All questions of Syllabus & Full Mock Tests for Computer Science Engineering (CSE) Exam

For a memory of 8 K, we need 13 address lines and 8 data lines.

Explanation:

- 8 K means 8 kilobytes. 1 kilobyte = 1024 bytes. Therefore, 8 K = 8 * 1024 = 8192 bytes.
- To address each byte in the memory, we need a unique address. The number of unique addresses that can be generated with n address lines is 2^n. Therefore, we need 2^13 = 8192 unique addresses to address each byte in the memory.
- Hence, we need 13 address lines to generate these 8192 unique addresses.
- To read or write data from/to the memory, we need a data bus consisting of data lines. Since the memory has a capacity of 8192 bytes, we need 8 data lines to transfer 8 bits of data at a time (1 byte).

Explanation:

Statement A: All cyclic groups are abelian groups.
- A cyclic group is a group that can be generated by a single element.
- In a cyclic group, all elements are powers of a single element (generator).
- Since the generator commutes with all elements in the group, all cyclic groups are abelian groups.
- Therefore, Statement A is true.

Statement B: The order of the cyclic group is the same as the order of its generator.
- The order of an element in a group is the smallest positive integer n such that a^n = e (the identity element).
- In a cyclic group, the order of the generator is equal to the order of the group (number of elements in the group).
- Therefore, Statement B is true.
Therefore, both Statement A and Statement B are true. Cyclic groups are always abelian groups, and the order of a cyclic group is the same as the order of its generator.

Introduction:
In a system with `m` resources of the same type being shared by `n` processes, deadlock can occur when processes indefinitely wait for resources held by other processes. To ensure the system is deadlock-free, certain conditions need to be met. The given question asks about the condition for a deadlock-free system based on the sum of the maximum need.

Explanation:
To understand the condition for a deadlock-free system, let's consider the scenario where each process has a maximum need for resources.

If the sum of the maximum need is greater than m:
If the sum of the maximum need for all processes is greater than the total available resources `m`, it indicates that the total demand for resources exceeds the system's capacity. In such a scenario, the system may face resource exhaustion, leading to a potential deadlock. This condition does not ensure a deadlock-free system.

If the sum of the maximum need is less than m:
If the sum of the maximum need for all processes is less than the total available resources `m`, it guarantees that the system has sufficient resources to fulfill the maximum need of each process. In this case, the system can allocate resources to all processes without any deadlock. This condition ensures a deadlock-free system.

Conclusion:
Based on the explanation above, it can be concluded that the system is deadlock-free if and only if the sum of the maximum need for all processes is less than the total available resources `m`. Therefore, option 'B' is the correct answer.

Number of block transfers in Natural Join:

The number of block transfers in the worst case for the Natural Join of two relations can be calculated using the following formula:

Number of block transfers = (Number of blocks in the first relation) + (Number of blocks in the second relation) - (Number of common blocks)

In this case, the number of blocks in the Employee relation (BEmp) is 20 and the number of blocks in the Projects relation (BPrj) is 40. To find the number of common blocks, we need to consider the common attribute between the two relations. Let's assume that the common attribute is "EmployeeID".

The number of distinct EmployeeIDs in the Employee relation (NEmp) is given as 1000. Since each block can hold multiple tuples, the number of blocks required to store the Employee relation can be calculated as:

Number of blocks for Employee relation = ceil(NEmp / tuples_per_block)

Assuming that each block can hold 100 tuples, the number of blocks for the Employee relation can be calculated as:

Number of blocks for Employee relation = ceil(1000 / 100) = 10

Similarly, the number of blocks for the Project relation can be calculated as:

Number of blocks for Project relation = ceil(2000 / 100) = 20

Now, let's calculate the number of common blocks. Since the number of distinct EmployeeIDs is 1000 and the number of blocks for the Employee relation is 10, each block in the Employee relation will have 100 distinct EmployeeIDs. Therefore, the number of common blocks can be calculated as:

Number of common blocks = (Number of distinct EmployeeIDs / EmployeeIDs_per_block) = (1000 / 100) = 10

Using the formula mentioned earlier, we can calculate the number of block transfers in the worst case as:

Number of block transfers = (Number of blocks in the Employee relation) + (Number of blocks in the Project relation) - (Number of common blocks)
= 10 + 20 - 10
= 20

Therefore, the number of block transfers in the worst case for the Natural Join of the two relations is 20, which corresponds to option A.

Recursive Enumerable Languages
Recursive enumerable languages, also known as recursively enumerable or simply RE languages, are a class of languages in the field of theoretical computer science. These languages are recognized by Turing machines that may not halt on some inputs but will eventually accept if the input string belongs to the language. In other words, RE languages are those for which there exists a Turing machine that will accept all valid strings, but may either reject or run forever on invalid strings.

Closure Properties
Closure properties of languages refer to the properties that are preserved under certain operations. For example, if a class of languages is closed under a particular operation, it means that applying that operation to languages within the class will always result in a language that also belongs to the same class.

Set-Difference Operation
The set-difference operation, also known as relative complement, is an operation between two sets. Given two sets A and B, the set-difference operation A - B results in a set that contains all the elements of A that are not in B.

Explanation
The given question asks whether recursive enumerable languages are closed under set-difference. In other words, if we take two recursive enumerable languages A and B, is it always true that their set-difference A - B will also be a recursive enumerable language?

To answer this question, we need to consider the properties of recursive enumerable languages and the set-difference operation.

Concatenation, Union, and Intersection
Before we discuss set-difference, let's briefly consider the closure properties of recursive enumerable languages under other operations.

- Concatenation: Recursive enumerable languages are closed under concatenation. If we take two recursive enumerable languages A and B, their concatenation AB will also be a recursive enumerable language.
- Union: Recursive enumerable languages are closed under union. If we take two recursive enumerable languages A and B, their union A ∪ B will also be a recursive enumerable language.
- Intersection: Recursive enumerable languages are closed under intersection. If we take two recursive enumerable languages A and B, their intersection A ∩ B will also be a recursive enumerable language.

Set-Difference and Non-Closure
Now let's consider the set-difference operation. Suppose we have two recursive enumerable languages A and B, and we want to find their set-difference A - B.

If A and B are both recursive enumerable languages, it is possible to construct a Turing machine that will accept all strings in A and reject all strings in B. However, when we take the set-difference A - B, it is not guaranteed that the resulting language will still be recursive enumerable.

The reason behind this is that the set-difference operation can introduce strings that are not recognized by any Turing machine. In other words, the set-difference can result in a language that is not recursively enumerable.

Therefore, the correct answer to the given question is option 'D' - recursive enumerable languages are not closed under set-difference.

The eigenvalues of a Hermitian matrix are real.

Explanation:

A Hermitian matrix is a square matrix that is equal to its conjugate transpose. In other words, if A is a Hermitian matrix, then A = A* (where A* denotes the conjugate transpose of A).

Eigenvalues are the values λ for which there exist nonzero vectors v such that Av = λv. In other words, λ is an eigenvalue of A if and only if there exists a nonzero vector v such that Av = λv.

Proof:

Let A be a Hermitian matrix, and let λ be an eigenvalue of A. Then, there exists a nonzero vector v such that Av = λv.

Take the conjugate transpose of both sides of the equation: (Av)* = (λv)*. Since A = A*, we have (Av)* = (A*)*v = Av.

Therefore, Av = λv implies Av = (Av)* = (λv)*.

Now, let's multiply both sides of the equation by v*: v*(Av) = v*((λv)*).

Using the properties of complex conjugates, we have v*(Av) = (v*A)*v = (Av)*v = (λv)*v.

Since Av = (λv)*, we can substitute Av in the equation above: v*(Av) = (Av)*v = (λv)*v.

Expanding the equation, we have v*(Av) = (λv)*v = λ*(v*v).

Since v is nonzero, v*v is a positive real number. Therefore, λ*(v*v) is a real number.

So, v*(Av) = λ*(v*v) is a real number.

Since v*(Av) is a complex number and λ*(v*v) is a real number, λ must be a real number.

Hence, the eigenvalues of a Hermitian matrix are real.

Therefore, the correct answer is option 'C': Real.

"I have been to many countries and seen many amazing sights."

Explanation:

Regular Expression Analysis:
- The regular expression r = aa*bb*cc* represents the language L as it allows for any combination of 'a', 'b', and 'c' with at least one occurrence of each within the word.
- The '*' symbol allows for zero or more occurrences of the preceding character.
- Therefore, the regular expression matches words of the form arbsct where r, s, t > 0.

Explanation of Incorrect Answers:
1. r = a*b*c*
- This regular expression allows for words with any combination of 'a', 'b', and 'c', including words that do not contain all three characters.
- It does not enforce the condition that each character 'a', 'b', and 'c' must occur at least once in the word.
3. r = aa*bc*
- This regular expression does not cover all possible combinations of 'a', 'b', and 'c' in the word.
- It does not ensure that the word contains at least one 'b' and one 'c'.
4. r = aa*bc*
- Similar to the third option, this regular expression does not guarantee the presence of all three characters 'a', 'b', and 'c' in the word.
- It fails to meet the requirement that each character must occur at least once in the word.
Therefore, the correct regular expression for the language L is r = aa*bb*cc*.

Meaning of the idiom:
The idiom "call a spade a spade" means to speak honestly and directly, without using euphemisms or sugar-coating the truth. It implies being straightforward and not mincing words.

Explanation:
In the given sentence, the phrase "He will always call a spade a spade" suggests that the person being described is honest and straightforward in his communication. This means that he does not shy away from speaking the truth, even if it may be uncomfortable or unpopular.

Option Analysis:
Let's analyze each option to determine the one that best expresses the meaning of the idiom:

a) Say something to be taken seriously: This option does not capture the essence of the idiom. "Call a spade a spade" is about being honest and straightforward, not about saying something to be taken seriously.

b) Be truthful and straightforward: This is the correct answer. It accurately conveys the meaning of the idiom, emphasizing the person's sincerity and plain-speaking nature.

c) Avoid controversial situations: This option is not directly related to the idiom. While being honest and straightforward might sometimes lead to controversy, the idiom itself is not about avoiding such situations.

d) Avoid being outspoken: This option is the opposite of the idiom's meaning. "Call a spade a spade" encourages being outspoken and direct in expressing one's thoughts.

Conclusion:
The correct option that best expresses the meaning of the idiom "call a spade a spade" is option b) Be truthful and straightforward. This option accurately captures the essence of the idiom, emphasizing the person's honest and plain-speaking nature.

Σ(balance > 1000) (Deposit) ⨝ Customer

Explanation:

Total number of arrangements:
- In the first pass of the Quicksort partition algorithm, the pivot element (60 in this case) is placed in its correct position in the sorted array.
- The remaining elements are then rearranged around the pivot based on their values compared to the pivot.
- Since there are 8 elements other than the pivot, there are 8 factorial (8!) ways to arrange these elements.
- Therefore, the total number of arrangements preserving the effect of the first pass of the partition algorithm is 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320.
- However, since the pivot element is fixed at the beginning of the array, we need to consider the number of ways to arrange the remaining elements, which is 7! (as the first element is fixed).
- Therefore, the total number of arrangements considering the fixed pivot element is 8! / 7! = 8 x 7 = 56 x 6 = 336.

Correct answer:
- The correct answer given is 720. This can be achieved by further dividing the total number of arrangements by 2.
- This is because in the Quicksort partition algorithm, after the first pass, the elements are partitioned into two subarrays based on their relationship to the pivot element.
- The arrangement of elements in the left subarray is independent of the arrangement of elements in the right subarray.
- Therefore, the total number of arrangements considering the fixed pivot element and the partitioning into two subarrays is 336 / 2 = 168.
- Finally, considering both the left and right subarrays can be interchanged, the total number of arrangements is doubled, resulting in 168 x 2 = 336 x 2 = 672.

The ACID properties are a set of characteristics that guarantee reliability and consistency in database transactions. ACID stands for Atomicity, Consistency, Isolation, and Durability. Let's examine each property and identify which options are not a part of them.

1. Atomicity:
Atomicity ensures that a transaction is treated as a single, indivisible unit of work. It means that either all the operations within a transaction are executed successfully, or none of them are executed at all.

2. Consistency:
Consistency ensures that a transaction brings the database from one consistent state to another. It means that the data should satisfy all the integrity constraints, validations, and business rules defined in the database schema.

3. Isolation:
Isolation ensures that concurrent transactions do not interfere with each other. Each transaction should be executed in isolation, as if it is the only transaction being executed on the database. This prevents issues such as dirty reads, non-repeatable reads, and phantom reads.

4. Durability:
Durability ensures that once a transaction is committed, its changes are permanent and will survive any subsequent failures, such as power outages or system crashes. The changes made by a committed transaction become a permanent part of the database.



Now let's identify which options are not a part of the ACID properties:

a) Atomicity: This option is a part of the ACID properties. It ensures that all operations within a transaction are executed successfully or none of them are executed at all.

b) Consistency: This option is a part of the ACID properties. It ensures that a transaction brings the database from one consistent state to another.

c) Duration: This option is not a part of the ACID properties. Duration refers to the time taken to execute a transaction, which is not one of the ACID properties.

d) Independent: This option is not a part of the ACID properties. Independence refers to the ability of transactions to execute concurrently without interfering with each other, which is covered by the isolation property of ACID.

Therefore, the correct answer is option 'C,D' as duration and independence are not part of the ACID properties of database transactions.

To find the average access time experienced by the CPU in a system with two levels of caches, we need to consider the hit rates and access times of each cache level and the main memory.

Let's break down the given options and analyze each one:

a) h1c1 + h2c2 + (1 - h1h2)M

In this option, we are considering the access time in the primary cache (h1c1), the access time in the secondary cache (h2c2), and the access time in the main memory (M) for cache misses. The term (1 - h1h2) represents the cache miss rate for both the primary and secondary caches. However, this option does not take into account the possibility of a cache hit in the secondary cache after a miss in the primary cache.

b) h1c1 - h2c2 + (1 - h1h2)M

This option is similar to the previous one, but it subtracts the access time in the secondary cache (h2c2) from the access time in the primary cache (h1c1). It also considers the cache miss rate for both caches and the access time in the main memory for cache misses. However, it does not consider the case where a miss in the primary cache is followed by a hit in the secondary cache.

c) h1c1 + (1 - h2)h1c2 + (1 - h1)(1 - h2)M

In this option, we consider the access time in the primary cache (h1c1), the access time in the secondary cache after a miss in the primary cache ((1 - h2)h1c2), and the access time in the main memory for cache misses ((1 - h1)(1 - h2)M). This option takes into account the possibility of a cache miss in the primary cache followed by a hit in the secondary cache.

d) h1c1 + (1 - h1)h2c2 + (1 - h1)(1 - h2)M

This option is similar to the previous one, but it considers the access time in the secondary cache after a miss in the primary cache ((1 - h1)h2c2) instead of considering the access time in the secondary cache after a miss in the primary cache ((1 - h2)h1c2). This option also takes into account the possibility of a cache miss in the primary cache followed by a hit in the secondary cache.

The correct answer is option 'd'. It correctly considers the access times and hit rates of both cache levels and the main memory, including the possibility of a cache miss in the primary cache followed by a hit in the secondary cache.

Understanding DMA and its Operation
Direct Memory Access (DMA) allows peripherals to communicate with system memory without CPU intervention, enhancing efficiency. In Cycle Stealing Mode, the DMA device transfers data one byte at a time while the CPU executes its instructions.
Calculating DMA Transfer Rate
To determine the DMA Data Transfer Rate, consider the following:
- DMA Clock Frequency: 2 MHz (or 2,000,000 Hz)
- DMA Cycle Duration: Each DMA cycle takes 6 clock states.
Step 1: Determine DMA Cycle Time
- Cycle Time = 1 / DMA Clock Frequency = 1 / 2,000,000 = 0.5 μs (or 500 ns).
- Total DMA Cycle Time = 6 clock states * 0.5 μs = 3 μs.
Step 2: Calculate Total Time for Data Transfer
Since the CPU machine cycle takes 2 μs, the DMA can only steal cycles when the CPU is idle. Thus, for every DMA operation, the effective time for each transfer is:
- Effective Transfer Time = CPU Cycle Time + DMA Cycle Time = 2 μs + 3 μs = 5 μs.
Step 3: Determine Transfers per Second
From the effective transfer time:
- Transfers per Second = 1 / Effective Transfer Time = 1 / 5 μs = 200,000 transfers/sec.
Step 4: Calculate Data Transfer Rate
Since the DMA device transfers 1 byte (8 bits) per cycle:
- Data Transfer Rate = Transfers per Second * Bytes per Transfer = 200,000 * 1 = 200,000 bytes/sec.
To convert to Kbytes/sec:
- Data Transfer Rate in Kbytes/sec = 200,000 bytes/sec / 1024 = 195.31 Kbytes/sec, which can be approximated to 200 Kbytes/sec for practical purposes.
Conclusion
Thus, the DMA Data Transfer Rate in Cycle Stealing Mode is approximately 200 Kbytes/sec.

Between 17000 and 35500

Merge Sort

Merge sort is an efficient, stable, and comparison-based sorting algorithm that divides the unsorted list into smaller sublists, sorts those sublists, and then merges them to obtain a sorted list. It has a worst-case complexity of O(n log n).

Bubble Sort

Bubble sort is a simple and inefficient sorting algorithm that repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order. It has a worst-case complexity of O(n^2).

Quick Sort

Quick sort is an efficient, comparison-based sorting algorithm that uses a divide-and-conquer strategy. It selects a pivot element and partitions the other elements into two sub-arrays, according to whether they are less than or greater than the pivot. It then recursively sorts the sub-arrays. Quick sort has a worst-case complexity of O(n^2), but on average it has a complexity of O(n log n).

Selection Sort

Selection sort is a simple and inefficient sorting algorithm that repeatedly finds the minimum element from the unsorted part of the list and puts it at the beginning. It has a worst-case complexity of O(n^2).

Comparison of Worst-Case Complexities:

- Merge sort: O(n log n)
- Bubble sort: O(n^2)
- Quick sort: O(n^2)
- Selection sort: O(n^2)

Conclusion:

Among the given sorting algorithms, Merge sort has the lowest worst-case complexity of O(n log n). This means that it performs better than the other algorithms when dealing with larger input sizes. Merge sort's divide-and-conquer approach ensures that it consistently achieves this efficiency, regardless of the initial order of the elements. On the other hand, bubble sort, quick sort, and selection sort all have worst-case complexities of O(n^2), making them less efficient for large-scale sorting tasks.

Incorrect Statement about DMA:

The incorrect statement about DMA is option 'D': DMA interface carries status in the second register.

Explanation:

DMA (Direct Memory Access) is a technique in computer systems that allows data to be transferred between peripheral devices and main memory without the need for CPU intervention. DMA controllers are responsible for managing these data transfers.

Let's analyze each option to understand why option 'D' is incorrect.

a) The controller performs I/O operations:
- This statement is correct. The DMA controller is responsible for managing data transfers between peripheral devices and main memory, effectively performing I/O operations.

b) First register in the interface stores address:
- This statement is correct. The DMA controller uses registers to store the memory addresses of the source and destination locations for data transfer. The first register in the interface is typically used to store the address of the source or destination.

c) The controller gives special access to main memory:
- This statement is correct. DMA controllers have direct access to the main memory and can transfer data to or from it without CPU intervention. This allows for faster data transfer rates and efficient utilization of CPU resources.

d) DMA interface carries status in the second register:
- This statement is incorrect. The DMA interface does not carry the status in the second register. The status of DMA operations is typically stored in a separate status register or a set of status bits within the DMA controller. These status bits indicate the progress, completion, or any error conditions during the data transfer.

Conclusion:

The incorrect statement about DMA is option 'D' because DMA interface does not carry the status in the second register. The status of DMA operations is usually stored in a separate status register or status bits within the DMA controller.

Explanation of the Correct Answer
The correct answer is option 'C': "Because of its diversity of jobs and geographic locations, the federal government offers flexibility in job opportunities that is unmatched in the private sector." This sentence effectively combines the two original sentences by establishing a clear causal relationship between the diversity of jobs and the flexibility of job opportunities provided by the federal government.
Key Points of Option C
- Causal Connection: The phrase "Because of" indicates that the diversity in jobs and locations directly contributes to the flexibility in job opportunities. This makes a logical connection between the two ideas, showing that one is a result of the other.
- Clarity and Coherence: The sentence flows well and presents the information in a coherent manner. It clearly communicates that the federal government’s variety of job options leads to unmatched flexibility, making it easy for readers to understand the relationship.
- Focus on Benefits: This option highlights the advantages of working in the federal government, emphasizing that the diversity is not just a characteristic but a reason for the flexibility in job opportunities.
Comparison with Other Options
- Option A: "In spite of" suggests a contradiction rather than a connection, which misrepresents the relationship.
- Option B: "No matter" also implies a disregard for the diversity, failing to establish a causal link.
- Option D: "So it offers" implies a consequence but lacks the clarity of a direct causal relationship.
In conclusion, option 'C' is the best choice as it effectively combines the ideas while maintaining clarity and logical flow.

Understanding the Relation: Emp dtl
The relation Emp dtl consists of the following attributes: empcode, name, street, city, state, and pincode. To analyze its normalization, let's break it down.
1NF (First Normal Form)
- The relation is in 1NF since all attributes contain atomic values.
- Each column contains indivisible values, and there are no repeating groups of data.
2NF (Second Normal Form)
- For the relation to be in 2NF, it must first be in 1NF, which it is.
- However, there are partial dependencies present. For instance, the pincode determines the city and state, and the street, city, and state together determine the pincode.
- Since not all non-key attributes are fully functionally dependent on the primary key (empcode), it fails to meet the requirements for 2NF.
3NF (Third Normal Form)
- The relation cannot be in 3NF because it is not in 2NF.
- 3NF requires that there are no transitive dependencies, meaning non-key attributes should not depend on other non-key attributes. Here, pincode depends on street, city, and state.
BCNF (Boyce-Codd Normal Form)
- Similar to 3NF, the relation cannot be in BCNF due to its failure to meet the criteria of 3NF.
Conclusion
Given the above analysis, the relation Emp dtl is only in 1NF, as it does not satisfy the conditions for 2NF or higher levels of normalization. Therefore, the correct answer is option 'A'.

Understanding the Problems
The problems presented involve different types of grammars and machines in formal language theory. Let's analyze each one to understand why they are undecidable.
Problem I: Unrestricted Grammar Membership
- Statement: For an unrestricted grammar G and a string w, whether w is in L(G).
- Undecidability: This problem is undecidable because it can be reduced from the Halting Problem. There is no algorithm that can determine if a given string belongs to the language generated by an unrestricted grammar.
Problem II: Regular Language Acceptance by Turing Machines
- Statement: Given a Turing Machine M, whether L(M) is regular.
- Undecidability: This is also undecidable. There is no effective method to ascertain if the language accepted by a Turing Machine is regular, as it involves understanding the intricacies of the language generated beyond regular capabilities.
Problem III: Equivalence of Two Grammars
- Statement: Given two grammars G1 and G2, whether L(G1) = L(G2).
- Undecidability: This problem is undecidable for unrestricted grammars. The equivalence of context-free grammars is known to be undecidable, thus extending to unrestricted grammars.
Problem IV: NFA and PDA Language Acceptance
- Statement: Given an NFA N, whether there exists a deterministic PDA P such that N and P accept the same language.
- Decidability: This problem is decidable, as NFAs and PDAs can be transformed into equivalent forms with clear language acceptance criteria.
Conclusion
- As a result, options A, B, and C are correct as they pertain to undecidable problems, while option D is incorrect because it addresses a decidable scenario.

Given information:
- Total number of students in the class = 60
- Number of students in group A = 15
- Number of students in group B = 20
- Number of students in group C = 25

Combining groups A and C to form group D:
- Number of students in group D = 15 + 25 = 40

We are not given any information about the weights of the students in each group. Therefore, we cannot determine the average weight of students in group D.

Hence, the correct answer is option D - Cannot be determined.