GATE 2022 CSE & IT

Which one of the following statements is TRUE for all positive functions f(n) ?

The ___________ is too high for it to be considered __________.

A function y(x) is defined in the interval [0, 1] on the x-axis as $$y(x) = \left\{ \matrix{ 2\,if\,0 \le x Which one of the following is the area under the curve for the interval...

Let r be a root of the equation x 2 + 2x + 6 = 0. Then the value of the expression (r + 2) (r + 3) (r + 4) (r + 5) is

Given below are four statements : Statement 1 : All students are inquisitive. Statement 2 : Some students are inquisitive. Statement 3 : No student is inquisitive. Statement 4 : So...

Some people believe that "what gets measured, improves". Some other believe that "what gets measured, gets gamed". One possible reason for the difference in the beliefs is the work...

In a recently conducted national entrance test, boys constituted 65% of those who appeared for the test. Girls constituted the remaining candidates and they accounted for 60% of th...

A box contains five balls of same size and shape. Three of them are green coloured balls and two of them are orange coloured balls. Balls are drawn from the box one at a time. If a...

Which one of the following statements is TRUE?

In a relational data model, which one of the following statements is TRUE?

Suppose we are given n keys, m has table slots, and two simple uniform hash functions h 1 and h 2 . Further suppose our hashing scheme uses h 1 for the odd keys and h 2 for the eve...

Which one of the following facilitates transfer of bulk data from hard disk to main memory with the highest throughput?

Let R1 and R2 be two 4-bit registers that store numbers in 2's complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overfl...

Consider the following threads, T 1 , T 2 and T 3 executing on a single processor, synchronized using three binary semaphore variables, S 1 , S 2 and S 3 , operated upon using stan...

Consider the following two statements with respect to the matrices A m $$\times$$ n , B n $$\times$$ m , C n$$\times$$ n and D n $$\times$$ n . Statement 1 : tr(AB) = tr(BA) Statem...

What is printed by the following ANSI C program? #include <stdio.h> int main(int argc, char *argv[ ]) { int x = 1, z[2] = {10, 11}; int *p = NULL; p = &x; *p = 10; p = &z[1]; *(&z[...

Let WB and WT be two set associative cache organizations that use LRU algorithm for cache block replacement. WB is a write back cache and WT is a write through cache. Which of the...

Consider the following three relations in a relational database. Employee ( $$\underline {eld} $$ , Name), Brand ( $$\underline {bld} $$ , bName), Own ( $$\underline {eld} $$ , $$\...

Which of the following statements is/are TRUE with respect to deadlocks?

Which of the following statements is/are TRUE for a group G?

Which of the properties hold for the adjacency matrix A of a simple undirected unweighted graph having n vertices?

Suppose a binary search tree with 1000 distinct elements is also a complete binary tree. The tree is stored using the array representation of binary heap trees. Assuming that the a...

Consider the augmented grammar with {+, *, (, ), id} as the set of terminals. S' $$\to$$ S S $$\to$$ S + R | R R $$\to$$ R * P | P P $$\to$$ (S) | id If I 0 is the set of two LR(0)...

Consider a simple undirected graph of 10 vertices. If the graph is disconnected, then the maximum number of edges it can have is __________.

Consider a relation R(A, B, C, D, E) with the following three functional dependencies. AB $$\to$$ C ; BC $$\to$$ D ; C $$\to$$ E; The number of superkeys in the relation R is _____...

The number of arrangements of six identical balls in three identical bins is ___________.

A cache memory that has a hit rate of 0.8 has an access latency 10 ns and miss penalty 100 ns. An optimization is done on the cache to reduce the miss rate. However, the optimizati...

The value of the following limit is _____________. $$\mathop {\lim }\limits_{x \to {0^ + }} {{\sqrt x } \over {1 - {e^{2\sqrt x }}}}$$

Consider the resolution of the domain name www.gate.org.in by a DNS resolver. Assume that no resource records are cached anywhere across the DNS servers and that iterative query me...

Which one of the following is the closed form for the generating function of the sequence (a n } n $$\ge$$ 0 defined below? $${a_n} = \left\{ {\matrix{ {n + 1,} & {n\,is\,odd} \cr...

Consider a simple undirected unweighted graph with at least three vertices. If A is the adjacency matrix of the graph, then the number of 3-cycles in the graph is given by the trac...

Which one of the following statements is FALSE?

Let R i (z) and W i (z) denote read and write operations on a data element z by a transaction T i , respectively. Consider the schedule S with four transactions. S : R 4 (x), R 2 (...

Consider four processes P, Q, R and S scheduled on a CPU as per round robin algorithm with a time quantum of 4 units. The processes arrive in the order P, Q, R, S, all at time t =...

What is printed by the following ANSI C program? #include <stdio.h> int main(int argc, char *argv[ ]) { int a[3][3][3] = {{1, 2, 3, 4, 5, 6, 7, 8, 9}, {10, 11, 12, 13, 14, 15, 16,...

Consider solving the following system of simultaneous equations using LU decomposition. x 1 + x 2 $$-$$ 2x 3 = 4 x 1 + 3x 2 $$-$$ x 3 = 7 2x 1 + x 2 $$-$$ 5x 3 = 7 where L and U ar...

Consider a simple undirected weighted graph G, all of whose edge weights are distinct. Which of the following statements about the minimum spanning trees of G is/are TRUE?

Which of the following is/are the eigenvector(s) for the matrix given below? $$\left( {\matrix{ { - 9} & { - 6} & { - 2} & { - 4} \cr { - 8} & { - 6} & { - 3} & { - 1} \cr {20} & {...

Consider a system with 2 KB direct mapped data cache with a block size of 64 bytes. The system has a physical address space of 64 KB and a word length of 16 bits. During the execut...

Consider routing table of an organization's router shown below : Subnet number Subnet mask Next hop 12.20.164.0 255.255.252.0 R1 12.20.170.0 255.255.254.0 R2 12.20.168.0 255.255.25...

Consider a 100 Mbps link between an earth station (sender) and a satellite (receiver) at an altitude of 2100 km. The signal propagates at a speed of 3 $$\times$$ 10 8 m/s. The time...

Consider the data transfer using TCP over a 1 Gbps link. Assuming that the maximum segment lifetime (MSL) is set to 60 seconds, the minimum number of bits required for the sequence...

The corners and mid-points of the sides of a triangle are named using the distinct letters P, Q, R, S, T and U, but not necessarily in the same order. Consider the following statem...

A processor X 1 operating at 2 GHz has a standard 5-stage RISC instruction pipeline having a base CPI (cycles per instruction) of one without any pipeline hazards. For a given prog...

Consider two files systems A and B, that use contiguous allocation and linked allocation, respectively. A file of size 100 blocks is already stored in A and also in B. Now, conside...

Consider a demand paging system with four page frames (initially empty) and LRU page replacement policy. For the following page reference string 7, 2, 7, 3, 2, 5, 3, 4, 6, 7, 7, 1,...

Consider the following grammar along with translation rules. S $$\to$$ S 1 # T {S.val = S 1 .val * T.val} S $$\to$$ T {S.val = T.val} T $$\to$$ T 1 %R {T.val = T 1 .val $$ \div $$...

Consider the following recurrence : f(1) = 1; f(2n) = 2f(n) $$-$$ 1, for n $$\ge$$ 1; f(2n + 1) = 2f(n) + 1, for n $$\ge$$ 1; Then, which of the following statements is/are TRUE?

Let G(V, E) be a directed graph, where V = {1, 2, 3, 4, 5} is the set of vertices and E is the set of directed edges, as defined by the following adjacency matrix A. $$A[i][j] = \l...

Which of the following statements is/are TRUE?

Which of the following is/are undecidable?

Consider the following languages: L 1 = {a n wa n | w $$\in$$ {a, b}*} L 2 = {wxw R | w, x $$\in$$ {a, b}*, | w | , | x | > 0} Note that w R is the reversal of the string w. Which...

Consider the following languages: $$\eqalign{ & {L_1} = \{ ww|w \in \{ a,b\} *\} \cr & {L_2} = \{ {a^n}{b^n}{c^m}|m,\,n \ge 0\} \cr & {L_3} = \{ {a^m}{b^n}{c^n}|m,\,n \ge 0\} \cr}...