Consider the following three functions.

f₁ = 10ⁿ, f₂ = n^logn, f₃ = n^√n

Which one of the following options arranges the functions in the increasing order of asymptotic growth rate?

Consider the following array.

23

32

45

69

72

73

89

97

Which algorithm out of the following options uses the least number of comparisons (among the array elements) to sort above array in ascending order?

A binary search tree T contains n distinct elements. What is the time complexity of picking an element in T that is smaller than the maximum element in T?

Consider the following recurrence relation.

$$T(n) = \left\{ {\begin{array}{*{20}{c}} {T(n/2) + T(2n/5) + 7n \ \ \ if\ n > 0}\\ {1\ \ \ \ \ \ \ if\ n = 0} \end{array}} \right.$$

Which one of the following option is correct?

Define R_n to be the maximum amount earned by cutting a rod of length n meters into one or more pieces of integer length and selling them. For i > 0, let p[i] denotes the selling price of a rod whose length is i meters. Consider the array of prices:

p[1] = 1, p[2] = 5, p[3] = 8, p[4] = 9, p[5] = 10, p[6] = 17, p[7] = 18

Which of the following statements is/are correct about R₇?

Consider the following statements.

S₁ : Every SLR(1) grammar is unambiguous but there are certain unambiguous grammars that are not SLR(1).

S₂ : For any context-free grammar, there is a parser that takes at most O(n³) time to parse a string of length n.

Which one of the following option is correct?

Consider the following context-free grammar where the set of terminals is {a, b, c, d, f}.

S → d a T | R f

T → a S | b a T | ϵ

R → c a T R | ϵ

The following is a partially-filled LL(1) parsing table.

Which one of the following choices represents the correct combination for the numbered cells in the parsing table ("blank" denotes that the corresponding cell is empty)?

Consider the following grammar (that admits a series of declarations, followed by expressions) and the associated syntax directed translation (SDT) actions, given as pseudo-code:

P → D* E*

D → int ID {record that ID.lexeme is of type int}

D → bool ID { record that ID.lexeme is of type bool}

E → E₁ + E₂ {check that E₁.type = E₂.type = int; set E.type := int}

E → !E₁ {check that E₁.type = bool; set E.type := bool}

E → ID {set E.type := int}

With respect to the above grammar; which one of the following choices is correct?

Consider the following C code segment:

a = b + c;

e = a + 1;

d = b + c;

f = d + 1;

g = e + f;

In a compiler, this code segment is represented internally as a directed acyclic graph (DAG). The number of nodes of nodes in the DAG is ______

Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check bits is d₈d₇d₆d₅c₈d₄d₃d₂c₄d₁c₂c₁, where the data bits and the check bits are given in the following tables:

Data bits
d8	d7	d6	d5	d4	d3	d2	d1
1	1	0	x	0	1	0	1

 

c8	c4	c2	c1
Y	0	1	0

Which one of the following choices gives the correct values of x and y?

Consider two hosts P and Q connected through a router R. The maximum transfer unit (MTU) value of the link between P and R is 1500 bytes, and between R and Q is 820 bytes.

A TCP segment of size 1400 bytes was transferred from P to Q through R, with IP identification value as 0 × 1234. Assume that the IP header size is 20 bytes. Further, the packet is allowed to be fragmented i. e, Don't Fragment (DF) flag in the IP header is not set by P.

Which of the following statements is/are correct?

Consider the sliding window flow-control protocol operating between a sender and a receiver over a full-duplex error-free link. Assume the following:

1. The time taken for processing the data frame by the receiver is negligible.

2. The time taken for processing the acknowledgement frame by the sender is negligible.

3. The sender has infinite number of frames available for transmission.

4. The size of the data frame is 2,000 bits and the size of the acknowledgment frame is 10 bits.

5. The link data rate in each direction is 1 Mbps (= 10⁶ bits per second).

6. One way propagation delay of the link is 100 milliseconds.

The minimum value of the sender's window size in terms of the number of frames, (rounded to the nearest integer) needed to achieve a link utilization of 50% is ______

A TCP server application is programmed to listen on port number P on host S. A TCP client connected to the TCP server over the network.

Consider that while the TCP connection was active, the server machine S crashed are rebooted. Assume that the client does not use the TCP keepalive timer.

Which of the following behaviours is/are possible?

Consider the following two statements.

S₁ : Destination MAC address of an ARP reply is a broadcast address.

S₂ : Destination MAC address of an ARP request is a broadcast address.

Which one of the following choices is correct?

A five-stage pipeline has stage delays of 150, 120, 150, 160 and 140 nanoseconds. The registers that are used between the pipeline stages have a delay of 5 nanoseconds each.

The total time to execute 100 independent instructions on this pipeline, assuming there are no pipeline stalls, is ______ nanoseconds.

Consider the following instruction sequence where register R1, R2 and R3 are general purpose and MEMORY[X] denotes the content at the memory location X.

Instruction	Semantics	Instruction Size (bytes)
MOV R1, (5000)	R1 ← MEMORY[5000]	4
MOV R2, (R3)	R2 ← MEMORY[R3]	4
ADD R2, R1	R2 ← R1 + R2	2
MOV (R3), R2	MEMORY[R3] ← R2	4
INC R3	R3 ← R3 + 1	2
DEC R1	R1 ← R1 – 1	2
BNZ 1004	Branch if not zero to the given absolute address	2
HALT	Stop	1

 

Assume that the content of the memory location 5000 is 10, and the content of the register R3 is 3000. The content of each of the memory locations from 3000 to 3010 is 50. The instruction sequence starts from the memory location 1000. All the numbers are in decimal format. Assume that the memory is byte addressable.

After the execution of the program, the content of memory location 3010 is ______

Consider a computer system with a byte-addressable primary memory of size 2³² bytes. Assume the computer system has a direct-mapped cache of size 32 KB (1 KB = 2¹⁰ bytes), and each cache block is of size 64 bytes.

The size of the tag field is ______ bits.

Consider the following undirected graph with edge weights as shown:

The number of minimum-weight spanning trees of the graph is ______

Consider the following sequence of operations on an empty stack.

push(54); push(52); pop(); push(55); push(62); s = pop();

Consider the following sequence of operations on an empty queue.

enqueue(21); enqueue(24); dequeue(); enqueue(28); enqueue(32); q = dequeue();

The value of s + q is ______

Consider a dynamic hashing approach for 4-bit integer keys:

1. There is a main hash table of size 4.

2. The 2 least significant bits of a key is used to index into the main hash table.

3. Initially, the main hash table entries are empty.

4. Thereafter, when more keys are hashed into it, to resolve collisions, the set of all keys corresponding to a main hash table entry is organized as a binary tree that grows on demand.

5. First, the 3^rd least significant bit is used to divide the keys into left and right subtrees.

6. to resolve more collisions, each node of the binary tree is further sub-divided into left and right subtrees based on 4^th least significant bit.

7. A split is done only if it is needed, i. e. only when there is a collision.

Consider the following state of the hash table.

Which of the following sequence of key insertions can cause the above state of the hash table (assume the keys are in decimal notation)?

Let P be an array containing n integers. Let t be the lowest upper bound on the number of comparisons of the array elements, required to find the minimum and maximum values in an arbitrary of n elements. Which one of the following choices is correct?

Consider the following statements.

S₁ : The sequence of procedure calls corresponds to a preorder traversal of the activation tree.

S₂ : The sequence of procedure returns corresponds to a postorder traversal of the activation tree.

Which one of the following options is correct?

Suppose a database system crashes again while recovering from a previous crash. Assume checkpointing is not done by the database either during the transactions or during recovery.

Which of the following statements is/are correct?

Consider a linear list based implementation in a file system. Each directory is a list of nodes, where each node contains the file name along with the file metadata, such as the list of pointers to the data blocks. Consider a given directory foo.

Which of the following operations will necessarily require a full scan of foo for successful completion?

A relation r(A, B) in a relational database has 1200 tuples. The attribute A has integer values ranging from 6 to 20, and the attribute B has integer values ranging from 1 to 20. Assume that the attributes A and B are independently distributed. The estimated number of tuples in the output of σ_{(A>10)∨(B=18)}(r) is ______

The following relation records the age of 500 employees of a company, where empNo (Indicating the employee number) is the key:

empAge(empNo, age)

Consider the following relational algebra expression:

π_empNo(empAge ⋈ _(age>age1) ρ_{empNo 1, age1}(empAge))

What does the above expression generate?

Consider the relation R(P, Q, S, T, X, Y, Z, W) with the following functional dependencies.

PQ → X; P → YX; Q → Y; Y → ZW

Consider the decomposition of the relation R into the constituent relations according to the following two decomposition schemes.

D₁ : R = [(P, Q, S, T); (P, T, X); (Q, Y); (Y, Z, W)]

D₂ : R = [(P, Q, S); (T, X); (Q, Y); (Y, Z, W)]

Which one of the following options is correct?

Let r_i(z) and w_i(z) denote read and write operations respectively on a data item z by a transaction T_i. Consider the following two schedules.

S₁ : r₁(x) r₁(y) r₂(x) r₂(y) w₂(y) w₁(x)

S₂ : r1(x) r₂(x) r2(y) w2(y) r₁(y) w1(x)

Which one of the following options is correct?

Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?

Consider the following Boolean expression.

$$F = (X + Y + Z)(\overline X + Y)(\overline Y + Z)$$

Which of the following Boolean expressions is/are equivalent to $$\overline F$$ (complement of F)?

Consider a 3-bit counter, designed using T flip-flop, as shown below:

Assuming the initial state of the counter given by PQR as 000, what are the next three states?

Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.

S: 1 E:   10000001    F : 11110000000000000000000

Here S, E and F denote the sign, exponent and fraction components of the floating point representation.

The decimal value corresponding to the above representation (rounded to 2 decimal places) is ______

Let p and q be two propositions. Consider the following two formulae in propositional logic.

S₁ : (¬p ∧ (p ∨ q)) → q

S₂ : q → (¬p ∧ (p ∨ q))

Which one of the following choices is correct?

There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that:

- The fastest computer gets the toughest job and the slowest computer gets the easiest job.

- Every computer gets at least one job.

The number of ways in which this can be done is ______

Consider the two statements.

S₁ : There exist random variables X and Y such that

(E[X - E(X)) (Y - E(Y))])² > Var[X] Var[Y]

S₂ : For all random variables X and Y,

Cov[X, Y] = E [|X - E[X]| |Y - E[Y]|]

Which one of the following choices is correct?

An articulation point in a connected graph is a vertex such that removing the vertex and its incident edges disconnects the graph into two or more connected components.

Let T be a DFS tree obtained by doing DFS in a connected undirected graph G. Which of the following option is/are correct?

A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?

The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2. For a randomly picked component of this type, the probability that, its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is ______.

Let G be a group order 6, and H be a subgroup of G such that 1 < |H| < 6. Which one of the following options is correct?

A sender (S) transmits a signal, which can be one of the two kinds: H and L with probabilities 0.1 and 0.9 respectively, to a receiver (R).

In the graph below, the weight of edge (u, v) is the probability of receiving v when u is transmitted, where u, v ∈ {H, L}. For example, the probability that the received signal is L given the transmitted signal was H, is 0.7.

If the received signal is H, the probability that the transmitted signal was H (rounded to 2 decimal places) is ______

Consider the following expression

$$\mathop {\lim }\limits_{x \to -3} \frac{{\sqrt {2x + 22} - 4}}{{x + 3}}$$

The value of the above expression (rounded to 2 decimal places) is ______

Let G = (V, E) be an undirected unweighted connected graph. The diameter of G is defined as:

diam(G) = $$\displaystyle\max_{u, x\in V}$$ {the length of shortest path between u and v}

Let M be the adjacency matrix of G.

Define graph G₂ on the same set of vertices with adjacency matrix N, where

$$N_{ij} =\left\{ {\begin{array}{*{20}{c}} {1 \ \ \text{if} \ \ {M_{ij}} > 0 \ \ \text{or} \ \ P_{ij} > 0, \ \text{where} \ \ P = {M^2}}\\ {0, \ \ \ \ \ \text{otherwise}} \end{array}} \right.$$

Which one of the following statements is true?

Consider the following matrix.

$$\left( {\begin{array}{*{20}{c}} 0&1&1&1\\ 1&0&1&1\\ 1&1&0&1\\ 1&1&1&0 \end{array}} \right)$$

The largest eigenvalue of the above matrix is ______

In an undirected connected planar graph G, there are eight vertices and five faces. The number of edges in G is ______

In the context operating systems, which of the following statements is/are correct with respect to paging?

Three processes arrive at time zero with CPU bursts of 16, 20, and 10 milliseconds. If the scheduler has prior knowledge about the length of the CPU bursts, the minimum achievable average waiting for these three processes in a non-preemptive scheduler (rounded to the nearest integer) is ______ milliseconds.

Which of the following standard C library functions will always invoke a system call when executed from a single-threaded process in a UNIX/Linux operating system?

Consider the following pseudocode, where S is a semaphore intialized to 5 in line#2 an counter is a shared variable intialized to 0 in line#1. Assume that the increment operation in line#7 is not atomic.

1. int counter = 0;

2. Semaphore S = init(5);

3. void parop(void)

4. {

5. wait (S);

6. wait (S);

7. counter++;

8. signal (S);

9. signal (S);

10. }

If five threads execute the function parop concurrently, which of the following program behavior (s) is/are possible?

Consider the following ANSI C program.

#include <stdio.h>

int main( ) {

int i, j, count;

count = 0;

i = 0;

for (j = -3; j <= 3; j++)  {

if ((j >= 0) && (i++))

count = count + j;

}

count = count + i;

printf("%d", count);

return 0;

}

Which one of the following options is correct?

Consider the following ANSI C function:

int SimpleFunction (int y[], int n, int x)

{

int total = y[0], loopIndex;

for (loopIndex = 1; loopIndex <= n - 1; loopIndex++)

total = x * total + y[loopIndex];

return total :

}

Let Z be an array of 10 elements with Z[i] = 1, for all i such that 0 ≤ i ≤ 9. The value returned by SimpleFunction (Z, 10, 2) is ______

Suppose that L₁ is a regular and L₂ is a context-free language, Which one of the following languages is NOT necessarily context-free?

For a Turing machine M, {M} denotes an encoding of M. Consider the following two languages.

L₁ = {(M) | M takes more than 2021 steps on all inputs}

L₂ = {(M) | M takes more than 2021 steps on some input}

Which one of the following options is correct?

In a pushdown automaton P = (Q, ∑, Γ, δ, q₀, F), a transition of the form,

where p, q ∈ Q, a ∈ Σ ∪ {ϵ}, and X, Y ∈ Γ ∪ {ϵ}, represents

(q, Y) ∈ δ(p, a, X).

Consider the following pushdown automaton over the input alphabet ∑ = {a, b} and stack alphabet Γ = {#, A}.

The number of strings of length 100 accepted by the above pushdown automaton is ______

Consider the following language.

L = { w ∈ {0, 1}* | w ends with the substring 011}

Which one of the following deterministic finite automata accepts L?

Let $$\left\langle M \right\rangle $$ denote an encoding of an automation M. Suppose that ∑ = {0, 1}. Which of the following languages is/are NOT recursive?

Given below are two statements I and II and two conclusions I and II :

Statement :

I. All bacteria are microorganisms.

II. All pathogens are microorganisms.

Conclusions :

I. Some pathogens are bacteria.

II. All pathogens are not bacteria

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.

The probability that at least two chocolates are identical is ________.

A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the filial folded state as shown and unfolded in the reverse order of folding, will look like _________.

We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm $$\times$$ 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is _______.

Consider the following sentences :

(i) Everybody in the class is prepared for the exam.

(ii) Babu invited Danish to his home because he enjoys playing chess,

Which of the following is the CORRECT observation about the above two sentences?

Some people suggest anti-obesity measures (AOM) such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality.

Which one of the following statements summarizes the passage?

________ is to surgery as writer is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

A polygon is convex if, for every pair of points. P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon.

Which one of the following is NOT a convex polygon?

Items	Cost	Profit%	Marked price
P	5400	-	5860
Q	-	25	10000

Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3 : 4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost

(Profit% = $${{Selling\,price - Cost} \over {Cost}} \times 100$$).

The discount on item Q, as a percentage of its marked price, is ________.

The ratio of boys to girls in a class is 7 to 3.

Among the options below, an acceptable value for the total number of students in the class is :