Answers by Arjun / GATE Overflow for GATE CSE

2 votes

201

TIFR CSE 2015 | Part A | Question: 9
Consider a square of side length $2$. We throw five points into the square. Consider the following statements: There will always be three points that lie on a straight line. There will always be a line connecting a pair of points such that two points lie on one side of ... $\text{(ii)}$ only $\text{(iii)}$ only $\text{(ii)}$ and $\text{(iii)}$ None of the above

Consider a square of side length $2$. We throw five points into the square. Consider the following statements:There will always be three points that lie on a straight lin...

998 views

answered Jun 20, 2019

0 votes

202

TIFR CSE 2018 | Part A | Question: 11
We are given a (possibly empty) set of objects. Each object in the set is colored either black or white, is shaped either circular or rectangular, and has a profile that is either fat or thin, Those properties obey the following principles: Each white ... $(i) \text{ and } (iii)$ only None of the statements must be TRUE All of the statements must be TRUE

We are given a (possibly empty) set of objects. Each object in the set is colored either black or white, is shaped either circular or rectangular, and has a profile that ...

1.6k views

answered Jun 18, 2019

4 votes

203

TIFR CSE 2014 | Part A | Question: 18
We are given a collection of real numbers where a real number $a_{i}\neq 0$ occurs $n_{i}$ times. Let the collection be enumerated as $\left\{x_{1}, x_{2},...x_{n}\right\}$ so that $x_{1}=x_{2}=...=x_{n_{1}}=a_{1}$ and so on, and $n=\sum _{i}n_{i}$ ... $\min_{i} |a_{i}|$ $\min_{i} \left(n_{i}|a_{i}|\right)$ $\max_{i} |a_{i}|$ None of the above

We are given a collection of real numbers where a real number $a_{i}\neq 0$ occurs $n_{i}$ times. Let the collection be enumerated as $\left\{x_{1}, x_{2},...x_{n}\right\...

992 views

answered Jun 17, 2019

26 votes

204

GATE CSE 1989 | Question: 13b
Find a solution to the following recurrence equation: $T(n)=\sqrt{n}+T\left(\frac{n}{2}\right)$ $T(1)=1$

Find a solution to the following recurrence equation:$T(n)=\sqrt{n}+T\left(\frac{n}{2}\right)$$T(1)=1$

4.2k views

answered Jun 16, 2019

3 votes

205

TIFR CSE 2011 | Part B | Question: 23
Suppose $(S_{1}, S_{2},\ldots,S_{m})$ is a finite collection of non-empty subsets of a universe $U.$ Note that the sets in this collection need not be distinct. Consider the following basic step to be performed on this sequence. While there exist ... finite universe $U$ and a choice of $S_{i}$ and $S_{j}$ in each step such that the process does not terminate

Suppose $(S_{1}, S_{2},\ldots,S_{m})$ is a finite collection of non-empty subsets of a universe $U.$ Note that the sets in this collection need not be distinct. Consider ...

2.1k views

answered Jun 16, 2019

2 votes

206

TIFR CSE 2015 | Part A | Question: 15
Let $A$ and $B$ be non-empty disjoint sets of real numbers. Suppose that the average of the numbers in the first set is $\mu_{A}$ and the average of the numbers in the second set is $\mu_{B}$; let the corresponding variances be $v_{A}$ and $v_{B}$ respectively. If the average of the ... $p.v_{A}+ (1 - p). v_{B} + (\mu_{A}- \mu_{B})^{2}$

Let $A$ and $B$ be non-empty disjoint sets of real numbers. Suppose that the average of the numbers in the first set is $\mu_{A}$ and the average of the numbers in the se...

1.1k views

answered Jun 16, 2019

8 votes

207

TIFR CSE 2018 | Part A | Question: 10
Let $C$ be a biased coin such that the probability of a head turning up is $p.$ Let $p_n$ denote the probability that an odd number of heads occurs after $n$ tosses for $n \in \{0,1,2,\ldots \},$ ... $p_{n}=1 \text{ if } n \text{ is odd and } 0 \text{ otherwise}.$

Let $C$ be a biased coin such that the probability of a head turning up is $p.$ Let $p_n$ denote the probability that an odd number of heads occurs after $n$ tosses for $...

2.1k views

answered Jun 16, 2019

4 votes

208

TIFR CSE 2019 | Part A | Question: 10
Avni and Badal alternately choose numbers from the set $\{1,2,3,4,5,6,7,8,9\}$ without replacement (starting with Avni). The first person to choose numbers of which any $3$ sum to $15$ wins the game (for example, Avni wins ... strategy Both of them have a winning strategy Neither of them has a winning strategy The Player that picks $9$ has a winning strategy

Avni and Badal alternately choose numbers from the set $\{1,2,3,4,5,6,7,8,9\}$ without replacement (starting with Avni). The first person to choose numbers of which any ...

1.2k views

answered Jun 16, 2019

4 votes

209

TIFR CSE 2013 | Part A | Question: 18
Consider three independent uniformly distributed (taking values between $0$ and $1$) random variables. What is the probability that the middle of the three values (between the lowest and the highest value) lies between $a$ and $b$ where $0 ≤ a < b ≤ 1$? $3 (1 - b) a (b - a)$ ... $(1 - b) a (b - a)$ $6 ((b^{2}- a^{2})/ 2 - (b^{3} - a^{3})/3)$.

Consider three independent uniformly distributed (taking values between $0$ and $1$) random variables. What is the probability that the middle of the three values (betwee...

1.3k views

answered Jun 15, 2019

4 votes

210

GATE CSE 1989 | Question: 4-viii
$P_{n} (t)$ is the probability of $n$ events occurring during a time interval $t$. How will you express $P_{0} (t + h)$ in terms of $P_{0} (h)$, if $P_{0} (t)$ has stationary independent increments? (Note: $P_{t} (t)$is the probability density function).

$P_{n} (t)$ is the probability of $n$ events occurring during a time interval $t$. How will you express $P_{0} (t + h)$ in terms of $P_{0} (h)$, if $P_{0} (t)$ has statio...

1.6k views

answered Jun 15, 2019

6 votes

211

TIFR CSE 2015 | Part A | Question: 12
Consider two independent and identically distributed random variables $X$ and $Y$ uniformly distributed in $[0, 1]$. For $\alpha \in \left[0, 1\right]$, the probability that $\alpha$ max $(X, Y) < XY$ is $1/ (2\alpha)$ exp $(1 - \alpha)$ $1 - \alpha$ $(1 - \alpha)^{2}$ $1 - \alpha^{2}$

Consider two independent and identically distributed random variables $X$ and $Y$ uniformly distributed in $[0, 1]$. For $\alpha \in \left[0, 1\right]$, the probability t...

1.9k views

answered Jun 15, 2019

3 votes

212

TIFR CSE 2013 | Part A | Question: 5
The late painter Maqbool Fida Husain once coloured the surface of a huge hollow steel sphere, of radius $1$ metre, using just two colours, Red and Blue. As was his style however, both the red and blue areas were a bunch of highly irregular disconnected ... $11 sq. metres$; None of the above.

The late painter Maqbool Fida Husain once coloured the surface of a huge hollow steel sphere, of radius $1$ metre, using just two colours, Red and Blue. As was his style ...

2.8k views

answered Jun 14, 2019

16 votes

213

GATE CSE 1990 | Question: 12b
Consider the following problem. Given $n$ positive integers $a_{1}, a_{2}\dots a_n,$ it is required to partition them in to two parts $A$ and $B$ ... that part whose sum in smaller at that step. Give an example with $n=5$ for which the solution produced by the greedy algorithm is not optimal.

Consider the following problem. Given $n$ positive integers $a_{1}, a_{2}\dots a_n,$ it is required to partition them in to two parts $A$ and $B$ such that, $\displaystyl...

2.6k views

answered Jun 14, 2019

5 votes

214

TIFR CSE 2018 | Part B | Question: 10
For two $n$ bit strings $x,y \in\{0,1\}^{n},$ define $z=x\oplus y$ to be the bitwise XOR of the two strings (that is, if $x_{i},y_{i},z_{i}$ denote the $i^{th}$ bits of $x,y,z$ respectively, then $z_{i}=x_{i}+y_{i} \bmod 2$ ... such linear functions for $n \geq 2$ is: $2^{n}$ $2^{n^{2}}$ $\large2^{\frac{n}{2}}$ $2^{4n}$ $2^{n^{2}+n}$

For two $n$ bit strings $x,y \in\{0,1\}^{n},$ define $z=x\oplus y$ to be the bitwise XOR of the two strings (that is, if $x_{i},y_{i},z_{i}$ denote the $i^{th}$ bits of $...

1.6k views

answered Jun 14, 2019

1 votes

215

GATE Overflow | General Aptitude | Test 2 | Question: 9
Pick the sentence which is grammatically incorrect Walking in the park it began to rain She was waiting for you but you never came We were to have a party here But I did do my homework!

Pick the sentence which is grammatically incorrectWalking in the park it began to rainShe was waiting for you but you never cameWe were to have a party hereBut I did do m...

851 views

answered Jun 9, 2019

20 votes

216

GATE Overflow | General Aptitude | Test 2 | Question: 1
Two liquids $A$ and $B$ are in the ratio $4:1$ in container $1$ and in container $2,$ they are in the ratio $1:3.$ In what ratio should the contents of the two containers be mixed so as to obtain a mixture of $A$ and $B$ in the ratio $1:1$? $5:6$ $4:3$ $3 :4$ $6:5$

Two liquids $A$ and $B$ are in the ratio $4:1$ in container $1$ and in container $2,$ they are in the ratio $1:3.$ In what ratio should the contents of the two containers...

978 views

answered Jun 9, 2019

3 votes

217

GATE Overflow | General Aptitude | Test 2 | Question: 2
Naveen wrote down all the different three-digit numbers that can be written using each of the numeral 1, 2 and 3 exactly once. What is the median of the numbers Naveen wrote down?

Naveen wrote down all the different three-digit numbers that can be written using each of the numeral 1, 2 and 3 exactly once. What is the median of the numbers Naveen wr...

486 views

answered Jun 9, 2019

2 votes

218

GATE Overflow | General Aptitude | Test 2 | Question: 3
Anupama and Swathy bought $1$ acre of land for Rs. $2$ lakhs in year $2010.$ Anupama planted coconut and lemon trees in the ratio $4:1$ on equal area of land. There were a total of $100$ lemon trees. The cost of one coconut was Rs.5 ... was the ratio of yields per acre of land for coconuts & lemons? $3:2$ $2:3$ $1:1 $ cannot be determined.

Anupama and Swathy bought $1$ acre of land for Rs. $2$ lakhs in year $2010.$ Anupama planted coconut and lemon trees in the ratio $4:1$ on equal area of land. There were ...

579 views

answered Jun 9, 2019

2 votes

219

GATE Overflow | General Aptitude | Test 2 | Question: 5
It takes a pendulum of a clock $5$ seconds to strike 2 o’clock. How much time (in seconds) will it take to strike 10 o’clock?

It takes a pendulum of a clock $5$ seconds to strike 2 o’clock. How much time (in seconds) will it take to strike 10 o’clock?

528 views

answered Jun 9, 2019

4 votes

220

GATE Overflow | General Aptitude | Test 2 | Question: 6
If $9$ apples cost Rs. $100$ and $10$ mangoes cost Rs. $100$ then the maximum number of fruits one can buy with Rs. $150$ is $\_\_\_\_$

If $9$ apples cost Rs. $100$ and $10$ mangoes cost Rs. $100$ then the maximum number of fruits one can buy with Rs. $150$ is $\_\_\_\_$

354 views

answered Jun 9, 2019

4 votes

221

GATE2016 EC-1: GA-6
A person moving through a tuberculosis prone zone has a $50$% probability of becoming infected. However, only $30$% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease? $15$ $33$ $35$ $37$

A person moving through a tuberculosis prone zone has a $50$% probability of becoming infected. However, only $30$% of infected people develop the disease. What percentag...

3.1k views

answered Jun 9, 2019

19 votes

222

TIFR CSE 2019 | Part A | Question: 13
Consider the integral $\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$ What is the value of this integral correct up to two decimal places? $0.00$ $0.02$ $0.10$ $0.33$ $1.00$

Consider the integral$$\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$$What is the value of this integral correct up to two decimal places?$0.00$$0.02$$0.10$$0.33$$1.00$

2.8k views

answered Jun 8, 2019

5 votes

223

GATE2010 MN: GA-9
A positive integer $m$ in base $10$ when represented in base $2$ has the representation $p$ and in base $3$ has the representation $q.$ We get $p-q=990$ where the subtraction is done in base $10.$ Which of the following is necessarily true$:$ $m\geq 14$ $9\leq m\leq 13$ $6\leq m\leq 8$ $m<6$

A positive integer $m$ in base $10$ when represented in base $2$ has the representation $p$ and in base $3$ has the representation $q.$ We get $p-q=990$ where the subtrac...

2.0k views

answered Jun 8, 2019

12 votes

224

GATE CSE 1990 | Question: 17c
Show that the elements of the lattice $(N, \leq)$, where $N$ is the set of positive intergers and $a \leq b$ if and only if $a$ divides $b$, satisfy the distributive property.

Show that the elements of the lattice $(N, \leq)$, where $N$ is the set of positive intergers and $a \leq b$ if and only if $a$ divides $b$, satisfy the distributive prop...

2.0k views

answered Jun 8, 2019

8 votes

225

TIFR CSE 2017 | Part B | Question: 6
Consider the First Order Logic (FOL) with equality and suitable function and relation symbols. Which of the following is FALSE? Partial orders cannot be axiomatized in FOL FOL has a complete proof system Natural numbers cannot be axiomatized in FOL Real numbers cannot be axiomatized in FOL Relational numbers cannot be axiomatized in FOL

Consider the First Order Logic (FOL) with equality and suitable function and relation symbols. Which of the following is FALSE?Partial orders cannot be axiomatized in FOL...

1.2k views

answered Jun 8, 2019

10 votes

226

TIFR CSE 2019 | Part B | Question: 12
Let $G=(V,E)$ be a directed graph with $n(\geq 2)$ vertices, including a special vertex $r$. Each edge $e \in E$ has a strictly positive edge weight $w(e)$. An arborescence in $G$ rooted at $r$ is a subgraph $H$ of $G$ ... is acyclic $w^*$ is less than the weight of the minimum weight directed Hamiltonian cycle in $G$, when $G$ has a directed Hamiltonian cycle

Let $G=(V,E)$ be a directed graph with $n(\geq 2)$ vertices, including a special vertex $r$. Each edge $e \in E$ has a strictly positive edge weight $w(e)$. An arborescen...

2.4k views

answered Jun 8, 2019

28 votes

227

GATE CSE 1987 | Question: 9e
How many true inclusion relations are there of the form $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?

How many true inclusion relations are there of the form $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?

3.2k views

answered Jun 7, 2019

9 votes

228

GATE2011 MN: GA-58
Choose the word or phrase that best completes the sentence below. ______________ in the frozen wastes of Arctic takes special equipment. To survive Surviving Survival That survival

Choose the word or phrase that best completes the sentence below.______________ in the frozen wastes of Arctic takes special equipment.To surviveSurvivingSurvivalThat sur...

2.0k views

answered Jun 7, 2019

3 votes

229

GATE CSE 1988 | Question: 14i
Consider the following well-formed formula: $\exists x \forall y [ \neg \: \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$ Express the above well-formed formula in clausal form.

Consider the following well-formed formula:$\exists x \forall y [ \neg \: \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$Express the above well-formed formula in c...

667 views

answered Jun 7, 2019

6 votes

230

GATE CSE 2014 Set 2 | Question: GA-2
Who ___________ was coming to see us this evening? you said did you say did you say that had you said

Who ___________ was coming to see us this evening?you saiddid you saydid you say thathad you said

4.5k views

answered Jun 6, 2019

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