AP PGECET Question Paper 2025 (Available) : Download Computer Science Engineering Question Paper

In how many ways can a chairperson, a secretary, and a treasurer be chosen from a group of 10 people, if each person can hold only one position?

• (1) 840
• (2) 5040
• (3) 1240
• (4) 720

A subgraph H of a graph G is called a clique if ____.

• (1) \( V(G) = V(H) \)
• (2) \( V(H) \subseteq V(G) \)
• (3) \( H \) contains all edges of \( G \)
• (4) \( H \) is also a complete graph

For a given graph G having \( v \) vertices and \( e \) edges which is connected and has no cycles, which of the following statements is true?

• (1) \( v = e \)
• (2) \( v = e + 1 \)
• (3) \( v + 1 = e \)
• (4) \( v = e - 1 \)

Assume G is a simple undirected graph and some vertices of G are of odd degree. Add a node \( v \) to G and make it adjacent to each odd degree vertex of G, then the resultant graph is sure to be ____.

• (1) Euler
• (2) Complete
• (3) Hamiltonian
• (4) Clique

Dijkstra's algorithm fails for graphs with ____.

• (1) Negative weights
• (2) Disconnected components
• (3) Directed edges
• (4) Self-loops

In propositional logic \( P \leftrightarrow Q \) is equivalent to \( \sim \) (denotes NOT) ____.

• (1) \( \sim (P \lor Q) \land \sim (Q \lor P) \)
• (2) \( (\sim P \lor Q) \land (\sim Q \lor P) \)
• (3) \( (P \lor Q) \land (Q \lor P) \)
• (4) \( (\sim P \lor Q) \rightarrow (\sim Q \lor P) \)

The Boolean function \( \sim (\sim P \land Q) \land (\sim (\sim P \land \sim Q)) \lor (P \lor R) \) is equal to the Boolean function:

• (1) Q
• (2) R
• (3) \( P \lor Q \)
• (4) P

A graph is self-complementary if it is isomorphic to its complement. For all self-complementary graphs on n vertices, \( n \) is ____.

• (1) a multiple of 4
• (2) even
• (3) odd
• (4) congruent to 0 mod 4 or 1 mod 4

Suppose \( R_1 \) and \( R_2 \) are reflexive relations on a set \( A \). Which of the following statements is correct?

• (1) \( R_1 \cap R_2 \) is reflexive and \( R_1 \cup R_2 \) is irreflexive
• (2) \( R_1 \cap R_2 \) is irreflexive and \( R_1 \cup R_2 \) is reflexive
• (3) Both \( R_1 \cap R_2 \) and \( R_1 \cup R_2 \) are irreflexive
• (4) Both \( R_1 \cap R_2 \) and \( R_1 \cup R_2 \) are reflexive

There are three cards in a box. Both sides of one card are black, both sides of one card are red, and the third card has one black side and one red side. We pick a card at random and observe only one side. What is the probability that the opposite side is the same colour as the one side we observed?

• (1) \( \frac{3}{4} \)
• (2) \( \frac{2}{3} \)
• (3) \( \frac{1}{2} \)
• (4) \( \frac{1}{3} \)

An 8-bit number \( X \) is \( 00001100 \), then \( -X \) is in 1's complement is ____.

• (1) 12 in binary
• (2) 243 binary code in 8 bit
• (3) 11101100
• (4) 11110101

Assuming 5-bit addition is done on registers, the sum \( 12 + 7 \) leads to ____.

• (1) Overflow
• (2) -12
• (3) 19
• (4) -14

In a 4-bit ripple carry adder, the worst-case delay occurs when ____.

• (1) All input bits are 0
• (2) A carry propagates through all full adders
• (3) No carry is generated
• (4) The sum exceeds 15

The output of a JK flip-flop for inputs \( J=1, K=1 \) and clock transition from 1 to 0 is ____.

• (1) No change
• (2) Reset
• (3) Toggle
• (4) Set

The IEEE 754 single-precision floating-point representation of 0.375 is ____.

• (1) \( 0 0111100 10000000000000000000000 \)
• (2) \( 0 0111101 10000000000000000000000 \)
• (3) \( 0 0111101 11000000000000000000000 \)
• (4) \( 0 0111100 11000000000000000000000 \)

In a hardwired control unit, the sequence of control signals is generated by ____.

• (1) Microprogrammed ROM
• (2) State machine/circuitry
• (3) Operating system
• (4) Interrupt handler

In DMA mode, the CPU is bypassed for data transfer between ____.

• (1) CPU and I/O devices
• (2) Registers and ALU
• (3) Memory and I/O devices
• (4) Cache and secondary storage

A 4-way set-associative cache with 256 blocks divides memory addresses into ____.

• (1) 256 sets
• (2) 64 sets
• (3) 4 sets
• (4) 16 sets

\( AB \oplus (A + B) \) is equivalent to ____.

• (1) \( A^1 B + AB^1 \)
• (2) \( AB + A^1 B^1 \)
• (3) \( A^1 B + A^1 B^1 \)
• (4) \( A + B \)

Which of these flip-flops cannot be used to construct a serial shift register?

• (1) D flip-flop
• (2) SR flip-flop
• (3) T flip-flop
• (4) JK flip-flop

How many AND gates are required to realize \( Y = CD + EF + G \)?

• (1) 4
• (2) 5
• (3) 3
• (4) 2

The purpose of an interrupt vector table is to ____.

• (1) Store CPU registers during context switch
• (2) Map interrupt requests to service routine addresses
• (3) Hold page tables for virtual memory
• (4) Cache frequently used instructions

What is the output of the following code fragment?


\texttt{int x = 24;

\texttt{printf("%d\n", x); printf("%3d %3d\n", x, x);

• (1) 24 24
  10
• (2) 24 24
  9
• (3) 24 24
  8
• (4) error

How many times “Hi” message will be displayed when we execute the following for loop?


\texttt{int i;

\texttt{for(i=0;i%2==0;i++)

\texttt{printf("Hi \textbackslash n");

• (1) 3
• (2) 2
• (3) 1
• (4) 0

If one wants to add and delete elements quickly without reshuffling the rest, then which data structure suits the best?

• (1) Linked list
• (2) Tree
• (3) B-Tree
• (4) Array

The height of a binary tree with 31 nodes (assuming no single-child nodes) is ____.

• (1) 4
• (2) 5
• (3) 6
• (4) 7

In a max-heap, the largest element is always located at the ____.

• (1) Leftmost leaf
• (2) Rightmost leaf
• (3) Root node
• (4) Middle of the heap

The recurrence T(n) = 2T(n/2) + n has a solution of ____.

• (1) O(n)
• (2) O(nlogn)
• (3) O(n²)
• (4) O(logn)

What is the time complexity to insert an element at the beginning of a dynamic array?

• (1) O(1)
• (2) O(n)
• (3) O(nlogn)
• (4) O(logn)

The inorder traversal of a BST gives elements in ____.

• (1) Level order
• (2) Ascending order
• (3) Descending order
• (4) Random order

A threaded binary tree is a binary tree in which every node that does not have right child has a thread to its ____.

• (1) Pre-order successor
• (2) In-order successor
• (3) In-order predecessor
• (4) Post-order successor

Which notation represents the tightest upper bound of an algorithm’s running time?

• (1) O(n)
• (2) \(\Omega(n)\)
• (3) \(\Theta(n)\)
• (4) \(\omega(n)\)

The minimum possible time complexity to sort \(n\) integers in the range [1, \(n^2\)] is ____ .

• (1) O(n)
• (2) O(n\log n)
• (3) O(n\(^2\))
• (4) O(\(\log n\))

The greedy approach is optimal for ____ .

• (1) 0/1 Knapsack
• (2) Fractional Knapsack
• (3) Longest Increasing Subsequence
• (4) Matrix Chain Multiplication

Best case complexity of insertion sorting is ____ .

• (1) O(n)
• (2) O(n\log n)
• (3) O(n\(^2\))
• (4) O(\(\log n\))

A problem is NP-complete if it is ____ .

• (1) Solvable in polynomial time
• (2) NP-hard and is NP
• (3) Reducible to P
• (4) Non-deterministic but decidable

The time complexity to compute the 15\(^th\) Fibonacci number using dynamic programming is ____ .

• (1) O(1)
• (2) O(n)
• (3) O(n\log n)
• (4) O(\(\log n\))

One way to build a heap is to start at the end of the array (the leaves) and push each new value up to the root. Its time complexity is ____ .

• (1) O(n)
• (2) O(\log n)
• (3) O(n \log n)
• (4) O(n\(^2\) \log n)

If the recursive call keeps calculating the same things over and over again, we can use ____ which stores partial results already calculated and to be used again.

• (1) Divide and conquer algorithm
• (2) Recursive
• (3) Dynamic Programming
• (4) Greedy method

The ____ process updates the costs of all the vertices \(V\), connected to a vertex \(U\), if we could improve the best estimate of the shortest path to \(V\) by including \((U,V)\) in the path to \(V\).

• (1) Relaxation
• (2) Improvement
• (3) Shortening
• (4) Costing

The minimum number of states in a DFA accepting \( L = \{ w | w ends with 01 \} \) over \( \Sigma = \{0, 1\} \) is ____ .

• (1) 2
• (2) 3
• (3) 4
• (4) 5

The language \( L = \{M | M halts on all inputs\} \) is ____ .

• (1) Decidable
• (2) Undecidable but recognizable
• (3) Not recognizable
• (4) Regular

Inherited attributes in SDTs are used for ____ .

• (1) Passing information up the parse tree
• (2) Passing information down the parse tree
• (3) Storing symbol table entries
• (4) Generating target code

The output of a syntax-directed translation scheme is ____ .

• (1) Abstract Syntax Tree
• (2) Three Address Code
• (3) Postfix Notation
• (4) Depends on the SDT rules

Subset Construction method refers to ____ .

• (1) Conversion of NFA to DFA
• (2) DFA minimization
• (3) Eliminating Null references
• (4) DFA to NFA

The maximum number of transitions which can be performed over a state in a DFA? \( \Sigma = \{a, b, c\} \)

• (1) 8
• (2) 2
• (3) 3
• (4) 7

Which of the following is a regular language?

• (1) A string whose length is a sequence of prime numbers
• (2) A string with substring ww\(^f\)
• (3) A palindrome
• (4) A string with even number of zero’s

The minimum number of nodes in a DFA that recognizes strings over \( \{a, b\} \) with length mod 3 = 0 are ____ .

• (1) 4
• (2) 2
• (3) 3
• (4) 1

If the production rules are given as:
\( S \to XY | W \)
\( X \to aXb | \epsilon \)
\( Y \to cY | \epsilon \)
\( W \to aWc | bZ | \epsilon \)
\( Z \to bZ | \epsilon \)

Then the language generated by these rules is ____ .

• (1) \( \{ a^i b^i \mid i \geq 0 \} \)
• (2) \( \{ a^i b^i \mid i \geq 1 \} \)
• (3) \( \{ a^i b^j c^k \mid i \geq 0, j \geq 0, k \geq 0 \} \)
• (4) \( \{ a^i b^j c^k \mid i = j or i = k \} \)

Let \( P \) be a regular language and \( Q \) be a context free language such that \( Q \) is a subset of \( P \). Then which of the following is ALWAYS regular?

• (1) \( P \cap Q \)
• (2) \( P - Q \)
• (3) \( \Sigma^* - P \)
• (4) \( \Sigma^* - Q \)

Which of the following is FALSE?

• (1) Every NFA can be converted to an equivalent PDA
• (2) Complement of every context free language is recursive
• (3) There is a unique minimal DFA for every regular language
• (4) Every nondeterministic PDA can be converted to an equivalent deterministic PDA

Which of the following is not a three-address code statement?

• (1) \( x = y + z \)
• (2) if \( x \) goto L
• (3) \( x = *y \)
• (4) \( x = y ** z \)

Which of the following is not shared among threads in the same process?

• (1) Heap memory
• (2) Stack
• (3) File Descriptors
• (4) Code section

The primary advantage of user-level threads over kernel-level threads is ____ .

• (1) Lower context-switch overhead
• (2) Better parallelism on multicore CPUs
• (3) No need for synchronization
• (4) Higher priority scheduling

A program uses environment variables to ____ .

• (1) Store data between login sessions
• (2) Pass configuration settings to other programs
• (3) Store data persistently
• (4) Pass data to the operating system

Which is not a CPU scheduling criterion?

• (1) CPU utilization
• (2) Reliability
• (3) Response time
• (4) Waiting time

Among priority inversion between two processes, one with high priority and other with low priority that share a critical section will cause which of the following problem?

• (1) High priority process executes before low priority process and finishes faster than it should.
• (2) Low priority process executes before high priority process and finishes faster than it should.
• (3) High priority process waits for low priority process to finish, but the low priority process never gets scheduled.
• (4) Low priority process changes priority temporarily to the priority of the high priority process.

A currently running process can be put on a ready queue or one of the I/O queues by each of the following except ____ .

• (1) The process issued an I/O request
• (2) The process did an illegal memory access
• (3) There was an interrupt
• (4) The process issued a system call

Which of the following component of program state is shared across threads in a multithreaded process?

• (1) Registers
• (2) Auto variables
• (3) Heap memory
• (4) Stack memory

Which of the following frees the CPU from having to deal with transfer of memory to or from I/O device?

• (1) Interrupts
• (2) Direct Memory Access
• (3) Buffer cache
• (4) Device Driver

In FCFS, I/O bound processes may have to wait long in the ready queue waiting for a CPU bound job to finish. This is known as ____ .

• (1) Aging
• (2) Convoy effect
• (3) Priority inversion
• (4) Belady's anomaly

In general, there will be ____ inodes than directories in Unix File system.

• (1) Zero
• (2) Less
• (3) Same
• (4) More

To ensure that the ____ condition never occurs in the system, we must guarantee that, whenever a process requests a resource, it does not have any other resource.

• (1) Mutual exclusion
• (2) No-preemption
• (3) Circular wait
• (4) Hold and wait

A ____ architecture assigns only a few essential functions to the kernel, including address spaces, Interprocess communication (IPC), and basic scheduling.

• (1) Monolithic kernel
• (2) Micro kernel
• (3) Macro kernel
• (4) Mini kernel

Among the four criteria for synchronization mechanism, which of the two criteria are mandatory?

• (1) Mutual exclusion and Progress
• (2) Progress and Architectural neutral
• (3) Bounded wait and mutual exclusion
• (4) Bounded wait and progress

Which SQL operation is not part of the ACID properties?

• (1) COMMIT
• (2) ROLLBACK
• (3) CREATE INDEX
• (4) SAVEPOINT

A B+ tree is preferred over a B-tree for databases because ____ .

• (1) It supports range queries efficiently
• (2) It has a smaller node size
• (3) It allows faster insertion/deletion
• (4) It uses less disk space

A relation \(R(A,B,C,D)\) with functional dependencies \{A→B, B→C\ is in ____ .

• (1) 1NF but not 2NF
• (2) 2NF but not 3NF
• (3) 3NF but not BCNF
• (4) BCNF

In two-phase locking (2PL), a transaction must be ____ .

• (1) Release all locks before acquiring new ones
• (2) Acquire all locks before releasing any
• (3) Use only shared locks
• (4) Avoid deadlocks by timeouts

The isolation level that prevents dirty reads but allows non-repeatable reads is ____ .

• (1) read uncommitted
• (2) read committed
• (3) repeatable read
• (4) serializable

The maximum number of keys in a B-tree of order 5 with height 3 is ____ .

• (1) 31
• (2) 156
• (3) 624
• (4) 3125

In ____ relation, each tuple has relation R within it.

• (1) primary
• (2) prime
• (3) nested
• (4) atomic

The rule which states that addition of same attributes to the right side and left side will result in other valid dependency is classified as ____ .

• (1) Augmentation rule
• (2) Inference rule
• (3) Referential rule
• (4) Reflexive rule

The separation of the data definition from program is known as ____ .

• (1) Data dictionary
• (2) Data independence
• (3) Data integrity
• (4) Referential integrity

Which is the candidate key for the relation R(ABCDE) with functional dependencies F={A→BC, B→D, CD→E, E→A}?

• (1) A
• (2) CD
• (3) B
• (4) E

Natural Join can also be termed as ____ .

• (1) combination of Union and Cartesian Product
• (2) combination of Selection and Cartesian Product
• (3) combination of Projection and Cartesian Product
• (4) combination of Projection and Union

If A \(\to\) B has trivial functional dependency, then _____.

• (1) B is a subset of A
• (2) A is a subset of B
• (3) A is a subset of A'
• (4) B is a subset of B'

Which of the following commands is used to delete all rows and free up space from a table?

• (1) Drop
• (2) Delete
• (3) Truncate
• (4) Alter

____ uses Quantifiers that can be either Existential (*) or Universal (V).

• (1) Domain Relational Calculus
• (2) Tuple Relational Calculus
• (3) Distributed Relational Calculus
• (4) NoSQL

The database design that consists of multiple tables that are linked together through matching data stored in each table is called a _____.

• (1) Relational database
• (2) Network database
• (3) Object oriented database
• (4) Hierarchical database

The incremental model of software development is _____.

• (1) a reasonable approach when requirements are well defined
• (2) a good approach when a working core product is required quickly
• (3) the best approach to use for projects with large development teams
• (4) a revolutionary model that is not used for commercial products

The cyclomatic complexity metric provides the designer with information regarding the number of _____.

• (1) cycles in the program
• (2) errors in the program
• (3) independent logic paths in the program
• (4) statements in the program

In the spiral model of software development, the primary determinant in selecting activities in each iteration is _____.

• (1) iteration size
• (2) cost
• (3) risk
• (4) adopted process such as rational unified process or extreme programming

The optimizer that explores the space of all query-evaluation plans is called _____.

• (1) cost-based
• (2) plan-based
• (3) estimate-based
• (4) count-based

The term that optimizes subexpressions shared by different expressions in a program is called _____.

• (1) multiple subexpression elimination
• (2) common subexpression elimination
• (3) parametric subexpression elimination
• (4) shared subexpression elimination

Frequency of failure and network recovery time after a failure are measures of the _____ of a network.

• (1) performance
• (2) reliability
• (3) security
• (4) feasibility

A Gantt chart is least useful for tracking _____.

• (1) task dependencies
• (2) resource allocation
• (3) critical path
• (4) code complexity

Which phase of the SDLC typically consumes the most resources?

• (1) Requirements gathering
• (2) Testing
• (3) Maintenance
• (4) Coding

Regression testing is performed to ensure that _____.

• (1) new code doesn't break existing functionality
• (2) all paths are covered
• (3) users accept the system
• (4) compliance with laws

The COCOMO model estimates _____.

• (1) project risk
• (2) software cost
• (3) team productivity
• (4) user satisfaction

At which OSI layer does MAC address filtering occur?

• (1) Network
• (2) Data Link
• (3) Transport
• (4) Physical

Token Ring networks avoid collisions by _____.

• (1) CSMA/CD
• (2) Token passing
• (3) Exponential backoff
• (4) Priority queuing

Which routing algorithm guarantees shortest paths even with negative edge weights?

• (1) Dijkstra's
• (2) Bellman-Ford
• (3) Link-State
• (4) OSPF

A TCP header includes all except _____.

• (1) Sequence number
• (2) Checksum
• (3) TTL
• (4) Window size

The three-way handshake in TCP ensures _____.

• (1) Encryption setup
• (2) Synchronized sequence numbers
• (3) QoS negotiation
• (4) Multicast membership

An IPv4 datagram with header length=5 and total length=400 bytes carries _____.

• (1) 380 bytes payload
• (2) 400 bytes payload
• (3) 20 bytes header
• (4) 320 bytes payload

Which protocol uses port 53 by default?

• (1) HTTP
• (2) FTP
• (3) DNS
• (4) SMTP

A switch differs from a hub because, it _____.

• (1) operates at Layer 1
• (2) broadcasts all frames
• (3) uses MAC tables for forwarding
• (4) only supports half-duplex

Digital signatures provide _____.

• (1) confidentiality
• (2) non-repudiation
• (3) key exchange
• (4) firewall bypass

In asynchronous transmission, the gap time between bytes is _____.

• (1) fixed
• (2) variable
• (3) a function of the data rate
• (4) zero

In Java, when we implement an interface method, it must be declared as _____.

• (1) private
• (2) protected
• (3) public
• (4) friend

Which of the following control fields in TCP header is used to specify whether the sender has no more data to transport?

• (1) FIN
• (2) RST
• (3) SYN
• (4) PSH

In XML, DOCTYPE declaration specifies to include a reference to _____ file.

• (1) document type declaration
• (2) document type definition
• (3) document type language
• (4) document transfer definition

The CSS used inside HTML elements alongside style attribute is called _____.

• (1) external CSS
• (2) internal CSS
• (3) inline CSS
• (4) outline CSS

A web client sends a request to a web server. The web server transmits a program to that client and is executed at client which creates a web document. Such web documents are _____.

• (1) dynamic
• (2) static
• (3) active
• (4) passive

Cascading Style Sheets define style and appearance using _____.

• (1) functions with parameters and return values
• (2) rules with selectors, properties and their values
• (3) techniques with block and inline elements
• (4) heuristics with rules and maps

What is the correct HTML for making a hyperlink?

• (1) \texttt{abc}
• (2) \texttt{abc}
• (3) \texttt{}
• (4) \texttt{url="http://abc.com">}

What is the correct HTML for adding a background color?

• (1) \texttt{
• (2) \texttt{
• (3) \texttt{yellow}
• (4) \texttt{

Which is the correct syntax to link XML file with CSS?

• (1) \texttt{}
• (2) \texttt{}
• (3) \texttt{}
• (4) \texttt{}

A Session variable is created _____.

• (1) when the application is first placed on a web server.
• (2) when the web server is first started.
• (3) when the first client requests a URL resource.
• (4) every time a new client interacts with the web application.

Let A, B be two events and \(\overline{A}\) be the complement of A. If \(P(A) = 0.7, P(B) = 0.7 and P(B|A) = 0.5, then P(A \cup B) = \_\_\_\).

• (1) 0.65
• (2) 0.85
• (3) 0.75
• (4) 0.50

Let a random variable X have a binomial distribution with mean 8 and standard deviation 2. If \(P(X < 2) = \frac{k}{216}, then the value of k is \_\_\_\).

• (1) 17
• (2) 16
• (3) 136
• (4) 137

Let \(A = \{1, 2, 3\}\). Which of the following is the number of distinct relations on A?

• (1) 256
• (2) 158
• (3) 512
• (4) 1024

In any Lattice \(L\), \(((a \wedge b) \vee a) \wedge b = \_\_\_\).

• (1) \(a \vee b\)
• (2) \(a \wedge b\)
• (3) \((a \wedge b) \vee a\)
• (4) \(((a \vee b) \wedge a) \vee b\)

If the system of linear equations \(x + 2y + z = 5, 2x + \lambda y + 4z = 12, 4x + 8y + 12z = 2\mu\)
have infinite number of solutions, then the values of \(\lambda\) and \(\mu\) are ___?

• (1) \(\lambda = 4, \mu = 28\)
• (2) \(\lambda = 4, \mu = 14\)
• (3) \(\lambda = 8, \mu = 14\)
• (4) \(\lambda = 8, \mu = 28\)

If the product and sum of eigenvalues of a 2 \(\times\) 2 matrix \(\begin{pmatrix} 3 & x
x & y \end{pmatrix}\)
are -3 and 5, respectively, then \(x + y = \_\_\_\)

• (1) -5
• (2) -6 \(\pm\) i\(\sqrt{3}\)
• (3) -2 \(\pm\) i3
• (4) -1

Given that the value of the integral \(\int_1^9 (x^2 - 2) dx\)
calculated using the Simpson's 1/3 rule with four uniform subintervals over the interval [1,9] is given by \(f(1) + \alpha^2 + \frac{8}{3}\), then the possible value of \(\alpha\) is ___

• (1) \(\alpha = 15\)
• (2) \(\alpha = 14\)
• (3) \(\alpha = 13\)
• (4) \(\alpha = 12\)

Let \(x \to 1\) \(\frac{x^x - x}{x - 1 - \log x}\) = ____

• (1) 0
• (2) 1
• (3) 2
• (4) 1/2

Which of the following integrals is un-bounded?

• (1) \( \int_0^{\frac{\pi}{4}} \tan(x) \, dx \)
• (2) \( \int_0^{\infty} e^{-x} \, dx \)
• (3) \( \int_0^a \frac{1}{a - x} \, dx \)
• (4) \( \int_0^{\infty} x e^x \, dx \)

Let \( f(x) = x^3 - \frac{9}{2}x^2 + 6x - 2 \) be a function defined on the closed interval [0, 3]. Then, the global maximum value of \( f(x) \) is ____

• (1) 4.5
• (2) 0.5
• (3) 2.5
• (4) 3.0