GATE CS question library

Consider the transition diagram of a PDA given below with input alphabet $\Sigma=\{a,b\}$ and stack alphabet $\Gamma = \{X,Z\}$. $Z$ is the initial stack symbol. Let $L$ denote the language accepted by the PDA Which one of the following is TRUE?

Consider the weighted undirected graph with $4$ vertices, where the weight of edge $\{i,j\}$ is given by the entry $W_{ij}$ in the matrix $W$. W=$\begin{bmatrix} 0&2 &8 &5 \\ 2&0 &5 &8 \\ 8&5 &0 &x \\ 5& 8 &x &0 \end{bmatrix}$ The largest possible integer value of $x$, for which at least one …

$G=(V, E)$ is an undirected simple graph in which each edge has a distinct weight, and $e$ is a particular edge of $G$. Which of the following statements about the minimum spanning trees $(MSTs)$ of $G$ is/are TRUE? If $e$ is the lightest edge of some cycle in $G$, then every MST of $G$ includes $e$. If $e$ is the heaviest edge of some …

What will be the output of the following $C$ program? void count (int n) { static int d=1; printf ("%d",n); printf ("%d",d); d++; if (n>1) count (n-1); printf ("%d",d); } void main(){ count (3); }

Let $G$ be a complete undirected graph on $4$ vertices, having $6$ edges with weights being $1, 2, 3, 4, 5,$ and $6$. The maximum possible weight that a minimum weight spanning tree of $G$ can have is __________

Consider the two cascade $2$ to $1$ multiplexers as shown in the figure . The minimal sum of products form of the output $X$ is

For a host machine that uses the token bucket algorithm for congestion control, the token bucket has a capacity of $1$ $\text{megabyte}$ and the maximum output rate is $20$ $\text{megabytes}$ per $\text{second}$. Tokens arrive at a rate to sustain output at a rate of $10$ $\text{megabytes}$ per $\text{second}$. The token bucket is currently …

Let $X$ be a recursive language and $Y$ be a recursively enumerable but not recursive language. Let $W$ and $Z$ be two languages such that $\overline{Y}$ reduces to $W$, and $Z$ reduces to $\overline{X}$ (reduction means the standard many-one reduction). Which one of the following statements is TRUE?

Consider the following proposed solution for the critical section problem. There are $n$ processes : $P_0....P_{n-1}$. In the code, function $\text{pmax}$ returns an integer not smaller than any of its arguments .For all $i,t[i]$ is initialized to zero. Code for $P_i$; do { c[i]=1; t[i]= pmax (t[0],....,t[n-1])+1; c[i]=0; for every j != i in …

A function $f: \Bbb{N^+} \rightarrow \Bbb{N^+}$ , defined on the set of positive integers $\Bbb{N^+}$, satisfies the following properties: $f(n)=f(n/2)$ if $n$ is even $f(n)=f(n+5)$ if $n$ is odd Let $R=\{ i \mid \exists{j} : f(j)=i \}$ be the set of distinct values that $f$ takes. The maximum possible size of $R$ is ___________.

Cylinder a disk queue with requests for $I/O$ to blocks on cylinders $47, 38, 121, 191, 87, 11, 92, 10.$ The C-LOOK scheduling algorithm is used. The head is initially at cylinder number $63$, moving towards larger cylinder numbers on its servicing pass. The cylinders are numbered from $0$ to $199$. The total head movement (in number of cylinders) …

Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.

An IP datagram of size $1000$ $\text{bytes }$arrives at a router. The router has to forward this packet on a link whose MTU (maximum transmission unit) is $100$ $\text{bytes }$. Assume that the size of the IP header is $20$ $\text{bytes }.$ The number of fragments that the IP datagram will be divided into for transmission is________.

Consider a computer system with ten physical page frames. The system is provided with an access sequence $(a_{1}, a_{2},....,a_{20}, a_{1}, a_{2},...a_{20})$, where each $a_{i}$ is a distinct virtual page number. The difference in the number of page faults between the last-in-first-out page replacement policy and the optimal page replacement policy …

Consider the following experiment. Step 1. Flip a fair coin twice. Step 2. If the outcomes are (TAILS, HEADS) then output $Y$ and stop. Step 3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output $N$ and stop. Step 4. If the outcomes are (TAILS, TAILS), then go to Step $1.$ The probability that the output of the experiment is $Y$ …

An operator delete$(i)$ for a binary heap data structure is to be designed to delete the item in the $i$-th node. Assume that the heap is implemented in an array and $i$ refers to the $i$-th index of the array. If the heap tree has depth $d$ (number of edges on the path from the root to the farthest leaf ), then what is the time complexity to …

Consider the following context-free grammars; $G_1 : S \to aS \mid B, B \to b \mid bB$ $G_2 : S \to aA \mid bB, A \to aA \mid B \mid \varepsilon,B \to bB \mid \varepsilon$ Which one of the following pairs of languages is generated by $G_1$ and $G_2$ ,respectively?

The following function computes the maximum value contained in an integer array $P[ \ ]$ of size $n$ $(n>=1)$. int max (int *p,int n) { int a = 0, b=n-1; while (__________) { if (p[a]<= p[b]) {a = a+1;} else {b = b-1;} } return p[a]; } The missing loop condition is:

Consider the following two phase locking protocol. Suppose a transaction $T$ accesses (for read or write operations), a certain set of objects $\{O_1,\ldots,O_k \}$. This is done in the following manner: $\text{Step 1}$. $T$ acquires exclusive locks to $O_1,\ldots,O_k$ in increasing order of their addresses. $\text{Step 2}$. The required …

What will be the output of the following pseudo-code when parameters are passed by reference and dynamic scoping is assumed? a = 3; void n(x) { x = x * a; print (x); } void m(y) { a = 1 ; a = y - a; n(a); print (a); } void main () { m(a); }