GATE CS question library

#include <stdio.h> int foo(int S[],int size) { if(size == 0) return 0; if(size == 1) return 1; if(S[0] != S[1]) return 1+foo(S+1,size-1); return foo(S+1,size-1); } int main() { int A[]={0,1,2,2,2,0,0,1,1}; printf("%d",foo(A,9)); return 0; } The value printed by the given $C$ program is ___________. (Answer in integer)

Let $\mathrm{LIST}$ be a datatype for an implementation of linked list defined as follows: typedef struct list { int data; struct list *next; } LIST; Suppose a program has created two linked lists, $L1$ and $L2$, whose contents are given in the figure below (code for creating $L1$ and $L2$ is not provided here). $L1$ contains $9$ nodes, and …

Consider the following C program: #include <stdio.h> int gate (int n) { int d, t, newnum, turn; newnum = turn = 0; t=1; while (n>=t) t *= 10; t /=10; while (t>0) { d = n/t; n = n%t; t /= 10; if (turn) newnum = 10*newnum + d; turn = (turn + 1) % 2; } return newnum; } int main () { printf ("%d", gate(14362)); return 0; } The value printed by the …

The maximum value of $\text{x}$ such that the edge between the nodes $\text{B}$ and $\text{C}$ is included in every minimum spanning tree of the given graph is _________. (answer in integer)

In a double hashing scheme, $h_{1}(k)=k \bmod 11$ and $h_{2}(k)=1+(k \bmod 7)$ are the auxiliary hash functions. The size $m$ of the hash table is $11$. The hash function for the $i$-th probe in the open address table is $\left[h_{1}(k)+i h_{2}(k)\right] \bmod m$. The following keys are inserted in the given order: $63,50,25,79,67,24$. The slot …

Consider two grammars $G_{1}$ and $G_{2}$ with the production rules given below: $G_{1} : S \rightarrow$ $if$ $E$ $then$ $S$ $|$ $if$ $E$ $then$ $S$ $else$ $S$ $|$ $a$ $E \rightarrow b$ $G_{2} :S \rightarrow$ $if$ $E$ $then$ $S$ $|$ $M$ $M \rightarrow$ $if$ $E$ $then$ $M$ $else$ $S$ $|$ $c$ …

Let $\Sigma=\{a, b, c\}$. For $x \in \Sigma^{*}$, and $\alpha \in \Sigma$, let $\#_{\alpha}(x)$ denote the number of occurrences of $\alpha$ in $x$. Which one or more of the following option(s) define(s) regular language(s)?

Consider the database transactions T1 and T2 , and data items X and Y . Which of the schedule(s) is/are conflict serializable? …

Consider the following relational schema: Students ($\underline{\text{rollno: integer}},$ name: string, age: integer, cgpa: real) Courses ($\underline{\text{courseno: integer}},$ cname: string, credits: integer) Enrolled ($\underline{\text{rollno: integer}},$ $\underline{\text{courseno: integer}},$ grade: string) Which of the following options is/are …

Given a computing system with two levels of cache (L1 and L2) and a main memory. The first level (L1) cache access time is $1$ nanosecond (ns) and the "hit rate" for L1 cache is $90 \%$ while the processor is accessing the data from L1 cache. Whereas, for the second level (L2) cache, the "hit rate" is $80 \%$ and the "miss penalty" for transferring …

A $5$-stage instruction pipeline has stage delays of $180,250,150,170$, and $250$, respectively, in nanoseconds. The delay of an inter-stage latch is $10$ nanoseconds. Assume that there are no pipeline stalls due to branches and other hazards. The time taken to process $1000$ instructions in microseconds is __________. (rounded off to two decimal …

In a $\mathrm{B}^{+}$- tree where each node can hold at most four key values, a root to leaf path consists of the following nodes: $$\mathrm{A}=(49,77,83,-), \mathrm{B}=(7,19,33,44), \mathrm{C}=\left(20^{*}, 22^{*}, 25^{*}, 26^{*}\right)$$ The $*$-marked keys signify that these are data entries in a leaf. Assume that a pointer between keys $k_{1}$ and …

A computer system supports a logical address space of $2^{32}$ bytes. It uses two-level hierarchical paging with a page size of $4096$ bytes. A logical address is divided into a $b$-bit index to the outer page table, an offset within the page of the inner page table, and an offset within the desired page. Each entry of the inner page table uses eight …

Consider the following algorithm someAlgo that takes an undirected graph $G$ as input. someAlgo (G) Let $v$ be any vertex in $G$. Run BFS on $G$ starting at $v$. Let $u$ be a vertex in $G$ at maximum distance from $v$ as given by the BFS. Run BFS on $G$ again with $u$ as the starting vertex. Let $z$ be the vertex at maximum distance …

Let $\Sigma=\{1,2,3,4\}$. For $x \in \Sigma^{*}$, let $\operatorname{prod}(x)$ be the product of symbols in $x$ modulo 7. We take $\operatorname{prod}(\epsilon)=1$, where $\epsilon$ is the null string. For example, $\operatorname{prod}(124)=(1 \times 2 \times 4) \bmod 7=1$. Define …

An application executes $6.4 \times 10^{8}$ number of instructions in $6.3$ seconds. There are four types of instructions, the details of which are given in the table. The duration of a clock cycle in nanoseconds is __________. (rounded off to one decimal place) …

Consider the following C program: #include<stdio.h> int main(){ int a; int arr[5] = {30,50,10}; int *ptr; ptr = &arr[0] + 1; a = *ptr; (*ptr)++; ptr++; printf("%d", a + (*ptr) + arr[1]); return 0; } The output of the above program is _________. (Answer in integer)

Consider the following C program: #include <stdio.h> int g(int n) { return (n+10); } int f(int n) { return g(n*2); } int main() { int sum, n; sum=0; for (n=1; n<3; n++) sum += g(f(n)); printf ("%d", sum); return 0; } The output of the given C program is ___________. (Answer in integer)

A quadratic polynomial $(x-\alpha)(x-\beta)$ over complex numbers is said to be square invariant if $(x-\alpha)(x-\beta)=\left(x-\alpha^{2}\right)\left(x-\beta^{2}\right)$. Suppose from the set of all square invariant quadratic polynomials we choose one at random. The probability that the roots of the chosen polynomial are equal is __________. (rounded …

The unit interval $(0,1)$ is divided at a point chosen uniformly distributed over $(0,1)$ in $\mathbb{R}$ into two disjoint subintervals. The expected length of the subinterval that contains $0.4$ is __________. (rounded off to two decimal places)