GATE CSE 2024 Set 1
Paper was held on Sat, Feb 10, 2024 4:00 AM
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## GATE CSE

Given an integer array of size $N$, we want to check if the array is sorted (in either ascending or descending order).
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Consider the following recurrence relation:$$T(n) = \begin{cases} \sqrt{n} T(\sqrt{n}) + n & \text{for } n \ge 1, \\ 1 & View Question Let G be a directed graph and T a depth first search (DFS) spanning tree in G that is rooted at a vertex v. Suppose T is View Question Which of the following is/are Bottom-Up Parser(s)? View Question Consider the following syntax-directed definition (SDD). table { width: 100%; border-collapse: collapse; margin: 20px 0; View Question Consider the following grammar G, with S as the start symbol. The grammar G has three incomplete productions denot View Question Consider the following pseudo-code. L1: t1 = -1L2: t2 = 0L3: t3 = 0L4: t4 = 4 * t3L5: t5 = 4 * t2L6: t View Question A user starts browsing a webpage hosted at a remote server. The browser opens a single TCP connection to fetch the entir View Question TCP client P successfully establishes a connection to TCP server Q. Let N_P denote the sequence number in the SYN sent View Question Which of the following fields is/are modified in the IP header of a packet going out of a network address translation (N View Question Consider a network path P—Q—R between nodes P and R via router Q. Node P sends a file of size 10^6 bytes to R via this View Question Consider the entries shown below in the forwarding table of an IP router. Each entry consists of an IP prefix and the co View Question Consider sending an IP datagram of size 1420 bytes (including 20 bytes of IP header) from a sender to a receiver over a View Question Which one of the following statements is FALSE? View Question Consider a 5-stage pipelined processor with Instruction Fetch (IF), Instruction Decode (ID), Execute (EX), Memory Access View Question Consider two set-associative cache memory architectures: WBC, which uses the write back policy, and WTC, which uses the View Question Consider a 512 GB hard disk with 32 storage surfaces. There are 4096 sectors per track and each sector holds 1024 bytes View Question The baseline execution time of a program on a 2 GHz single core machine is 100 nanoseconds (ns). The code corresponding View Question A given program has 25% load/store instructions. Suppose the ideal CPI (cycles per instruction) without any memory stall View Question An array [82, 101, 90, 11, 111, 75, 33, 131, 44, 93] is heapified. Which one of the following options represents the f View Question Consider a binary min-heap containing 105 distinct elements. Let k be the index (in the underlying array) of the maximum View Question Let S be the specification: "Instructors teach courses. Students register for courses. Courses are allocated classrooms. View Question In a B+ tree, the requirement of at least half-full (50%) node occupancy is relaxed for which one of the following cases View Question Which of the following statements about a relation R in first normal form (1NF) is/are TRUE? View Question Consider the following two relations, R(A, B) and S(A, C): table { width: 100%; border-collapse: collapse; margin: 20px View Question The symbol &rarr; indicates functional dependency in the context of a relational database. Which of the following option View Question Consider the following read-write schedule S over three transactions T_{1}, T_{2}, and T_{3}, where the subscrip View Question Consider a system that uses 5 bits for representing signed integers in 2’s complement format. In this system, two intege View Question Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur i View Question Consider a Boolean expression given by F(X, Y, Z) = \\Sigma(3,5,6,7).Which of the following statements is/are CORRECT? View Question Consider a digital logic circuit consisting of three 2-to-1 multiplexers M1, M2, and M3 as shown below. X1 and X2 are in View Question Let f : \mathbb{R} \rightarrow \mathbb{R} be a function such that f(x) = \max \{x, x^3\}, x \in \mathbb{R}, where \ View Question The product of all eigenvalues of the matrix \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} is View Question Consider a permutation sampled uniformly at random from the set of all permutations of {1, 2, 3, ..., n} for some n ≥ 4. View Question Let A and B be two events in a probability space with P(A) = 0.3, P(B) = 0.5, and P(A \cap B) = 0.1. Which of the View Question Let A and B be non-empty finite sets such that there exist one-to-one and onto functions (i) from A to B and (ii View Question Consider the operator precedence and associativity rules for the integer arithmetic operators given in the table below. View Question The number of spanning trees in a complete graph of 4 vertices labelled A, B, C, and D is __________ View Question Let A be any n x m matrix, where m &gt; n. Which of the following statements is/are TRUE about the system of linear equa View Question The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let G be any View Question Consider the operators \diamond and \square defined by a \diamond b=a+2 b, a \square b=a b, for positive integers. View Question The number of edges present in the forest generated by the DFS traversal of an undirected graph G with 100 vertices is 4 View Question A bag contains 10 red balls and 15 blue balls. Two balls are drawn randomly without replacement. Given that the first ba View Question Which of the following statements about threads is/are TRUE? View Question Which of the following process state transitions is/are NOT possible? View Question Consider the following two threads T1 and T2 that update two shared variables a and b. Assume that initially a = 1 and View Question Consider the following code snippet using the fork() and wait() system calls. Assume that the code compiles and runs cor View Question Consider a memory management system that uses a page size of 2 KB. Assume that both the physical and virtual addresses s View Question Consider the following C program: #include &ltstdio.h&gt; int main() { int a = 6; int b = 0; while(a Wh View Question Consider the following C program: #include &lt;stdio.h&gt; void fX(); int main() { fX(); return 0;} void fX( View Question Consider the following C function definition. int f(int x, int y) { for (int i=0; i&lt;y; i++) { x=x+x+y; View Question Let L_1, L_2 be two regular languages and L_3 a language which is not regular. Which of the following statements is/ View Question Consider the 5-state DFA M accepting the language L(M) \subseteq (0+1)^* shown below. For any string w \in (0+1)^* View Question Let G = (V, Σ, S, P) be a context-free grammar in Chomsky Normal Form with Σ = { a, b, c } and V containing 10 variabl View Question Consider the following two regular expressions over the alphabet {0,1}:$$r = 0^* + 1^*s = 01^* + 10^*The total num
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## General Aptitude

Consider the following sample of numbers:9, 18, 11, 14, 15, 17, 10, 69, 11, 13The median of the sample is
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The 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
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If ‘→’ denotes increasing order of intensity, then the meaning of the words [dry → arid → parched] is analogous to [diet
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If two distinct non-zero real variables $x$ and $y$ are such that $(x + y)$ is proportional to $(x - y)$ then the value
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For positive non-zero real variables $p$ and $q$, if$\log \left(p^2 + q^2\right) = \log p + \log q + 2 \log 3$,then, the
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In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks. Steve was advised to keep
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A rectangular paper sheet of dimensions 54 cm &times; 4 cm is taken. The two longer edges of the sheet are joined togeth
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The pie chart presents the percentage contribution of different macronutrients to a typical 2,000 kcal diet of a person.
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A rectangular paper of 20 cm &times; 8 cm is folded 3 times. Each fold is made along the line of symmetry, which is perp
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The least number of squares to be added in the figure to make AB a line of symmetry is
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