Recent questions tagged goclasses2024-mockgate-13

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A total of $n$ points are equally spaced around a circle and are labelled with the integers $1$ to $n$, in order. Two points are called diametrically opposite if the line...
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In a factory, Erika assembles $3$ calculators in the same amount of time that Nick assembles $2$ calculators. Also, Nick assembles $1$ calculator in the same amount of ti...
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A small square is drawn inside a larger square as shown. The area of the shaded region and the area of the unshaded region are each $18 \mathrm{~cm}^2$. What is the side ...
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Chris received a mark of $50 \%$ on a recent test. Chris answered $13$ of the first $20$ questions correctly. Chris also answered $25 \%$ of the remaining questions on th...
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A positive integer $n$ is a multiple of $7.$ The square root of $n$ is between $17$ and $18.$ How many possible values of $n$ are there?$2$$3$$4$$5$
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Ben participates in a prize draw. He receives one prize that is equally likely to be worth $\$ 5, \$ 10$ or $\$ 20$. Jamie participates in a different prize draw. She rec...
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Five balls, numbered $1$ to $5,$ are placed in order on a table. A sequence of steps is performed on the balls. In step $1,$ the rightmost ball is picked up and put in th...
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Reading from left to right, the sequence consists of $6\;\text{X's},$ followed by $24\; \text{Y's},$ followed by $96\;\text{X's}.$ Hence, there are a total of $126$ lette...
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The significance of the Magna Carta lies not in its ________ provisions, but in its broader impact: it made the king subject to the law.specificrevolutionaryimplicitcontr...
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Let $f(x)$ be a real-valued function all of whose derivatives exist. Recall that a point $x_0$ in the domain is called an inflection point of $f(x)$ if the second derivat...
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Let $x$ be a random variable possessing the probability density function$$f(x)= \begin{cases}c x & , x \in[0,10] \\ 0 & , \text { otherwise }\end{cases}$$where $c \in \ma...
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If $A$ is a $3 \times 3$ matrix such that $A\left(\begin{array}{l}0 \\ 1 \\ 2\end{array}\right)=\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)$ and $A\left(\begin{ar...
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Given that $f(n)=O(g(n))$ (where $\mathrm{O}$ is Big-O) and $f(n)=\Omega(g(n))$, which of the following statement is always true?$f(n)=o(g(n))$ (here $o$ is small-$o).$$f...
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Professor Fiorina uses the following algorithm to merge $k$ sorted lists, each containing $n / k$ elements.She takes the first list and merges it with the second list usi...
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Suppose we constructed the binary search tree shown by starting with an empty tree and inserting one element at a time from an input sequence, without any rotations or ot...
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Suppose that a binary min-heap stores six elements with priorities $10,20,30,40,50$, and $60$ in its array $\text{A}.$ What is the largest of these items that could be st...
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What will be output printed by the following program?#include<stdio.h main() { int c=4; switch(c) { c=c-1; case 4: printf("IITB ")...
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What will be the output of the following program?#include <stdio.h int main() { int a = { {1, 2}, {3, 4} }; int (*p) ; p = &a; printf("%d", (*p)[0] ); return 0; }$1$$2...
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Suppose we have a multi-level index file system, and this file system has $512$ Bytes blocks, inodes with $3$ direct, $1$ single-indirect, $2$ double-indirect, and $1$ tr...
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Consider a virtual memory system that uses paging. Virtual and physical addresses are both $32$ bits long, and the page size is $4 \textsf{KB}=2^{12}$ bytes. A process $\...
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An IP router implementing Classless Inter-domain Routing (CIDR) receives a packet with address $128.96.39.10.$The router's routing table has the following entries:$$\begi...
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Which of the following statements is/are false?If a context-free grammar $\mathrm{G}$ is in Chomsky's normal form, then $\mathrm{G}$ is not ambiguous.For every number $n$...
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Let $\mathrm{M}$ be a $8$-state Deterministic Finite Automaton over the alphabet $\{a, b, c\}$. If the language accepted by $\text{M}$ i.e. $\text{L(M)}$ is finite, then ...
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A garage door opens if it ever sees the password $011$ in a transmission. More formally, this FSM takes a bitstring consisting of $\text{0's}$ and $\text{1's}$ as its inp...
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The figure below represents the Karnaugh map for a function $\text{F(A,B,C,D).}$ Note, $\text{‘X’}$ stands for don’t care.The simplified logical expression in the s...
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What statement is correct for $f(A, B)$ in the following circuit?$f(A, B)=\overline{\overline{A \cdot B} \cdot(A+B)}$ when Control $=1$$f(A, B)=A \cdot B$ when Control $=...
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A group $G$ in which $(a b)^2=a^2 b^2$ for all $a, b$ in $G$ is necessarilyfinitecyclicabeliannone of the above
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In two's complement, what is the minimum number of bits needed to represent the numbers $-1$ and the number $1$ respectively?$1$ and $2$$2$ and $2$$2$ and $1$$1$ and $1$
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Let $\text{R}_1, \text{R}_2, \ldots,\text{ }R_n$ be a decomposition of schema $\text{U}$. Let $u(\text{U})$ be a relation, and let $r_i=\Pi_{\text{R}_i}(u)$Which of the f...