restrictions.**2. Basic feasible solution**: A feasible solution to a transportation problem is said to be a basic feasible solution if it contains no more than m + n – 1 non – negative allocations, where m is the number of rows and n is the number of columns of the transportation problem.**3. Optimal solution**: A feasible solution (not necessarily basic) that minimizes (maximizes) the transportation cost (profit) is called an optimal solution.**4. Non-degenerate basic feasible solution**: A basic feasible solution to a (m x n) transportation problem is said to be non – degenerate if, the total number of non-negative allocations is exactly m + n – 1 (i.e., number of independent constraint equations), and these m + n – 1 allocations are in independent positions.**5. Degenerate basic feasible solution**: A basic feasible solution in which the total number of non-negative allocations is less than m + n – 1 is called degenerate basic feasible solution.Note: It is very standard and regular question and asked in UGC-NET Dec-2015 paper-3

Ref-https://solutionsadda.in/ugc-net-cs-2015-dec-paper-3/

Question 86 |

Given following equation:

(142)

_{b}+ (112)

_{b-2}= (75)

_{8}. Find base b.

3 | |

6 | |

7 | |

5 |

Question 86 Explanation:

Option-A: Definitely wrong. Because 142 having 4 in a number but base is 3 only. So,eliminate it.

Option-B:

Step-1: Converting (142)

1*5

4*5

2*5

Adding all to get (47)

Step-2: Converting (112)

1*3

1*3

2*3

Adding all to get (14)

Step-3: Convert (61)

8|_61

8|_7 → 5

8|_7 → 7

Ans:(75)

No need to check Option-C & D.

Option-B:

Step-1: Converting (142)

_{5 }to base 10.1*5

^{2}=254*5

^{1}=202*5

^{0}=2Adding all to get (47)

_{10}Step-2: Converting (112)

_{3}to base 10.1*3

^{2}=91*3

^{1}=32*3

^{0}=2Adding all to get (14)

_{10}Step-3: Convert (61)

_{10}to (?)_{8}// 47+14=61. Both are in decimal so we can add directly.8|_61

8|_7 → 5

8|_7 → 7

Ans:(75)

_{8}No need to check Option-C & D.

Question 87 |

Consider the following models:

M1: Mamdani model

M2: Takagi-Sugeno-Kang model

M3: Kosko's additive model(SAM)

Which of the following option contains example of additive rule model?

Only M1 and M2 | |

Only M2 and M3 | |

Only M1 and M3 | |

M1, M2 and M3 |

Question 87 Explanation:

**Mamdani Fuzzy Inference Systems**

Mamdani fuzzy inference was first introduced as a method to create a control system by synthesizing a set of linguistic control rules obtained from experienced human operators [1]. In a Mamdani system, the output of each rule is a fuzzy set.

Since Mamdani systems have more intuitive and easier to understand rule bases, they are well-suited to expert system applications where the rules are created from human expert knowledge, such as medical diagnostics.

**Sugeno Fuzzy Inference Systems**

Sugeno fuzzy inference, also referred to as Takagi-Sugeno-Kang fuzzy inference, uses singleton output membership functions that are either constant or a linear function of the input values. The defuzzification process for a Sugeno system is more computationally efficient compared to that of a Mamdani system, since it uses a weighted average or weighted sum of a few data points rather than compute a centroid of a two-dimensional area.

You can convert a Mamdani system into a Sugeno system using the convert To Sugeno function. The resulting Sugeno system has constant output membership functions that correspond to the centroids of the Mamdani output membership functions.

Question 88 |

A fuzzy conjunction operators, t(x,y), and a fuzzy disjunction operator, s(x,y) from a pair if they satisfy:

t(x,y)=1-s(1-x, 1-y).

If t(x,y)= xy/ (x+y-xy) then s(x,y) is given by

(x+y)/1-xy | |

(x+y-2xy)/1-xy | |

(x+y-xy)/1-xy | |

(x+y-xy)/1+xy |

Question 88 Explanation:

t(x,y)= xy/ (x+y-xy) ---> (1)

t(x,y)=1-s(1-x, 1-y) --->(2)

Substitute (1) in (2)

s(1-x,1-y)=1- xy/ (x+y-xy) = (x+y-xy)-xy /(x+y-xy) = x(1-y)+y(1-x)/(x(1-y)+y

t(x,y)=1-s(1-x, 1-y) --->(2)

Substitute (1) in (2)

s(1-x,1-y)=1- xy/ (x+y-xy) = (x+y-xy)-xy /(x+y-xy) = x(1-y)+y(1-x)/(x(1-y)+y

Question 89 |

How many reflexive relations are there on a set with 4 elements?

2^4 | |

2^12 | |

4^2 | |

2 |

Question 89 Explanation:

Reflexive Relation : A Relation R on A a set A is said to be Reflexive if xRx for every element of x

The number of reflexive relations on an n-element set is 2^(n^2)-n.

Here, n=4

= (n

=12

= 2

The number of reflexive relations on an n-element set is 2^(n^2)-n.

Here, n=4

= (n

^{2})-n=12

= 2

^{12}is the final answer.Question 90 |

Which of the following algorithms is not used for line clipping?

Cohen-Sutherland algorithm
| |

Southerland-Hodgeman algorithm | |

Liang-barsky algorithm | |

Nicholl-Lee-Nicholl algorithm |

Question 90 Explanation:

The Cohen–Sutherland algorithm is a computer-graphics algorithm used for line clipping. The algorithm divides a two-dimensional space into 9 regions and then efficiently determines the lines and portions of lines that are visible in the central region of interest (the viewport).

A convex polygon and a convex clipping area are given. The task is to clip polygon edges using the Sutherland–Hodgman Algorithm. Input is in the form of vertices of the polygon in clockwise order.

The Liang-Barsky algorithm is a line clipping algorithm. This algorithm is more efficient than Cohen–Sutherland line clipping algorithm and can be extended to 3-Dimensional clipping.

The Nicholl–Lee–Nicholl algorithm is a fast line clipping algorithm that reduces the chances of clipping a single line segment multiple times, as may happen in the Cohen–Sutherland algorithm.

A convex polygon and a convex clipping area are given. The task is to clip polygon edges using the Sutherland–Hodgman Algorithm. Input is in the form of vertices of the polygon in clockwise order.

The Liang-Barsky algorithm is a line clipping algorithm. This algorithm is more efficient than Cohen–Sutherland line clipping algorithm and can be extended to 3-Dimensional clipping.

The Nicholl–Lee–Nicholl algorithm is a fast line clipping algorithm that reduces the chances of clipping a single line segment multiple times, as may happen in the Cohen–Sutherland algorithm.

Question 91 |

A flow graph F with entry node (1) and exit node (11) is shown below:

How many predicate nodes are there and what are their names

Three: (1, (2,3), 6) | |

Three: (1, 4, 6) | |

Four: ((2,3), 6, 10, 11) | |

Four: ((2,3), 6, 9, 10) |

Question 91 Explanation:

Predicate is a node that contains condition. It means at least 2 outgoing edges required to qualify as a predicate.

The vertex 1 is contains 2 outgoing edges are (2,3) and 11

The vertex (2,3) contains 2 outgoing edges are 6 and (4,5)

The vertex 6 contains 2 outgoing edges are 7 and 8.

Total number of predicates are THREE.

The vertex 1 is contains 2 outgoing edges are (2,3) and 11

The vertex (2,3) contains 2 outgoing edges are 6 and (4,5)

The vertex 6 contains 2 outgoing edges are 7 and 8.

Total number of predicates are THREE.

Question 92 |

A flow graph F with entry node (1) and exit node (11) is shown below:

How many regions are there in flow graph F

2 | |

3 | |

4 | |

5 |

Question 92 Explanation:

The region is nothing but a combination of closed cycle and outer cycle. Any graph must have one outer cycle.

Here, 3 closed cycles are available and one outer cycle is available.

Closed cycles are:

→ 1,(2,3), (4,5) and 10

→ 6, 7, 8, 9

→ (2,3), 6,7,8,9,10 and (4,5)

Outer cycle is one. So, the total number of regions are 4.

Here, 3 closed cycles are available and one outer cycle is available.

Closed cycles are:

→ 1,(2,3), (4,5) and 10

→ 6, 7, 8, 9

→ (2,3), 6,7,8,9,10 and (4,5)

Outer cycle is one. So, the total number of regions are 4.

Question 93 |

A flow graph F with entry node (1) and exit node (11) is shown below:

What is the cyclomatic complexity of flowgraph F

2 | |

3 | |

4 | |

5 |

Question 93 Explanation:

To find cyclomatic complexity we have 3 formulas

1. The number of regions(R) corresponds to the cyclomatic complexity. Total number of regions(R) are 4.

2. V(G),Flow graph is defined as V(G)=E-N+2 where E is the number of flow graph edges, and N is the number of flow graph nodes.

Predicates are 3+1=4

3. V(G),Flow graph is defined as V(G)=P+1 where p is the number of predicate nodes contained in the flow graph G.

Edges(E)-Nodes(N)+2

= 11-9+2

= 2+2

= 4

1. The number of regions(R) corresponds to the cyclomatic complexity. Total number of regions(R) are 4.

2. V(G),Flow graph is defined as V(G)=E-N+2 where E is the number of flow graph edges, and N is the number of flow graph nodes.

Predicates are 3+1=4

3. V(G),Flow graph is defined as V(G)=P+1 where p is the number of predicate nodes contained in the flow graph G.

Edges(E)-Nodes(N)+2

= 11-9+2

= 2+2

= 4

Question 94 |

A flow graph F with entry node (1) and exit node (11) is shown below:

How many nodes are there in the longest independent path?

6 | |

7 | |

8 | |

9 |

Question 94 Explanation:

The longest independent path nodes are 8 but it have 2 possibilities

1 → (2,3) → 6 → 7 → 9 → 10 → 1 → 11

(or)

1 → (2,3) → 6 → 8 → 9 → 10 → 1 → 11

1 → (2,3) → 6 → 7 → 9 → 10 → 1 → 11

(or)

1 → (2,3) → 6 → 8 → 9 → 10 → 1 → 11

Question 95 |

A flow graph F with entry node (1) and exit node (11) is shown below:

How many nodes are there in flowgraph F?

9 | |

10 | |

11 | |

12 |

Question 95 Explanation:

The nodes are nothing but vertices.

Above graph contains 9 nodes and 11 edges.

The nodes are 1, (2,3), (4,5), 6, 7, 8, 9, 10, 11

Above graph contains 9 nodes and 11 edges.

The nodes are 1, (2,3), (4,5), 6, 7, 8, 9, 10, 11

Question 96 |

**Comprehension:**

Answer question (96-100) based on the problem statement given below:

An organization needs to maintain database having five attributes A, B, C, D, E. These attributes are functionally dependent on each other for which functionally dependency set F is given as : F: {A→ BC, D → E, BC → D, A →D}. Consider a universal relation R(A, B, C, D, E) with functional dependency set F. Also all attributes are simple and take atomic values only.

:→ Minimal cover F’ of functional dependency set F is

F’ = {A → B, A → C, BC → D, D →E} | |

F’ = {A → BC, B → D, D → E} | |

F’ = {A → B, A → C, A → D, D → E} | |

F’ = {A → B, A → C, B → D, C → D.D → E} |

Question 96 Explanation:

Steps to find minimal cover:

Step1: Write all FDs in such a way that the RHS of each FD contain only one attribute.

A→ B

A→ C

D → E

BC → D

A →D

Step2: Then for each FD see whether that RHS attribute can be driven by the LHS attribute using remaining FDs, if yes then remove that FD otherwise keep it. So step 1 results in following FDs:

A→ B

A→ C

D → E

BC → D

Step3: Now see the FD which is having 2 or more attributes in its LHS.Then find the closure of LHS attributes and then eliminate the attributes from LHS which are common in clsure. Above BC are two attributes in LHS.

B

C

Since nothing is common in closure so keep both attributes in LHS.

Hence minimal cover is

A→ B

A→ C

D → E

BC → D

Step1: Write all FDs in such a way that the RHS of each FD contain only one attribute.

A→ B

A→ C

D → E

BC → D

A →D

Step2: Then for each FD see whether that RHS attribute can be driven by the LHS attribute using remaining FDs, if yes then remove that FD otherwise keep it. So step 1 results in following FDs:

A→ B

A→ C

D → E

BC → D

Step3: Now see the FD which is having 2 or more attributes in its LHS.Then find the closure of LHS attributes and then eliminate the attributes from LHS which are common in clsure. Above BC are two attributes in LHS.

B

^{+}= {B}C

^{+}= {C}Since nothing is common in closure so keep both attributes in LHS.

Hence minimal cover is

A→ B

A→ C

D → E

BC → D

Question 97 |

**Comprehension:**

Answer question (96-100) based on the problem statement given below:

An organization needs to maintain database having five attributes A, B, C, D, E. These attributes are functionally dependent on each other for which functionally dependency set F is given as : F: {A→ BC, D → E, BC → D, A →D}. Consider a universal relation R(A, B, C, D, E) with functional dependency set F. Also all attributes are simple and take atomic values only.

→ Assume that given table R is decomposed in two tables

Which of the following option is true w.r.t. given decomposition?

Dependency preservation property is followed | |

R _{1} and R_{2} are both in 2 NF | |

R _{2} is in 2 NF and R_{3} is in 3 NF | |

R _{1} is in 3 NF and R_{2} is in 2 NF |

Question 97 Explanation:

Since In R1 and R2 BC can’t determine BC → D of relation “R”. Hence R1 and R2
are not following the Dependency preservation property.

Candidate key of R1 is “A”. And since KHS of R1 contains only “A” so R1 is in 3NF.

Candidate key of R2 is “A” , But Since D→E neither have Super key in its LHS nor have a prime key attribute in its RHS, So R2 is in 2NF but not in 3NF.

Candidate key of R1 is “A”. And since KHS of R1 contains only “A” so R1 is in 3NF.

Candidate key of R2 is “A” , But Since D→E neither have Super key in its LHS nor have a prime key attribute in its RHS, So R2 is in 2NF but not in 3NF.

Question 98 |

**Comprehension:**

Answer question (96-100) based on the problem statement given below:

An organization needs to maintain database having five attributes A, B, C, D, E. These attributes are functionally dependent on each other for which functionally dependency set F is given as : F: {A→ BC, D → E, BC → D, A →D}. Consider a universal relation R(A, B, C, D, E) with functional dependency set F. Also all attributes are simple and take atomic values only.

→ Identify the redundant functional dependency in F

BC→D | |

D→E | |

A→D | |

A→BC |

Question 98 Explanation:

A→D is redundant because A can determine D using FD’s A→ BC and BC → D.

Question 99 |

**Comprehension:**

Answer question (96-100) based on the problem statement given below:

An organization needs to maintain database having five attributes A, B, C, D, E. These attributes are functionally dependent on each other for which functionally dependency set F is given as : F: {A→ BC, D → E, BC → D, A →D}. Consider a universal relation R(A, B, C, D, E) with functional dependency set F. Also all attributes are simple and take atomic values only.

→ Identify primary key of table R with functional dependency set F

BC | |

AD | |

A | |

AB |

Question 99 Explanation:

Since “A” is not in RHS of any FD so “A” is the key of relation R. NOw to see whether “A” is the primary key of “R” or not find its closure.

A

A

^{+}= { A,B,C,D,E}. Hence A is the primary key of relation RQuestion 100 |

**Comprehension:**

Answer question (96-100) based on the problem statement given below:

An organization needs to maintain database having five attributes A, B, C, D, E. These attributes are functionally dependent on each other for which functionally dependency set F is given as : F: {A→ BC, D → E, BC → D, A →D}. Consider a universal relation R(A, B, C, D, E) with functional dependency set F. Also all attributes are simple and take atomic values only.

→ Identify the normal form in which relation R belong to

1 NF | |

2 NF | |

3 NF | |

BCNF |

Question 100 Explanation:

Since “A” is the primary key or “R” and there is no partial dependency So “R” is in 2NF.

Since, D → E, BC → D neither have a super key in their LHS nor a prime key attribute in their RHS so “R” is not in 3NF.

Since “R” is not in 3NF it can’t be in BCNF.

Hence option(B) is correct

Since, D → E, BC → D neither have a super key in their LHS nor a prime key attribute in their RHS so “R” is not in 3NF.

Since “R” is not in 3NF it can’t be in BCNF.

Hence option(B) is correct

There are 100 questions to complete.