Answers by rfzahid / GATE Overflow for GATE CSE

1 votes

1

GATE CSE 2004 | Question: 61
Consider the partial implementation of a $2-bit$ counter using $T$ flip-flops following the sequence $0-2-3-1-0,$ as shown below. To complete the circuit, the input $X$ should be $Q_2^c$ $Q_2 + Q_1$ $\left(Q_1 + Q_2\right)^c$ $Q_1 \oplus Q_2$

Consider the partial implementation of a $2-bit$ counter using $T$ flip-flops following the sequence $0-2-3-1-0,$ as shown below.To complete the circuit, the input $X$ sh...

19.3k views

answered Jan 5, 2019

3 votes

2

GATE CSE 2018 | Question: 35
Consider the following languages: $\{a^mb^nc^pd^q \mid m+p=n+q, \text{ where } m, n, p, q \geq 0 \}$ $\{a^mb^nc^pd^q \mid m=n \text{ and }p=q, \text{ where } m, n, p, q \geq 0 \}$ ... Which of the above languages are context-free? I and IV only I and II only II and III only II and IV only

Consider the following languages:$\{a^mb^nc^pd^q \mid m+p=n+q, \text{ where } m, n, p, q \geq 0 \}$$\{a^mb^nc^pd^q \mid m=n \text{ and }p=q, \text{ where } m, n, p, q \ge...

21.2k views

answered Dec 27, 2018

0 votes

3

GATE CSE 1992 | Question: 8
Let $T$ be a Depth First Tree of a undirected graph $G$. An array $P$ indexed by the vertices of $G$ is given. $P[V]$ is the parent of vertex $V$, in $T$. Parent of the root is the root itself. Give a method for finding ... to the length of the cycle. Describe the algorithm in a PASCAL $(C)$ - like language. Assume that the variables have been suitably declared.

Let $T$ be a Depth First Tree of a undirected graph $G$. An array $P$ indexed by the vertices of $G$ is given. $P[V]$ is the parent of vertex $V$, in $T$. Parent of the r...

5.0k views

answered Oct 28, 2018

0 votes

4

GATE CSE 2006 | Question: 54
Given two arrays of numbers $a_{1},...,a_{n}$ and $b_{1},...,b_{n}$ where each number is $0$ or $1$, the fastest algorithm to find the largest span $(i, j)$ such that $ a_{i}+a_{i+1}+\dots+a_{j}=b_{i}+b_{i+1}+\dots+b_{j}$ ... time in the key comparison mode Takes $\Theta (n)$ time and space Takes $O(\sqrt n)$ time only if the sum of the $2n$ elements is an even number

Given two arrays of numbers $a_{1},...,a_{n}$ and $b_{1},...,b_{n}$ where each number is $0$ or $1$, the fastest algorithm to find the largest span $(i, j)$ such that $ a...

29.3k views

answered Oct 21, 2018

2 votes

5

ISI 2014
Number of integers $x$ between $1$ and $95$ such that $96$ divides $60x$ is $0$ $7$ $8$ $11$

Number of integers $x$ between $1$ and $95$ such that $96$ divides $60x$ is$0$$7$$8$$11$

388 views

answered Mar 15, 2018

3 votes

6

NIELIT 2017 DEC Scientist B - Section B: 45
The string $1101$ does not belong to the set represented by $(00+(11)^*0)$ $1(0+1)^*101$ $(10)^*(01)^*(00+11)^*$ $110^*(0+1)$

The string $1101$ does not belong to the set represented by$(00+(11)^*0)$$1(0+1)^*101$$(10)^*(01)^*(00+11)^*$$110^*(0+1)$

1.6k views

answered Dec 18, 2017

1 votes

7

NIELIT 2017 DEC Scientist B - Section B: 35
Which of the following regular expression is equal to $(r_1+r_2)^*$? $r_1^*r_2^*$ $(r_1r_2)^*$ $r_1^*r_2^*+r_1r_2$ $(r_1^*r_2^*)^*$

Which of the following regular expression is equal to $(r_1+r_2)^*$?$r_1^*r_2^*$$(r_1r_2)^*$$r_1^*r_2^*+r_1r_2$$(r_1^*r_2^*)^*$

711 views

answered Dec 18, 2017

2 votes

8

Probability
From a gift pack of 5 items, 3 items are drawn, found that all of them are in red color. What is the probability that all are red?

From a gift pack of 5 items, 3 items are drawn, found that all of them are in red color. What is the probability that all are red?

318 views

answered Dec 11, 2017

8 votes

9

TIFR CSE 2018 | Part A | Question: 8
A crime has been committed with four people at the scene of the crime. You are responsible for finding out who did it. You have recorded the following statements from the four witnesses, and you know one of them has committed the crime. ... $\text{Desmond}$ $\text{Either Anuj or Binky; the information is insufficient to pinpoint the criminal}$

A crime has been committed with four people at the scene of the crime. You are responsible for finding out who did it. You have recorded the following statements from the...

1.6k views

answered Dec 11, 2017

5 votes

10

TIFR CSE 2018 | Part B | Question: 6
Consider the following implementation of a binary tree data strucrure. The operator $+$ denotes list-concatenation. That is, $[a,b,c]+[d,e]=[a,b,c,d,e].$ struct TreeNode: int value TreeNode leftChild TreeNode rightChild function preOrder(T): if T == null: ... $\text{Cannot be uniquely determined from given information.}$

Consider the following implementation of a binary tree data strucrure. The operator $+$ denotes list-concatenation.That is, $[a,b,c]+[d,e]=[a,b,c,d,e].$struct TreeNode: i...

1.4k views

answered Dec 11, 2017

1 votes

11

TIFR CSE 2018 | Part B | Question: 1
What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$

What is the remainder when $4444^{4444}$ is divided by $9?$$1$$2$$5$$7$$8$

3.3k views

answered Dec 10, 2017

30 votes

12

TIFR CSE 2018 | Part A | Question: 9
How many ways are there to assign colours from range $\left\{1,2,\ldots,r\right\}$ to vertices of the following graph so that adjacent vertices receive distinct colours? $r^{4}$ $r^{4} - 4r^{3}$ $r^{4}-5r^{3}+8r^{2}-4r$ $r^{4}-4r^{3}+9r^{2}-3r$ $r^{4}-5r^{3}+10r^{2}-15r$

How many ways are there to assign colours from range $\left\{1,2,\ldots,r\right\}$ to vertices of the following graph so that adjacent vertices receive distinct colours?...

4.6k views

answered Dec 10, 2017

7 votes

13

GATE2016 CE-2: GA-10
Ananth takes $6$ hours and Bharath takes $4$ hours to read a book. Both started reading copies of the book at the same time. After how many hours is the number of pages to be read by Ananth, twice that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace. $1$ $2$ $3$ $4$

Ananth takes $6$ hours and Bharath takes $4$ hours to read a book. Both started reading copies of the book at the same time. After how many hours is the number of pages t...

8.8k views

answered Oct 3, 2017

1 votes

14

NPTEL Question
Find the particular solution of the given Recurrence relation or Difference equation. ar - 5ar-1 + 6ar-2 = 2r + r

Find the particular solution of the given Recurrence relation or Difference equation.ar - 5ar-1 + 6ar-2 = 2r + r

3.4k views

answered Sep 3, 2017

10 votes

15

Equivalence and Inverse of Relation.
Proof the following statement. 1. If R1 and R2 are the equivalence relation on X then R1 $\cap$ $R2^{-1}$ (Inverse of R2) is also an equivalence relation. 2. If R is reflexive and transitive relation on X then R $\cap$ $R^{-1}$ is an equivalence relation.

Proof the following statement.1. If R1 and R2 are the equivalence relation on X then R1 $\cap$ $R2^{-1}$ (Inverse of R2) is also an equivalence relation.2. If R is reflex...

1.6k views

answered Sep 3, 2017

29 votes

16

GATE CSE 1998 | Question: 10b
Let $R$ be a binary relation on $A = \{a, b, c, d, e, f, g, h\}$ represented by the following two component digraph. Find the smallest integers $m$ and $n$ such that $m < n$ and $R^m = R^n$.

Let $R$ be a binary relation on $A = \{a, b, c, d, e, f, g, h\}$ represented by the following two component digraph. Find the smallest integers $m$ and $n$ such that $m <...

4.2k views

answered Aug 23, 2017

23 votes

17

GATE1991-15,a
Show that the product of the least common multiple and the greatest common divisor of two positive integers $a$ and $b$ is $a\times b$.

Show that the product of the least common multiple and the greatest common divisor of two p...

2.0k views

answered Aug 13, 2017

8 votes

18

TIFR CSE 2010 | Part B | Question: 37
Consider the program where $a, b$ are integers with $b > 0$. x:=a; y:=b; z:=0; while y > 0 do if odd (x) then z:= z + x; y:= y - 1; else y:= y % 2; x:= 2 * x; fi Invariant of the loop is a condition which is ... terminate for some values of $a, b$ but when it does terminate, the condition $z = a * b$ will hold. The program will terminate with $z=a^{b}$

Consider the program where $a, b$ are integers with $b 0$.x:=a; y:=b; z:=0; while y 0 do if odd (x) then z:= z + x; y:= y - 1; else y:= y % 2; x:= 2 * x; fiInvariant of...

3.3k views

answered Apr 7, 2017

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