List of practice Questions

Consider the table Student with attributes (rollNum, name, gender, marks). The primary key is rollNum. The SQL query is:

SELECT *
FROM Student
WHERE gender = 'F' AND marks > 65;

The number of rows returned by this query is:

A new reliable byte-stream protocol (myTCP) runs over a 100 Mbps network with RTT = 150 ms and maximum segment lifetime (MSL) = 2 minutes. Which of the following are valid sequence number field lengths?

Let \(X\) be a set and \(2^{X}\) denote the power set of \(X\). Define a binary operation \(\,\Delta\,\) on \(2^{X}\) by \(A \Delta B = (A-B)\cup(B-A)\) (symmetric difference). Let \(H=(2^{X},\Delta)\). Which of the following statements about \(H\) is/are correct?

Suppose in a web browser you click on www.gate-2023.in. The browser cache is empty. The DNS address is not cached, so an iterative DNS lookup across 3 tiers is required. Let RTT denote the round trip time between your host and either a DNS server or the web server. RTT between local host and web server is also equal to RTT. The HTML page is very small and references 10 small objects from the same server. Neglect transmission and rendering time. Which of the following statements is/are CORRECT about the minimum elapsed time between clicking the URL and full rendering?

Consider a random experiment where two fair coins are tossed. Let $A$ be the event that denotes HEAD on both throws, $B$ the event that denotes HEAD on the first throw, and $C$ the event that denotes HEAD on the second throw. Which of the following statements is/are TRUE?

Consider functions Function_1 and Function_2 as follows. Let \(f_1(n)\) and \(f_2(n)\) be the number of times the statement \(x = x + 1\) executes in Function_1 and Function_2, respectively. Which statements are TRUE?

Function_1                          Function_2
while n>1 do                      for i = 1 to 100 * n do
  for i = 1 to n do                   x = x + 1;
    x = x + 1;                      end for
  end for
  n = floor(n/2);
end while

Let \(G\) be a simple, finite, undirected graph with vertex set \(\{v_1, \ldots, v_n\}\). Let \(\Delta(G)\) denote the maximum degree of \(G\) and let \(\mathbb{N}=\{1,2,\ldots\}\) denote the set of all possible colors. Color the vertices of \(G\) using the following greedy strategy: for \(i = 1, \ldots, n\), \[ \text{color}(v_i) \leftarrow \min\{j \in \mathbb{N} : \ \text{no neighbour of } v_i \text{ is colored } j\}. \] Which of the following statements is/are TRUE?

Let $f:A\to B$ be an onto (surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on $A$ by $a_1\sim a_2$ iff $f(a_1)=f(a_2)$. Let $\mathcal{E=\{[x]:x\in A\}$ be the set of all equivalence classes under $\sim$. Define $F:\mathcal{E}\to B$ by $F([x])=f(x)$ for all classes $[x]\in\mathcal{E}$. Which of the following statements is/are TRUE?}

Consider the IEEE-754 single precision floating point numbers $P=0xC1800000$ and $Q=0x3F5C2EF4$. Which one of the following corresponds to the product $P \times Q$, represented in IEEE-754 single precision format?

Consider the two functions incr and decr below. Five threads each call incr once and three threads each call decr once on the same shared variable \(X\) (initially \(10\)). There are two semaphore implementations:

I-1: \(s\) is a binary semaphore initialized to \(1\).
I-2: \(s\) is a counting semaphore initialized to \(2\).

Let \(V_1, V_2\) be the values of \(X\) at the end of all threads for I-1 and I-2, respectively. Which choice gives the minimum possible values of \(V_1, V_2\)?

incr(){              
  wait(s);           
  X = X + 1;         
  signal(s);         
}

decr(){
  wait(s);
  X = X - 1;
  signal(s);
}

Consider the context-free grammar \(G\) below: \[ S \;\to\; aSb \;|\; X \] \[ X \;\to\; aX \;|\; Xb \;|\; a \;|\; b \] where \(S\) and \(X\) are non-terminals, and \(a\) and \(b\) are terminal symbols. The starting non-terminal is \(S\). Which one of the following statements is CORRECT?

A particular number is written as $132$ in radix-$4$ representation. The same number in radix-$5$ representation is ________

Consider a 3-stage pipelined processor having a delay of 10 ns, 20 ns, and 14 ns for the first, second, and third stages, respectively. Assume that there is no other delay and the processor does not suffer from any pipeline hazards. Also assume that one instruction is fetched every cycle.
The total execution time for executing 100 instructions on this processor is ________ ns.

A keyboard connected to a computer is used at a rate of 1 keystroke per second. The computer polls the keyboard every 10 ms, each poll takes 100 \(\mu s\). If a key is detected, an additional 200 \(\mu s\) is used for processing. Let \(T_1\) be the fraction of a second spent in polling and processing a keystroke. In an alternative implementation with interrupts, each keystroke requires 1 ms to service and process. Let \(T_2\) be the fraction of a second in the interrupt method. Find the ratio \(T_1/T_2\).

The integer value printed by the ANSI-C program given below is ________.

int funcp(){
    static int x = 1;
    x++;
    return x;
}

int main(){
    int x,y;
    x = funcp();
    y = funcp() + x;
    printf("%d\n", (x+y));
    return 0;
}

The value of the definite integral \(\displaystyle \int_{-3}^{3}\int_{-2}^{2}\int_{-1}^{1}\big(4x^{2}y - z^{3}\big)\,dz\,dy\,dx\) is ________. (Rounded off to the nearest integer)

Let \[ f(x) = x^3 + 15x^2 - 33x - 36 \] be a real-valued function. Which of the following statements is/are TRUE?

Let $f$ and $g$ be functions of natural numbers given by $f(n)=n$ and $g(n)=n^2$. Which of the following statements is/are TRUE?

Which one or more of the following need to be saved on a context switch from one thread (T1) of a process to another thread (T2) of the same process?

Which one or more of the following options guarantee that a computer system will transition from user mode to kernel mode?

Which of the following statements is/are CORRECT?

Which of the following statements is/are INCORRECT about the OSPF (Open Shortest Path First) routing protocol used in the Internet?

Geetha has a conjecture about integers, of the form \[ \forall x \big(P(x) \Rightarrow \exists y \, Q(x,y)\big) \] where \(P\) is a statement about integers and \(Q\) is a statement about pairs of integers. Which of the following option(s) would imply Geetha's conjecture?

Which one or more of the following CPU scheduling algorithms can potentially cause starvation?

Which one of the options given below refers to the degree (or arity) of a relation in relational database systems?