1
At a room temperature of $300K$, calculate the thermal noise generated by two resistors of $10K\Omega$ and $20K\Omega$ when the bandwidth is $10KHz$. $1.2868\times10^{-6}V, 1.819\times10^{-6}V$ $6.08\times10^{-6}V, 15.77\times10^{-6}V$ $16.66\times10^{-6}V, 2.356\times10^{-6}V$ $1.66\times10^{-6}V, 0.23\times10^{-6}V$
2
In testing phase, the effort distribution is upto 10% 20% 40% 50%
3
HTML (HyperText Markup Language) has language element which permit certain actions other than describing the structure of the web document. Which one of the following actions is NOT supported by pure HTML (without any server or client side scripting) pages? (A) Embed ... a specified interval (C) Automatically redirect to another page upon download (D) Display the client time as part of the page
4
Which of the following statements is/are true? P : An XML document with correct syntax as specified by W3C is called Well Formed . Q : An XML documented validated against a DTD is both Well formed and valid . R : <xml version= 1.0 encoding = UTF-8 > is syntactly ... document. Select the correct answer from the options given below: P and Q only P and R only Q and R only All of P, Q and R
5
Consider the Boolean function $z(a,b,c)$. Which one of the following minterm lists represents the circuit given above? $z=\sum (0,1,3,7)$ $z=\sum (1,4,5,6,7)$ $z=\sum (2,4,5,6,7)$ $z=\sum (2,3,5)$
6
Suppose $\begin{pmatrix} 0&1 &0&0&0&1 \\ 1&0&1&0&0&0 \\ 0&1&0&1&0&1 \\ 0&0&1&0&1&0 \\ 0&0&0&1&0&1 \\ 1&0&1&0&1&0 \end{pmatrix}$ is the adjacency matrix of an undirected graph with six vertices: that is, the rows and columns are indexed by vertices of the graph, and an entry is $1$ if the ... has the above adjacency matrix? Only $(i)$ Only $(ii)$ Only $(iii)$ Only $(iv)$ $(i)$ and $(ii)$
7
An organization requires a range of IP address to assign one to each of its $1500$ computers. The organization has approached an Internet Service Provider (ISP) for this task. The ISP uses CIDR and serves the requests from the available IP address space $202.61.0.0/17$. The ISP wants to assign an ... $202.61.64.0/21$ $202.61.144.0/21$ I and II only II and III only III and IV only I and IV only
8
The figure below shows an annular ring with outer and inner as $b$ and $a$, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum $n$ ... $\pi [(b^{2}-a^{2})+n(b-a)^{2}]$
9
Two transactions $T_1$ and $T_2$ are given as $T_1:r_1(X)w_1(X)r_1(Y)w_1(Y)$ $T_2:r_2(Y)w_2(Y)r_2(Z)w_2(Z)$ where $r_i(V)$ denotes a $\textit{read}$ operation by transaction $T_i$ on a variable $V$ and $w_i(V)$ denotes a $\textit{write}$ operation by transaction $T_i$ on a variable $V$. The total number of conflict serializable schedules that can be formed by $T_1$ and $T_2$ is ______
10
Consider the recurrence function $T(n) = \begin{cases} 2T(\sqrt{n})+1, & n>2 \\ 2, & 0 < n \leq 2 \end{cases}$ Then $T(n)$ in terms of $\Theta$ notation is $\Theta(\log \log n)$ $\Theta( \log n)$ $\Theta (\sqrt{n})$ $\Theta(n)$
11
If the characteristic polynomial of a 3 $\times$ 3 matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \mathbb{R}$, and one eigenvalue of $M$ is 2, then the largest among the absolute values of the eigenvalues of $M$ is _______
12
Consider the following languages. $L_1 = \{a^p \mid p \text{ is a prime number} \}$ $L_2 = \{ a^nb^mc^{2m} \mid n \geq 0, m \geq 0 \}$ $L_3 = \{a^n b^n c^{2n} \mid n \geq 0 \}$ $L_4 = \{ a^n b^n \mid n \geq 1\}$ Which of the ... $L_2$ is not context free $L_3$ is not context free but recursive $L_4$ is deterministic context free I, II and IV only II and III only I and IV only III and IV only
13
Consider a machine with a byte addressable main memory of $2^{32}$ bytes divided into blocks of size 32 bytes. Assume that a direct mapped cache having 512 cache lines is used with this machine. The size of the tag field in bits is _______
14
Let $L(R)$ be the language represented by regular expression $R$. Let $L(G)$ be the language generated by a context free grammar $G$. Let $L(M)$ be the language accepted by a Turing machine $M$. Which of the following decision problems are undecidable? Given a regular expression $R$ and a ... $w$, is $w \in L(M)$? I and IV only II and III only II, III and IV only III and IV only
15
The read access times and the hit ratios for different caches in a memory hierarchy are as given below: $\begin{array}{|l|c|c|} \hline \text {Cache} & \text{Read access time (in nanoseconds)}& \text{Hit ratio} \\\hline \text{$ ... are for instruction fetch and $40$% are for memory operand fetch. The average read access time in nanoseconds (up to $2$ decimal places) is _________
16
$G$ is an undirected graph with $n$ vertices and $25$ edges such that each vertex of $G$ has degree at least $3$. Then the maximum possible value of $n$ is _________ .
17
Match the following according to input (from the left column) to the compiler phase (in the right column) that processes it: ... $\text{P-iii; Q-iv; R-i; S-ii}$ $\text{P-i; Q-iv; R-ii; S-iii}$
18
In a B+ Tree , if the search-key value is $8$ bytes long , the block size is $512$ bytes and the pointer size is $2$ B , then the maximum order of the B+ Tree is ____
19
Consider the set of process with arrival time (in milliseonds), CPU burst time (in millisecods) and priority ($0$ ... The average waiting time (in milli seconds) of all the process using premtive priority scheduling algorithm is ______
20
Consider two hosts $X$ and $Y$, connected by a single direct link of rate $10^6 \hspace{0.1cm} bits/sec$. The distance between the two hosts is $10,000 \hspace{0.1cm} km$ and the propagation speed along the link is $2 \times 10^8 \hspace{0.1cm} m/sec$. Host $X$ ... value of $p$ and $q$ are $p=50$ and $q=100$ $p=50$ and $q=400$ $p=100$ and $q=50$ $p=400$ and $q=50$
21
$X$ is a $30$ digit number starting with the digit $4$ followed by the digit $7$. Then the number $X^3$ will have $90$ digits $91$ digits $92$ digits $93$ digits
22
A test has twenty questions worth $100$ marks in total. There are two types of questions. Multiple choice questions are worth $3$ marks each and essay questions are worth $11$ marks each. How many multiple choice questions does the exam have? $12$ $15$ $18$ $19$
23
A system shares $9$ ... of the following best describes current state of the system? Safe, Deadlocked Safe, Not Deadlocked Not Safe, Deadlocked Not Safe, Not Deadlocked
24
The representation of the value of a $16-bit$ unsigned integer $X$ in hexadecimal number system is $BCA9$. The representation of the value of $X$ in octal number system is $571244$ $736251$ $571247$ $136251$
25
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 _______
26
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 $\Theta(n \sqrt{n})$ $\Theta(n^2)$ $\Theta(n \: \log n)$ $\Theta(n^2 \log n)$
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 $\frac{2}{\pi}$ and $\frac{16}{\pi}$ $\frac{2}{\pi}$ and 0 $\frac{4}{\pi}$ and 0 $\frac{4}{\pi}$ and $\frac{16}{\pi}$
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: $0, 0$ $0, 1$ $1, 0$ $1, 1$