GATE CS question library

Consider the following expression grammar $G$: $E \rightarrow E-T \mid T$ $T \rightarrow T + F \mid F$ $F \rightarrow (E) \mid id$ Which of the following grammars is not left recursive, but is equivalent to $G$?

For any discrete random variable $X$, with probability mass function $P(X=j)=p_j, p_j \geq 0, j \in \{0, \dots , N \}$, and $\Sigma_{j=0}^N \: p_j =1$, define the polynomial function $g_x(z) = \Sigma_{j=0}^N \: p_j \: z^j$. For a certain discrete random variable $Y$, there exists a scalar $\beta \in [0,1]$ such that …

In a two-level cache system, the access times of $L_1$ and $L_2$ caches are $1$ and $8$ clock cycles, respectively. The miss penalty from the $L_2$ cache to main memory is $18$ clock cycles. The miss rate of $L_1$ cache is twice that of $L_2$. The average memory access time (AMAT) of this cache system is $2$ cycles. The miss rates of …

Given $f(w, x, y, z) = \Sigma_m(0,1, 2, 3, 7, 8, 10) + \Sigma_d(5, 6, 11, 15)$; where $d$ represents the 'don't-care' condition in Karnaugh maps. Which of the following is a minimum product-of-sums (POS) form of $f(w, x, y, z)$?

$P$ and $Q$ are considering to apply for a job. The probability that $P$ applies for the job is $\dfrac{1}{4},$ the probability that $P$ applies for the job given that $Q$ applies for the job is $\dfrac{1}{2},$ and the probability that $Q$ applies for the job given that $P$ applies for the job is $\dfrac{1}{3}.$ Then the probability that …

Let $P = \begin{bmatrix}1 & 1 & -1 \\2 & -3 & 4 \\3 & -2 & 3\end{bmatrix}$ and $Q = \begin{bmatrix}-1 & -2 &-1 \\6 & 12 & 6 \\5 & 10 & 5\end{bmatrix}$ be two matrices. Then the rank of $P+Q$ is ___________ .

Which of the following statements about parser is/are CORRECT? $\text{Canonical LR}$ is more powerful than $\text{SLR}$ $\text{SLR}$ is more powerful than $\text{LALR}$ $\text{SLR}$ is more powerful than $\text{Canonical LR}$

Consider the following statements about the routing protocols. Routing Information Protocol (RIP) and Open Shortest Path First (OSPF) in an $\textsf{IPv4}$ network. RIP uses distance vector routing RIP packets are sent using UDP OSPF packets are sent using TCP OSPF operation is based on link-state routing Which of the above statements are CORRECT?

The representation of the value of a $16\text{-bit}$ unsigned integer $X$ in hexadecimal number system is $\textsf{BCA9}$. The representation of the value of $X$ in octal number system is

Consider the following C program. #include<stdio.h> #include<string.h> int main() { char* c="GATECSIT2017"; char* p=c; printf("%d", (int)strlen(c+2[p]-6[p]-1)); return 0; } The output of the program is _______

Consider the following C function int fun(int n) { int i, j; for(i=1; i<=n; i++) { for (j=1; j<n; j+=i) { printf("%d %d", i, j); } } } Time complexity of $fun$ in terms of $\Theta$ notation is

Consider the following C program. #include<stdio.h> int main () { int m=10; int n, n1; n=++m; n1=m++; n--; --n1; n-=n1; printf(“%d”, n); return 0; } The output of the program is ______

Consider the set $X=\{a, b, c, d, e\}$ under partial ordering $R=\{(a,a), (a, b), (a, c), (a, d), (a, e), (b, b), (b, c), (b, e), (c, c), (c, e), (d, d), (d, e), (e, e) \}$ The Hasse diagram of the partial order $(X, R)$ is shown below. The minimum number of ordered pairs that need to be added to $R$ to make $(X, R)$ a lattice is ______

If $f(x) = R \: \sin ( \frac{\pi x}{2}) + S, f’\left(\frac{1}{2}\right) = \sqrt{2}$ and $\int_0^1 f(x) dx = \frac{2R}{\pi}$, then the constants $R$ and $S$ are

A circular queue has been implemented using a singly linked list where each node consists of a value and a single pointer pointing to the next node. We maintain exactly two external pointers FRONT and REAR pointing to the front node and the rear node of the queue, respectively. Which of the following statements is/are CORRECT for such a circular queue, so …

Consider the following function implemented in C: void printxy(int x, int y) { int *ptr; x=0; ptr=&x; y=*ptr; *ptr=1; printf(“%d, %d”, x, y); } The output of invoking $printxy(1,1)$ is:

Identify the language generated by the following grammar, where $S$ is the start variable. $S \rightarrow XY$ $X \rightarrow aX \mid a$ $Y \rightarrow aYb \mid \epsilon$

Which of the following is/are shared by all the threads in a process? Program counter Stack Address space Registers

Consider the following tables $T1$ and $T2.$ …

Consider socket API on a Linux machine that supports connected UDP sockets. A connected UDP socket is a UDP socket on which connect function has already been called. Which of the following statements is/are CORRECT? A connected UDP socket can be used to communicate with multiple peers simultaneously. A process can successfully call connect function again for …