Recent activity by s.abhishek1992 / GATE Overflow for GATE CSE

3 answers

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GATE CSE 2014 Set 1 | Question: 3
Let $G=(V,E)$ be a directed graph where $V$ is the set of vertices and $E$ the set of edges. Then which one of the following graphs has the same strongly connected components as $G$ ? $G_1$ = $(V,E_1)$ ... $u$ to $v$ in $E\}$ $G_4$ = $(V_4,E)$ where $V_4$ is the set of vertices in $G$ which are not isolated

Let $G=(V,E)$ be a directed graph where $V$ is the set of vertices and $E$ the set of edges. Then which one of the following graphs has the same strongly connected compon...

17.1k views

commented Oct 22, 2017

4 answers

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GATE CSE 1997 | Question: 14
Let $R$ be a reflexive and transitive relation on a set $A$. Define a new relation $E$ on $A$ as $E=\{(a, b) \mid (a, b) \in R \text{ and } (b, a) \in R \}$ Prove that $E$ is an equivalence relation on $A$. Define a relation $\leq$ on the equivalence ... $\exists a, b$ such that $a \in E_1, b \in E_2 \text{ and } (a, b) \in R$. Prove that $\leq$ is a partial order.

Let $R$ be a reflexive and transitive relation on a set $A$. Define a new relation $E$ on $A$ as$E=\{(a, b) \mid (a, b) \in R \text{ and } (b, a) \in R \}$Prove that $E$ ...

4.0k views

commented Oct 7, 2017

5 answers

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TIFR CSE 2014 | Part B | Question: 16
Consider the ordering relation $x\mid y \subseteq N \times N$ over natural numbers $N$ such that $x \mid y$ if there exists $z \in N$ such that $x ∙ z = y$. A set is called lattice if every finite subset has a least upper bound and greatest lower ... $(N, \mid)$ is a complete lattice. $(N, \mid)$ is a lattice but not a complete lattice.

Consider the ordering relation $x\mid y \subseteq N \times N$ over natural numbers $N$ such that $x \mid y$ if there exists $z \in N$ such that $x ∙ z = y$. A set is ca...

5.3k views

commented Oct 6, 2017

4 answers

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TIFR CSE 2012 | Part B | Question: 4
Let $\wedge $, $\vee $ denote the meet and join operations of lattice. A lattice is called distributive if for all $x, y, z,$ ... , but not distributive lattice. Distributive lattice. Lattice but not a complete lattice. Under the give ordering positive integers do not form a lattice.

Let $\wedge $, $\vee $ denote the meet and join operations of lattice. A lattice is called distributive if for all $x, y, z,$$x\wedge \left ( y\vee z \right )= \left ( x\...

4.5k views

commented Oct 3, 2017

5 answers

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TIFR CSE 2013 | Part A | Question: 14
An unbiased die is thrown $n$ times. The probability that the product of numbers would be even is $\dfrac{1}{(2n)}$ $\dfrac{1}{[(6n)!]}$ $1 - 6^{-n}$ $6^{-n}$ None of the above

An unbiased die is thrown $n$ times. The probability that the product of numbers would be even is$\dfrac{1}{(2n)}$$\dfrac{1}{[(6n)!]}$$1 - 6^{-n}$$6^{-n}$None of the abov...

1.7k views

commented Jul 29, 2017

6 answers

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GATE CSE 2004 | Question: 78
Two $n$ bit binary strings, $S_1$ and $S_2$ are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings differ) is equal to $d$ is $\dfrac{^{n}C_{d}}{2^{n}}$ $\dfrac{^{n}C_{d}}{2^{d}}$ $\dfrac{d}{2^{n}}$ $\dfrac{1}{2^{d}}$

Two $n$ bit binary strings, $S_1$ and $S_2$ are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of b...

7.5k views

commented Jul 29, 2017

2 answers

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TIFR CSE 2012 | Part A | Question: 19
An electric circuit between two terminals $A$ and $B$ is shown in the figure below, where the numbers indicate the probabilities of failure for the various links, which are all independent. What is the probability that $A$ and $B$ ... $\left(\dfrac{1}{1200}\right)$ $\left(\dfrac{1199}{1200}\right)$ $\left(\dfrac{59}{60}\right)$

An electric circuit between two terminals $A$ and $B$ is shown in the figure below, where the numbers indicate the probabilities of failure for the various links, which a...

2.6k views

commented Jul 29, 2017

6 answers

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TIFR CSE 2010 | Part A | Question: 19, TIFR CSE 2014 | Part A | Question: 6
Karan tells truth with probability $\dfrac{1}{3}$ and lies with probability $\dfrac{2}{3}.$ Independently, Arjun tells truth with probability $\dfrac{3}{4}$ and lies with probability $\dfrac{1}{4}.$ Both watch a cricket match. Arjun tells ... $\left(\dfrac{5}{6}\right)$ $\left(\dfrac{6}{7}\right)$

Karan tells truth with probability $\dfrac{1}{3}$ and lies with probability $\dfrac{2}{3}.$ Independently, Arjun tells truth with probability $\dfrac{3}{4}$ and lies with...

6.1k views

commented Jul 28, 2017

11 answers

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TIFR CSE 2012 | Part A | Question: 1
Amar and Akbar both tell the truth with probability $\dfrac{3 } {4}$ and lie with probability $\dfrac{1}{4}$. Amar watches a test match and talks to Akbar about the outcome. Akbar, in turn, tells Anthony, "Amar told me that India won". What ... $\left(\dfrac{7}{16}\right)$ $\left(\dfrac{10}{16}\right)$ None of the above

Amar and Akbar both tell the truth with probability $\dfrac{3 } {4}$ and lie with probability $\dfrac{1}{4}$. Amar watches a test match and talks to Akbar about the outco...

9.5k views

commented Jul 28, 2017

3 answers

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GATE CSE 1994 | Question: 21
Consider the following recursive function: function fib (n:integer);integer; begin if (n=0) or (n=1) then fib := 1 else fib := fib(n-1) + fib(n-2) end; The above function is run on a computer with a stack of $64$ bytes. Assuming ... an address takes $2$ bytes each, estimate the maximum value of $n$ for which the stack will not overflow. Give reasons for your answer.

Consider the following recursive function:function fib (n:integer);integer; begin if (n=0) or (n=1) then fib := 1 else fib := fib(n-1) + fib(n-2) end;The above function i...

25.7k views

commented Jul 26, 2017

3 answers

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GATE CSE 1991 | Question: 1,vi
Consider the following PASCAL program segment: if i mod 2 = 0 then while i >= 0 do begin i := i div 2; if i mod 2 < > 0 then i := i - 1; else i := i – 2; end; An appropriate loop-invariant for the while-loop is ________

Consider the following PASCAL program segment:if i mod 2 = 0 then while i >= 0 do begin i := i div 2; if i mod 2 < 0 then i := i - 1; else i := i – 2; end;An appropria...

4.6k views

commented Jul 24, 2017

2 answers

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#probability
An urn contains 3 red and 7 black balls. Players A and B withdraw balls from the urn consecutively until a red ball is selected. Find the probability that A selects the red ball. (A draws the first ball, then B, and so on. There is no replacement of the balls drawn.)

An urn contains 3 red and 7 black balls. Players Aand B withdraw balls from the urn consecutivelyuntil a red ball is selected. Find the probability thatA selects the red ...

980 views

commented Jun 2, 2017

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