Answers by Sourajit25 / GATE Overflow for GATE CSE

1 votes

1

ISI2017-PCB-CS-8-b
Consider a simple code $\mathcal{C}$ for error detection and correction. Each codeword in $\mathcal{C}$ consists of $2$ data bits $[d_1, d_0]$ followed by check bits $[c_2, c_1, c_0]$ ... . Write down all the codewords for $\mathcal{C}$ Determine the minimum Hamming distance between any two distinct codewords of $\mathcal{C}$

Consider a simple code $\mathcal{C}$ for error detection and correction. Each codeword in $\mathcal{C}$ consists of $2$ data bits $[d_1, d_0]$ followed by check bits $[c_...

773 views

answered Aug 24, 2020

1 votes

2

Kenneth Rosen Edition 7 Exercise 6.1 Question 6 (Page No. 396)
There are four major auto routes from Boston to Detroit and six from Detroit to Los Angeles. How many major auto routes are there from Boston to Los Angeles via Detroit?

There are four major auto routes from Boston to Detroit and six from Detroit to Los Angeles. How many major auto routes are there from Boston to Los Angeles via Detroit?

3.8k views

answered Apr 28, 2020

5 votes

3

TIFR CSE 2020 | Part A | Question: 6
What is the maximum number of regions that the plane $\mathbb{R}^{2}$ can be partitioned into using $10$ lines? $25$ $50$ $55$ $56$ $1024$ Hint: Let $A(n)$ be the maximum number of partitions that can be made by $n$ lines. Observe that $A(0) = 1, A(2) = 2, A(2) = 4$ etc. Come up with a recurrence equation for $A(n)$.

What is the maximum number of regions that the plane $\mathbb{R}^{2}$ can be partitioned into using $10$ lines?$25$$50$$55$$56$$1024$Hint: Let $A(n)$ be the maximum numbe...

830 views

answered Feb 11, 2020

2 votes

4

TIFR CSE 2020 | Part A | Question: 10
In a certain year, there were exactly four Fridays and exactly four Mondays in January. On what day of the week did the $20^{th}$ of the January fall that year (recall that January has $31$ days)? Sunday Monday Wednesday Friday None of the others

In a certain year, there were exactly four Fridays and exactly four Mondays in January. On what day of the week did the $20^{th}$ of the January fall that year (recall th...

2.2k views

answered Feb 11, 2020

3 votes

5

TIFR CSE 2020 | Part A | Question: 9
A contiguous part, i.e., a set of adjacent sheets, is missing from Tharoor's GRE preparation book. The number on the first missing page is $183$, and it is known that the number on the last missing page has the same three digits, but in a different ... front and one at the back. How many pages are missing from Tharoor's book? $45$ $135$ $136$ $198$ $450$

A contiguous part, i.e., a set of adjacent sheets, is missing from Tharoor’s GRE preparation book. The number on the first missing page is $183$, and it is known that t...

895 views

answered Feb 11, 2020

2 votes

6

Is L CFL or not?
L ={ww | w ∈{a, b}∗} Is compliment of L, CFL? Support with reason

L ={ww | w ∈{a, b}∗}Is compliment of L, CFL? Support with reason

3.0k views

answered Jan 21, 2020

4 votes

7

#ADDRESS INSTRUCTION
Consider the hypothetical processor is supports both 2 address and one address instructions.It has 128 word memory A 16-bit instruction is placed in the one memory word. Q1.What is the range of two address and one address instructions are supported. A)1 to ... 2-address instructions are already existed.How many one address instructions can be supported ? A)128 B)2 C)256 D)32

Consider the hypothetical processor is supports both 2 address and one address instructions.It has 128 word memory A 16-bit instruction is placed in the one memory word.Q...

16.7k views

answered Jan 17, 2020

1 votes

8

How much time will the processor be slowed down due to DMA activity?
A processor is fetching instructions at the rate of 1 MIPS.A DMA module is used to transfer characters to RAM from a device transmitting at 9600 bps.How much time will the processor be slowed down due to DMA activity? a)9.6 ms b)4.8 ms c)2.4 ms d)1.2 ms

A processor is fetching instructions at the rate of 1 MIPS.A DMA module is used to transfer characters to RAM from a device transmitting at 9600 bps.How much time will th...

11.0k views

answered Dec 30, 2019

54 votes

9

GATE CSE 2006 | Question: 24
Given a set of elements $N = {1, 2, ..., n}$ and two arbitrary subsets $A⊆N$ and $B⊆N$, how many of the n! permutations $\pi$ from $N$ to $N$ satisfy $\min(\pi(A)) = \min(\pi(B))$, where $\min(S)$ is the smallest integer in the set of integers $S$, and $\pi$(S) is the set of ... $n! \frac{|A ∩ B|}{|A ∪ B|}$ $\dfrac{|A ∩ B|^2}{^n \mathrm{C}_{|A ∪ B|}}$

Given a set of elements $N = {1, 2, ..., n}$ and two arbitrary subsets $A⊆N$ and $B⊆N$, how many of the n! permutations $\pi$ from $N$ to $N$ satisfy $\min(\pi(A)) = ...

11.2k views

answered Nov 7, 2019

3 votes

10

ISI2014-DCG-5
Consider the sets defined by the real solutions of the inequalities $A = \{(x,y):x^2+y^4 \leq 1\} \:\:\:\:\:\:\: B=\{(x,y):x^4+y^6 \leq 1\}$ Then $B \subseteq A$ $A \subseteq B$ Each of the sets $A – B, \: B – A$ and $A \cap B$ is non-empty none of the above

Consider the sets defined by the real solutions of the inequalities$A = \{(x,y):x^2+y^4 \leq 1\} \:\:\:\:\:\:\: B=\{(x,y):x^4+y^6 \leq 1\}$ Then$B \subseteq A$$A \subsete...

1.2k views

answered Oct 1, 2019

0 votes

11

ISI2014-DCG-30
Consider the equation $P(x) =x^3+px^2+qx+r=0$ where $p,q$ and $r$ are all real and positive. State which of the following statements is always correct. All roots of $P(x) = 0$ are real The equation $P(x)=0$ has at least one real root The equation $P(x)=0$ has no negative real root The equation $P(x)=0$ must have one positive and one negative real root

Consider the equation $P(x) =x^3+px^2+qx+r=0$ where $p,q$ and $r$ are all real and positive. State which of the following statements is always correct.All roots of $P(x) ...

419 views

answered Sep 24, 2019

1 votes

12

ISI2014-DCG-24
Let $f(x) = \dfrac{2x}{x-1}, \: x \neq 1$. State which of the following statements is true. For all real $y$, there exists $x$ such that $f(x)=y$ For all real $y \neq 1$, there exists $x$ such that $f(x)=y$ For all real $y \neq 2$, there exists $x$ such that $f(x)=y$ None of the above is true

Let $f(x) = \dfrac{2x}{x-1}, \: x \neq 1$. State which of the following statements is true.For all real $y$, there exists $x$ such that $f(x)=y$For all real $y \neq 1$, ...

419 views

answered Sep 24, 2019

10 votes

13

ISI2014-DCG-1
Let $(1+x)^n = C_0+C_1x+C_2x^2+ \dots + C_nx^n$, $n$ being a positive integer. The value of $\left( 1+\dfrac{C_0}{C_1} \right) \left( 1+\dfrac{C_1}{C_2} \right) \cdots \left( 1+\dfrac{C_{n-1}}{C_n} \right)$ is $\left( \frac{n+1}{n+2} \right) ^n$ $ \frac{n^n}{n!} $ $\left( \frac{n}{n+1} \right) ^n$ $ \frac{(n+1)^n}{n!} $

Let $(1+x)^n = C_0+C_1x+C_2x^2+ \dots + C_nx^n$, $n$ being a positive integer. The value of$$\left( 1+\dfrac{C_0}{C_1} \right) \left( 1+\dfrac{C_1}{C_2} \right) \cdots \l...

752 views

answered Sep 24, 2019

0 votes

14

ISI2015-DCG-32
The set of vectors constituting an orthogonal basis in $\mathbb{R} ^3$ is $\begin{Bmatrix} \begin{pmatrix} 1 \\ -1 \\ 0 \end{pmatrix}, & \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}, & \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \end{Bmatrix}$ ... None of these

The set of vectors constituting an orthogonal basis in $\mathbb{R} ^3$ is$\begin{Bmatrix} \begin{pmatrix} 1 \\ -1 \\ 0 \end{pmatrix}, & \begin{pmatrix} 1 \\ 1 \\ 0 \end{p...

991 views

answered Sep 23, 2019

2 votes

15

Linear Algebra (Self Doubt)
Let $A$ be a $n \times n$ square matrix whose all columns are independent. Is $Ax = b$ always solvable? Actually, I know that $Ax= b$ is solvable if $b$ is in the column space of $A$. However, I am not sure if it is solvable for all values of $b$.

Let $A$ be a $n \times n$ square matrix whose all columns are independent. Is $Ax = b$ always solvable?Actually, I know that $Ax= b$ is solvable if $b$ is in the column s...

671 views

answered Jun 7, 2019

4 votes

16

ACE Test series: Database

967 views

answered Jun 7, 2019

16 votes

17

WHAT AN INTERESTING DBMS QUESTION!!
Let $E1$ and $E2$ be two entities and $R$ is a relation between $E1$ and $E2$, then what is the minimum no of tables required to represent $E1, E2$ and $R$ if - 1. $E1$ and $E2$ have $1:m$ cardinality($E1$ on $1$ side ... $E1$ and $E2$ have total participation. Assume that there is no multi-valued attribute is present in any of the $10$ cases.

Let $E1$ and $E2$ be two entities and $R$ is a relation between $E1$ and $E2$, then what is the minimum no of tables required to represent $E1, E2$ and $R$ if -1. $E1$ an...

11.2k views

answered Jan 18, 2019

10 votes

18

toc dovetailing
can someone explain Dovetailing in TOC in simple terms and with examples what it is? why and where it is used? how it is used and how to visualize it ?

can someone explain Dovetailing in TOC in simple terms and with exampleswhat it is?why and where it is used?how it is used and how to visualize it ?

1.8k views

answered Aug 21, 2018

1 votes

19

GATE 2013
Its GATE 2013 question Consider the following operation along with Enqueue and Dequeue operations on queues, where k is a global parameter. MultiDequeue(Q){ m = k while (Q is not empty) and (m > 0) { Dequeue(Q) m = m - 1 } } What is the worst case time complexity of a ... performed on non-empty or full queue?? Due to this change will the answer remain same?? Θ(n) Θ(n + k) Θ(nk) Θ(n2)

Its GATE 2013 questionConsider the following operation along with Enqueue and Dequeue operations on queues, where kis a global parameter. MultiDequeue(Q){ m = k while (Q ...

1.0k views

answered May 1, 2018

0 votes

20

CMI2017-A-05
Let $G$ be an arbitrary graph on $n$ vertices with $4n − 16$ edges. Consider the following statements: There is a vertex of degree smaller than $8$ in $G$. There is a vertex such that there are less than $16$ vertices at a distance exactly $2$ from it. Which of the following is true: I Only II Only Both I and II Neither I nor II

Let $G$ be an arbitrary graph on $n$ vertices with $4n − 16$ edges. Consider the following statements:There is a vertex of degree smaller than $8$ in $G$.There is a ver...

1.2k views

answered Feb 10, 2018

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