Recent questions in Others / GATE Overflow for GATE CSE

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1321

CMI-2020-DataScience-B: 17
Consider the following code, where $A$ is an array of integers of size $\text{size(A)}$ with values $A[0] \;to\;A[\text{size(A)-1}]$, and $\text{reverse(A,i,j)}$ reverses the segment $\text{A[i]}$ to $\text{A[j]}$ if $\text{i<=j}$ and has ... this code on an input array $A$? Suppose $\text{size(A)}$ is $1000$. How many times is the test $\text{A[i]>A[p]}$ executed?

Consider the following code, where $A$ is an array of integers of size $\text{size(A)}$ with values $A[0] \;to\;A[\text{size(A)-1}]$, and $\text{reverse(A,i,j)}$ reverses...

soujanyareddy13

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soujanyareddy13 asked Jan 29, 2021

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1 answer

1322

CMI-2020-DataScience-B: 18
Eight students are to be seated around a circular table in a circular room. Two seatings are regarded as defining the same arrangements if each student has the same student on his or her right in both seatings: it does not matter which way they face. How ... of these $8$ students are there with $2$ chosen students, say student $A$ and student $B$, always sitting together?

Eight students are to be seated around a circular table in a circular room. Two seatings are regarded as defining the same arrangements if each student has the same stude...

soujanyareddy13

245 views

soujanyareddy13 asked Jan 29, 2021

0 votes

1 answer

1323

CMI-2020-DataScience-B: 19
Let $f$ be a continuous bijection from closed unit interval $[0,1]$ onto itself. (Recall the Intermediate Value Theorem: let $f$ be a real valued continuous function on an interval $[a,b]$. Let $c,d\in [a,b]$ ... point. Give an example of such a function where in the fixed point is unique and an example of a function with more than one fixed point.

Let $f$ be a continuous bijection from closed unit interval $[0,1]$ onto itself. (Recall the Intermediate Value Theorem: let $f$ be a real valued continuous function on a...

soujanyareddy13

270 views

soujanyareddy13 asked Jan 29, 2021

4 votes

3 answers

1324

CMI2020-A: 1
Which of the following languages over the alphabet $\{0,1\}$ are $not$ recognized by deterministic finite state automata $(DFA)$ with $three$ states? Words which do not have $11$ as a contiguous subword Binary representations of multiples of three Words that have $11$ as a suffix Words that do not contain $101$ as a contiguous subword

Which of the following languages over the alphabet $\{0,1\}$ are $not$ recognized by deterministic finite state automata $(DFA)$ with $three$ states?Words which do not ha...

soujanyareddy13

701 views

soujanyareddy13 asked Jan 28, 2021

0 votes

2 answers

1325

CMI2020-A: 2
Consider the following regular expressions over alphabet$\{a,b\}$, where the notation $(a+b)^+$ means $(a+b)(a+b)^*$: $r_1=(a+b)^+a(a+b)^*$ $r_2=(a+b)^*b(a+b)^+$ Let $L_1$ and $L_2$ be the languages defined by $r_1$ and $r_2$, respectively. Which of the following regular expressions define $L_1\cap L_2$? ... $(a+b)^*a\;b(a+b)^*$ $(a+b)^*b(a+b)^*a(a+b)^*$ $(a+b)^*a(a+b)^*b(a+b)^*$

Consider the following regular expressions over alphabet$\{a,b\}$, where the notation $(a+b)^+$ means $(a+b)(a+b)^*$:$$r_1=(a+b)^+a(a+b)^*$$$$r_2=(a+b)^*b(a+b)^+$$Let $L_...

soujanyareddy13

341 views

soujanyareddy13 asked Jan 28, 2021

0 votes

1 answer

1326

CMI2020-A: 3
Some children are given boxes containing sweets. Harish is happy if he gets either gems or toffees. Rekha is happy if she gets both bubble gums and peppermints. Some of the boxes are special, which means that if the box contains either gems or toffees, then it ... we infer? Harish is happy No bubble gums in Rekha's box No toffees in Harish's box There are peppermints in Rekha's box

Some children are given boxes containing sweets. Harish is happy if he gets either gems or toffees. Rekha is happy if she gets both bubble gums and peppermints. Some of t...

soujanyareddy13

296 views

soujanyareddy13 asked Jan 28, 2021

0 votes

1 answer

1327

CMI2020-A: 4
In a class, every student likes exactly one novelist and one musician. If two students like the same novelist, they also like the same musician. The class can be divided into novelist groups, each group consisting of all the students who like one novelist. ... For every musician group, there is a bigger novelist group For every novelist group, there is a musician group of the same size

In a class, every student likes exactly one novelist and one musician. If two students like the same novelist, they also like the same musician. The class can be divided ...

soujanyareddy13

201 views

soujanyareddy13 asked Jan 28, 2021

0 votes

1 answer

1328

CMI2020-A: 5
A boolean function on $n$ variables is a function $f$ that takes an n-tuple of boolean values $x \in \{0,1\}^n$ as input and produces a boolean value $f(x)\in \{0,1\}$ as output. We say that a boolean function $f$ ... boolean functions on $n$ variables? $n+1$ $n!$ $\displaystyle \sum^n_{i=0} \begin{pmatrix} n\\i \end{pmatrix}$ $2^{n+1}$

A boolean function on $n$ variables is a function $f$ that takes an n-tuple of boolean values $x \in \{0,1\}^n$ as input and produces a boolean value $f(x)\in \{0,1\}$ as...

soujanyareddy13

305 views

soujanyareddy13 asked Jan 28, 2021

0 votes

1 answer

1329

CMI2020-A: 6
There are $n$ songs segregated into $3$ playlists. Assume that each playlist has at least one song. For all $n$, the number of ways of choosing three songs consisting of one song from each playlist is: $>\frac{n^3}{27}$ $\underline<\frac{n^3}{27}$ $\begin{pmatrix} n\\3 \end{pmatrix}$ $n^3$

There are $n$ songs segregated into $3$ playlists. Assume that each playlist has at least one song. For all $n$, the number of ways of choosing three songs consisting of ...

soujanyareddy13

284 views

soujanyareddy13 asked Jan 28, 2021

0 votes

1 answer

1330

CMI2020-A: 7
Basketball shots are classified into $close-range,\;mid-range$ and $long-range$ shots. Long range shots are worth $3$ points, while close-range and mid-range shots are worth $2$ points. Of the shots that LeBron James attempts, $45\%$ are close-range, $25\%$ ... that a LeBron shot attempt is successful? $\frac{1}{2}$ $\frac{4}{5}$ $\frac{3}{5}$ $\frac{4}{7}$

Basketball shots are classified into $close-range,\;mid-range$ and $long-range$ shots. Long range shots are worth $3$ points, while close-range and mid-range shots are w...

soujanyareddy13

147 views

soujanyareddy13 asked Jan 28, 2021

0 votes

1 answer

1331

CMI2020-A: 8
Basketball shots are classified into $close-range,\;mid-range$ and $long-range$ shots. Long range shots are worth $3$ points, while close-range and the mid-range shots are worth $2$ points. Of the shots that LeBron James attempts, $45\%$ are close-range, $25\%$ ... attempt by LeBron is a close-range shot? $\frac{2}{5}$ $\frac{3}{5}$ $\frac{3}{7}$ $\frac{3}{4}$

Basketball shots are classified into $close-range,\;mid-range$ and $long-range$ shots. Long range shots are worth $3$ points, while close-range and the mid-range shots a...

soujanyareddy13

152 views

soujanyareddy13 asked Jan 28, 2021

1 votes

2 answers

1332

CMI2020-A: 9
A fair coin is repeatedly tossed. Each time a head appears, $1$ rupee is added to the first bag. Each time a tail appears, $2$ rupees are put in the second bag. What is the probability that both the bags have the same amount of money after $6$ coin tosses? $\frac{1}{2^6}$ $\frac{6!}{2!\cdot 4!\cdot 2^6}$ $\frac{2^2}{2^6}$ $\frac{6!}{2^6}$

A fair coin is repeatedly tossed. Each time a head appears, $1$ rupee is added to the first bag. Each time a tail appears, $2$ rupees are put in the second bag.What is th...

soujanyareddy13

229 views

soujanyareddy13 asked Jan 28, 2021

1 votes

2 answers

1333

CMI2020-A: 10
We have a procedure $P(n)$ that makes multiple calls to a procedure $Q(m)$, and runs in polynomial time in $n$. Unfortunately, a significant flaw was discovered in $Q(m)$, and it had to be replaced by $R(m)$, which runs in exponential time in $m$. Thankfully, $P$ is ... is proportional to $log\;n.$ $P(n)$ runs in polynomial time in $n$ if, for each call $Q(m),m \underline<log \;n.$

We have a procedure $P(n)$ that makes multiple calls to a procedure $Q(m)$, and runs in polynomial time in $n$. Unfortunately, a significant flaw was discovered in $Q(m)$...

soujanyareddy13

301 views

soujanyareddy13 asked Jan 28, 2021

0 votes

1 answer

1334

CMI2020-B: 1
There are two cities, City $X$ and City $Y$. Each city has a metro system consisting of three different lines - red line, blue line, and green line. Each station (in both cities) is classified as either $interesting\; or\; uninteresting,$ depending on ... colours following which one can reach an interesting destination from the City Centre in $X$, but not from the City Centre in $Y$.

There are two cities, City $X$ and City $Y$. Each city has a metro system consisting of three different lines – red line, blue line, and green line. Each station (in bo...

soujanyareddy13

179 views

soujanyareddy13 asked Jan 28, 2021

0 votes

1 answer

1335

CMI2020-B: 2
A graph is finite if it has a finite number of vertices, and simple if it has no self-loops or multiple edges. Assume we are dealing with finite, undirected, simple graphs with at least two vertices. A graph is connected if there is a path between any two ... there exist a graph $G$ with at least two vertices such that both $G$ and $\overline G$ are connected? Justify your answer.

A graph is finite if it has a finite number of vertices, and simple if it has no self-loops or multiple edges. Assume we are dealing with finite, undirected, simple graph...

soujanyareddy13

182 views

soujanyareddy13 asked Jan 28, 2021

0 votes

1 answer

1336

CMI2020-B: 3
A graph is finite if it has a finite number of vertices, and simple if it has no self-loops or multiple edges. Prove or disprove: There exists a finite, undirected, simple graph with at least two vertices in which each vertex has a different degree. To give ... draw an example of such a graph. To disprove the result, you should provide an argument as to why such a graph cannot exist.

A graph is finite if it has a finite number of vertices, and simple if it has no self-loops or multiple edges.Prove or disprove: There exists a finite, undirected, simple...

soujanyareddy13

151 views

soujanyareddy13 asked Jan 28, 2021

0 votes

1 answer

1337

CMI2020-B: 4
Consider the procedure $\text{MYSTERY}$ described in pseudocode below. The procedure takes two non-negative integers as arguments. For a real number $x$ the notation $[x]$ denotes the largest integer which is not larger than $x$. $\text{MYSTERY (p,q)}$ ... $MYSTERY(m,n)$ return for $m,n\underline> 0?$ Justify your answer with a proof.

Consider the procedure $\text{MYSTERY}$ described in pseudocode below. The procedure takes two non-negative integers as arguments. For a real number $x$ the notation $[x]...

soujanyareddy13

193 views

soujanyareddy13 asked Jan 28, 2021

1 votes

1 answer

1338

CMI2020-B: 5
Let $\Sigma=\{a,b\}.$ For two non-empty languages $L_1$ and $L_2$ over $\Sigma$, we define $Mix(L_1,L_2)$ to be $\{w_1\;u\;w_2\;v\;w_3|\;u\in L_1,v\in L_2,w_1,w_2,w_3\in \Sigma^*\}$. Give two languages $L_1$ and $L_2$ ... are regular, the language $Mix(L_1,L_2)$ is also regular. Provide languages $L_1$ and $L_2$ that are not regular, for which $Mix(L_1,L_2)$ is regular.

Let $\Sigma=\{a,b\}.$ For two non-empty languages $L_1$ and $L_2$ over $\Sigma$, we define $Mix(L_1,L_2)$ to be $\{w_1\;u\;w_2\;v\;w_3|\;u\in L_1,v\in L_2,w_1,w_2,w_3\in ...

soujanyareddy13

158 views

soujanyareddy13 asked Jan 28, 2021

0 votes

2 answers

1339

CMI2020-B: 6
A password contains exactly $6$ characters. Each character is either a lowercase letter $\{a,b,\dots,z\}$ or a digit $\{ 0,1,\dots,9\}$. A valid password should contain at least one digit. What is the total number of valid passwords? Here is an incorrect ... a justification for your answer. You do not need to simplify your expressions (for example, you can write $26^5, 5!, etc.$).

A password contains exactly $6$ characters. Each character is either a lowercase letter $\{a,b,\dots,z\}$ or a digit $\{ 0,1,\dots,9\}$. A valid password should contain a...

soujanyareddy13

380 views

soujanyareddy13 asked Jan 28, 2021

0 votes

1 answer

1340

CMI2020-B: 7
We are given an array of $N$ words $W[1\dots N],$ and a length array $L[1\dots N]$, where each $L[i]$ denotes the length (number of characters) of $W[i]$. We are also given a line width $M$ ... $N$?

We are given an array of $N$ words $W[1\dots N],$ and a length array $L[1\dots N]$, where each $L[i]$ denotes the length (number of characters) of $W[i]$. We are also giv...

soujanyareddy13

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soujanyareddy13 asked Jan 28, 2021

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score	score:10
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