GATE CSE 2024 Set 2 | GATE CSE Year Wise Previous Years Questions (2024)

1. Let $T(n)$ be the recurrence relation defined as follows:$T(0) = 1$$T(1) = 2$, and$T(n) = 5T(n - 1) - 6T(n - 2)$ for $n 2. Let $A$ be an array containing integer values. The distance of $A$ is defined as the minimum number of elements in $A$ t 3. Let $G$ be an undirected connected graph in which every edge has a positive integer weight. Suppose that every spanning 4. The number of distinct minimum-weight spanning trees of the following graph is ________ 5. Consider the following two sets:Set XP. Lexical AnalyzerQ. Syntax AnalyzerR. Intermediate Code GeneratorS. Code Optimize 6. Which of the following statements is/are FALSE? 7. Consider the following context-free grammar where the start symbol is S and the set of terminals is {a,b,c,d}.$ S \right 8. Consider the following expression: $x[i] = (p + r) * -s[i] + \frac{u}{w}$. The following sequence shows the list of trip 9. Consider the following augmented grammar, which is to be parsed with a SLR parser. The set of terminals is $\{ a, b, c, 10. Node X has a TCP connection open to node Y. The packets from X to Y go through an intermediate IP router R. Ethernet swi 11. Which of the following statements about IPv4 fragmentation is/are TRUE? 12. Which of the following fields of an IP header is/are always modified by any router before it forwards the IP packet? 13. Which one of the following CIDR prefixes exactly represents the range of IP addresses 10.12.2.0 to 10.12.3.255? 14. Consider a TCP connection operating at a point of time with the congestion window of size 12 MSS (Maximum Segment Size), 15. Consider an Ethernet segment with a transmission speed of $10^8$ bits/sec and a maximum segment length of 500 meters. If 16. Consider a computer with a 4 MHz processor. Its DMA controller can transfer 8 bytes in 1 cycle from a device to main mem 17. An instruction format has the following structure:Instruction Number: Opcode destination reg, source reg-1, source reg-2 18. A processor with 16 general purpose registers uses a 32-bit instruction format. The instruction format consists of an op 19. A non-pipelined instruction execution unit operating at 2 GHz takes an average of 6 cycles to execute an instruction of 20. A processor uses a 32-bit instruction format and supports byte-addressable memory access. The ISA of the processor has 1 21. You are given a set $V$ of distinct integers. A binary search tree $T$ is created by inserting all elements of $V$ one b 22. Let S1 and S2 be two stacks. S1 has capacity of 4 elements. S2 has capacity of 2 elements. S1 already has 4 elements: 10 23. Once the DBMS informs the user that a transaction has been successfully completed, its effect should persist even if the 24. In the context of owner and weak entity sets in the ER (Entity-Relationship) data model, which one of the following stat 25. Which of the following file organizations is/are I/O efficient for the scan operation in DBMS? 26. Which of the following statements about the Two Phase Locking (2PL) protocol is/are TRUE? 27. The relation schema, Person($\underline{\text{pid}}$, $city$), describes the city of residence for every person uniquely 28. A functional dependency $F: X \to Y$ is termed as a useful functional dependency if and only if it satisfies all the fol 29. The format of a single-precision floating-point number as per the IEEE 754 standard is:table { width: 100%; border-colla 30. For a Boolean variable x, which of the following statements is/are FALSE? 31. Which of the following is/are EQUAL to 224 in radix-5 (i.e., base-5) notation? 32. Consider 4-variable functions $f1, f2, f3, f4$ expressed in sum-of-minterms form as given below.$f1 = \sum(0,2,3,5,7,8,1 33. Let p and q be the following propositions:p: Fail grade can be given.q: Student scores more than 50% marks.Consider the 34. Let $f(x)$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ such that$f(x) = 1 - f(2 - x)$Which one of the fol 35. Let $A$ be the adjacency matrix of a simple undirected graph $G$. Suppose $A$ is its own inverse. Which one of the follo 36. When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers (i.e., 1, 2, 3, 4, 5, 37. Let $P$ be the partial order defined on the set {1,2,3,4} as follows: $P = \{(x, x) \mid x \in \{1,2,3,4\}\} \cup \{(1,2 38. Let $ x $ and $ y $ be random variables, not necessarily independent, that take real values in the interval $[0,1]$. Let 39. Let A be an n × n matrix over the set of all real numbers ℝ. Let B be a matrix obtained from A by swapping two rows. Whi 40. The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic 41. Let Zn be the group of integers {0, 1, 2, ..., n − 1} with addition modulo n as the group operation. The number of eleme 42. Which of the following tasks is/are the responsibility/responsibilities of the memory management unit (MMU) in a system 43. Consider a process P running on a CPU. Which one or more of the following events will always trigger a context switch by 44. Consider a single processor system with four processes A, B, C, and D, represented as given below, where for each proces 45. Consider a multi-threaded program with two threads T1 and T2. The threads share two semaphores: s1 (initialized to 1) an 46. Consider a disk with the following specifications: rotation speed of 6000 RPM, average seek time of 5 milliseconds, 500 47. Consider a 32-bit system with 4 KB page size and page table entries of size 4 bytes each. Assume 1 KB = $2^{10}$ bytes. 48. Consider the following C program. Assume parameters to a function are evaluated from right to left.#include <studio 49. Consider the following C function definition. int fX(char *a) { char *b = a; while(*b) b++; retu 50. What is the output of the following C program?#include <studio.h>int main() {  double a[2]={20.0, 25.0}, *p, * 51. Consider an array X that contains n positive integers. A subarray of X is defined to be a sequence of array locations wi 52. Which one of the following regular expressions is equivalent to the language accepted by the DFA given below? 53. Let M be the 5-state NFA with ε-transitions shown in the diagram below.Which one of the following regular expressions r 54. Consider a context-free grammar $G$ with the following 3 rules. $S \rightarrow aS, \ S \rightarrow aSbS, S \rightarrow 55. Let L1 be the language represented by the regular expression b*ab*(ab*ab*)* and L2 = { w ∈ (a + b)* | |w| ≤ 4 }, where |

1. If ‘→’ denotes increasing order of intensity, then the meaning of the words [walk → jog → sprint] is analogous to [bothe 2. Two wizards try to create a spell using all the four elements, water, air, fire, and earth. For this, they decide to mix 3. In an engineering college of 10,000 students, 1,500 like neither their core branches nor other branches. The number of s 4. For positive non-zero real variables $x$ and $y$, if $\ln \left( \frac{x + y}{2} \right) = \frac{1}{2} [ \ln (x) + \ln ( 5. In the sequence 6, 9, 14, $x$, 30, 41, a possible value of $x$ is 6. Sequence the following sentences in a coherent passage.P: This fortuitous geological event generated a colossal amount 7. A person sold two different items at the same price. He made 10% profit in one item, and 10% loss in the other item. In 8. The pie charts depict the shares of various power generation technologies in the total electricity generation of a count 9. A cube is to be cut into 8 pieces of equal size and shape. Here, each cut should be straight and it should not stop till 10. In the $4 \times 4$ array shown below, each cell of the first three rows has either a cross (X) or a number. The number

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