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GATE CS 2024 Set 1

All 65 solved GATE CS 2024 Set 1 questions in exam order. Open any question for the official answer and a step-by-step solution.

Questions

65

Total marks

100

By type: MCQ (29)MSQ (20)NAT (16)
Difficulty: Easy (24)Medium (37)Hard (4)

General Aptitude

  1. Q1If ‘→\rightarrow’ denotes increasing order of intensity, then the meaning of the words [dry →\rightarrow arid →\rightarrow parched] is analogous to [diet…MCQ · +1 marks
  2. Q2If two distinct non-zero real variables xx and yy are such that (x+y)(x + y) is proportional to (x−y)(x - y) then the value of xy\frac{x}{y}MCQ · +1 marks
  3. Q5For positive non-zero real variables pp and qq, if log⁡(p2+q2)=log⁡p+log⁡q+2log⁡3,\log (p^2 + q^2) = \log p + \log q + 2 \log 3 , then, the value of p4+q4p2q2\frac{p^4 + q^4}{p^2 q^2} isMCQ · +1 marks
  4. Q7A rectangular paper sheet of dimensions 54 cm×4 cm54 \text{ cm} \times 4 \text{ cm} is taken. The two longer edges of the sheet are joined together to create a…MCQ · +2 marks
  5. Q8The pie chart presents the percentage contribution of different macronutrients to a typical 2,000 kcal diet of a person. [figure] The typical energy density…MCQ · +2 marks
  6. Q10The least number of squares to be added in the figure to make AB a line of symmetry is [figure]MCQ · +2 marks

General Aptitude (GA)

  1. Q3Consider the following sample of numbers: 9,18,11,14,15,17,10,69,11,139, 18, 11, 14, 15, 17, 10, 69, 11, 13 The median of the sample isMCQ · +1 marks
  2. Q4The number of coins of ₹1, ₹5, and ₹10 denominations that a person has are in the ratio 5:3:13. Of the total amount, the percentage of money in ₹5 coins isMCQ · +1 marks
  3. Q6In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks. Steve was advised to keep his head _____(i)______ before…MCQ · +2 marks
  4. Q9A rectangular paper of 20 cm×8 cm20 \text{ cm} \times 8 \text{ cm} is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long…MCQ · +2 marks

Computer Science and Information Technology

  1. Q11Let f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} be a function such that f(x)=max⁡{x,x3},x∈Rf(x) = \max\{x, x^3\}, x \in \mathbb{R}, where R\mathbb{R} is the set of all real…MCQ · +1 marks
  2. Q12The product of all eigenvalues of the matrix [123456789]\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} isMCQ · +1 marks
  3. Q14Consider a permutation sampled uniformly at random from the set of all permutations of {1,2,3,…,n}\{1, 2, 3, \dots, n\} for some n≥4n \geq 4. Let XX be the event that 1…MCQ · +1 marks
  4. Q15Which one of the following statements is FALSE?MCQ · +1 marks
  5. Q16A user starts browsing a webpage hosted at a remote server. The browser opens a single TCP connection to fetch the entire webpage from the server. The webpage…MCQ · +1 marks
  6. Q17Given an integer array of size NN, we want to check if the array is sorted (in either ascending or descending order). An algorithm solves this problem by…MCQ · +1 marks
  7. Q18Consider the following C program: [code] Which one of the following statements is CORRECT?MCQ · +1 marks
  8. Q19Consider the following C program: [code] Assume that the input to the program from the command line is 1234 followed by a newline character. Which one of the…MCQ · +1 marks
  9. Q20Let S be the specification: "Instructors teach courses. Students register for courses. Courses are allocated classrooms. Instructors guide students." Which one…MCQ · +1 marks
  10. Q21In a B+B^+ tree, the requirement of at least half-full (50%) node occupancy is relaxed for which one of the following cases?MCQ · +1 marks
  11. Q22Which of the following statements about a relation R\mathbf{R} in first normal form (1NF) is/are TRUE ?MSQ · +1 marks
  12. Q23Let L1,L2L_1, L_2 be two regular languages and L3L_3 a language which is not regular. Which of the following statements is/are always TRUE?MSQ · +1 marks
  13. Q25Which of the following process state transitions is/are NOT possible?MSQ · +1 marks
  14. Q26Which of the following is/are Bottom-Up Parser(s)?MSQ · +1 marks
  15. Q27Let AA and BB be two events in a probability space with P(A)=0.3P(A) = 0.3, P(B)=0.5P(B) = 0.5, and P(A∩B)=0.1P(A \cap B) = 0.1. Which of the following statements is/are TRUE?MSQ · +1 marks
  16. Q28Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no…MSQ · +1 marks
  17. Q30Consider a 5-stage pipelined processor with Instruction Fetch (IF), Instruction Decode (ID), Execute (EX), Memory Access (MEM), and Register Writeback (WB)…MSQ · +1 marks
  18. Q31Which of the following fields is/are modified in the IP header of a packet going out of a network address translation (NAT) device from an internal network to…MSQ · +1 marks
  19. Q32Let AA and BB be non-empty finite sets such that there exist one-to-one and onto functions (i) from AA to BB and (ii) from A×AA \times A to A∪BA \cup B. The…NAT · +1 marks
  20. Q33Consider the operator precedence and associativity rules for the integer arithmetic operators given in the table below. | Operator | Precedence | Associativity…NAT · +1 marks
  21. Q34The number of spanning trees in a complete graph of 4 vertices labelled A, B, C, and D is _________NAT · +1 marks
  22. Q35Consider the following two relations, R(A,B) and S(A,C): Relation R | A | B | |---|---| | 10 | 20 | | 20 | 30 | | 30 | 40 | | 30 | 50 | | 50 | 95 |…NAT · +1 marks
  23. Q36Consider a network path P—Q—R between nodes P and R via router Q. Node P sends a file of size 10610^6 bytes to R via this path by splitting the file into chunks…MCQ · +2 marks
  24. Q38Consider the following grammar GG, with SS as the start symbol. The grammar GG has three incomplete productions denoted by (1), (2), and (3).…MCQ · +2 marks
  25. Q42Consider the following recurrence relation: T(n)={nT(n)+nfor n≥1,1for n=1.T(n) = \begin{cases} \sqrt{n}T(\sqrt{n}) + n & \text{for } n \ge 1, \\ 1 & \text{for } n = 1. \end{cases} Which…MCQ · +2 marks
  26. Q46Consider the following read-write schedule SS over three transactions T1,T2T_1, T_2, and T3T_3, where the subscripts in the schedule indicate transaction IDs:…MSQ · +2 marks
  27. Q48Consider the following C function definition. [code] Which of the following statements is/are TRUE about the above function?MSQ · +2 marks
  28. Q50Consider the 5-state DFA MM accepting the language L(M)⊂(0+1)∗L(M) \subset (0 + 1)^* shown below. For any string w∈(0+1)∗w \in (0 + 1)^* let n0(w)n_0(w) be the number of 0's in…MSQ · +2 marks
  29. Q52Consider the operators ⋄\diamond and □\Box defined by a⋄b=a+2ba \diamond b = a + 2b, a□b=aba \Box b = ab, for positive integers. Which of the following statements…MSQ · +2 marks
  30. Q53Consider two set-associative cache memory architectures: WBC, which uses the write back policy, and WTC, which uses the write through policy. Both of…MSQ · +2 marks
  31. Q54Consider a 512 GB hard disk with 32 storage surfaces. There are 4096 sectors per track and each sector holds 1024 bytes of data. The number of cylinders in the…NAT · +2 marks
  32. Q55The baseline execution time of a program on a 2 GHz single core machine is 100 nanoseconds (ns). The code corresponding to 90% of the execution time can be…NAT · +2 marks
  33. Q56A given program has 25% load/store instructions. Suppose the ideal CPI (cycles per instruction) without any memory stalls is 2. The program exhibits 2% miss…NAT · +2 marks
  34. Q59Let G=(V,Σ,S,P)G = (V, \Sigma, S, P) be a context-free grammar in Chomsky Normal Form with Σ={a,b,c}\Sigma = \{a, b, c\} and VV containing 10 variable symbols including the…NAT · +2 marks
  35. Q60The number of edges present in the forest generated by the DFS traversal of an undirected graph GG with 100 vertices is 40. The number of connected components…NAT · +2 marks
  36. Q61Consider the following two regular expressions over the alphabet {0,1}\{0,1\}: r=0∗+1∗r = 0^* + 1^* s=01∗+10∗s = 01^* + 10^* The total number of strings of length less…NAT · +2 marks
  37. Q62Consider a memory management system that uses a page size of 2 KB2\text{ KB}. Assume that both the physical and virtual addresses start from 00. Assume that the…NAT · +2 marks
  38. Q63A bag contains 10 red balls and 15 blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability…NAT · +2 marks
  39. Q64Consider a digital logic circuit consisting of three 2-to-1 multiplexers M1, M2, and M3 as shown below. X1X_1 and X2X_2 are inputs of M1. X3X_3 and X4X_4 are…NAT · +2 marks

Computer Science and Information Technology Set 1 (CS1)

  1. Q13Consider a system that uses 5 bits for representing signed integers in 2’s complement format. In this system, two integers AA and BB are represented as…MCQ · +1 marks
  2. Q24Which of the following statements about threads is/are TRUE?MSQ · +1 marks
  3. Q29TCP client PP successfully establishes a connection to TCP server QQ. Let NPN_P denote the sequence number in the SYN sent from PP to QQ. Let NQN_Q denote…MSQ · +1 marks
  4. Q37Consider the following syntax-directed definition (SDD). | Production | Semantic Rules | | ------ | ------ | | S → DHTU |…MCQ · +2 marks
  5. Q39Consider the following pseudo-code. [code] Which one of the following options CORRECTLY specifies the number of basic blocks and the number of instructions in…MCQ · +2 marks
  6. Q40Consider the following two threads T1 and T2 that update two shared variables a and b. Assume that initially a = b = 1. Though context switching between…MCQ · +2 marks
  7. Q41An array [82,101,90,11,111,75,33,131,44,93][82, 101, 90, 11, 111, 75, 33, 131, 44, 93] is heapified. Which one of the following options represents the first three elements in the heapified…MCQ · +2 marks
  8. Q43Consider a binary min-heap containing 105 distinct elements. Let kk be the index (in the underlying array) of the maximum element stored in the heap. The…MCQ · +2 marks
  9. Q44The symbol →\rightarrow indicates functional dependency in the context of a relational database. Which of the following options is/are TRUE?MSQ · +2 marks
  10. Q45Let GG be a directed graph and TT a depth first search (DFS) spanning tree in GG that is rooted at a vertex vv. Suppose TT is also a breadth first search…MSQ · +2 marks
  11. Q47Consider a Boolean expression given by F(X,Y,Z)=∑(3,5,6,7)F(X, Y, Z) = \sum(3,5,6,7). Which of the following statements is/are CORRECT?MSQ · +2 marks
  12. Q49Let AA be any n×mn \times m matrix, where m>nm > n. Which of the following statements is/are TRUE about the system of linear equations Ax=0Ax = \mathbf{0} ?MSQ · +2 marks
  13. Q51The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let GG be any graph with nn vertices and…MSQ · +2 marks
  14. Q57Consider the following code snippet using the fork() and wait() system calls. Assume that the code compiles and runs correctly, and that the system calls…NAT · +2 marks
  15. Q58Consider the entries shown below in the forwarding table of an IP router. Each entry consists of an IP prefix and the corresponding next hop router for packets…NAT · +2 marks
  16. Q65Consider sending an IP datagram of size 1420 bytes (including 20 bytes of IP header) from a sender to a receiver over a path of two links with a router between…NAT · +2 marks

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