Search results for tifr2014 / GATE Overflow for GATE CSE

16 votes

3 answers

1

TIFR CSE 2014 | Part A | Question: 17
A fair dice (with faces numbered $1, . . . , 6$) is independently rolled repeatedly. Let $X$ denote the number of rolls till an even number is seen and let $Y$ denote the number of rolls till $3$ is seen. Evaluate $E(Y |X = 2)$. $6\frac{5}{6}$ $6$ $5\frac{1}{2}$ $6\frac{1}{3}$ $5\frac{2}{3}$

A fair dice (with faces numbered $1, . . . , 6$) is independently rolled repeatedly. Let $X$ denote the number of rolls till an even number is seen and let $Y$ denote the...

makhdoom ghaya

4.0k views

makhdoom ghaya asked Nov 19, 2015

7 votes

3 answers

2

TIFR CSE 2014 | Part A | Question: 10
A person went out between $4$pm and $5$pm to chat with her friend and returned between $5$pm and $6$pm. On her return, she found that the hour-hand and the minute-hand of her (well-functioning) clock had just exchanged their positions with respect to ... $\dfrac{1}{3}$ minutes past $4$pm. Twenty eight minutes past $4$pm. None of the above.

A person went out between $4$pm and $5$pm to chat with her friend and returned between $5$pm and $6$pm. On her return, she found that the hour-hand and the minute-hand of...

makhdoom ghaya

1.3k views

makhdoom ghaya asked Nov 9, 2015

18 votes

4 answers

3

TIFR CSE 2014 | Part B | Question: 15
Consider the set $N^{*}$ of finite sequences of natural numbers with $x \leq_{p}y$ denoting that sequence $x$ is a prefix of sequence $y$. Then, which of the following is true? $N^{*}$ is uncountable. $\leq_{p}$ is a total order. Every non ... -empty subset of $N^{*}$ has a greatest lower bound. Every non-empty finite subset of $N^{*}$ has a least upper bound.

Consider the set $N^{*}$ of finite sequences of natural numbers with $x \leq_{p}y$ denoting that sequence $x$ is a prefix of sequence $y$. Then, which of the following is...

makhdoom ghaya

3.6k views

makhdoom ghaya asked Nov 20, 2015

25 votes

2 answers

4

TIFR CSE 2014 | Part B | Question: 14
Which the following is FALSE? Complement of a recursive language is recursive. A language recognized by a non-deterministic Turing machine can also be recognized by a deterministic Turing machine. Complement of a context free language can ... enumerable then it is recursive. Complement of a non-recursive language can never be recognized by any Turing machine.

Which the following is FALSE?Complement of a recursive language is recursive.A language recognized by a non-deterministic Turing machine can also be recognized by a deter...

makhdoom ghaya

7.6k views

makhdoom ghaya asked Nov 20, 2015

49 votes

7 answers

5

TIFR CSE 2014 | Part B | Question: 9
Given a set of $n$ distinct numbers, we would like to determine the smallest three numbers in this set using comparisons. Which of the following statements is TRUE? These three elements can be determined using $O\left(\log^{2}n\right)$ ... $O(n)$ comparisons. None of the above.

Given a set of $n$ distinct numbers, we would like to determine the smallest three numbers in this set using comparisons. Which of the following statements is TRUE?These ...

makhdoom ghaya

10.0k views

makhdoom ghaya asked Nov 19, 2015

40 votes

4 answers

6

TIFR CSE 2014 | Part B | Question: 20
Consider the following game. There is a list of distinct numbers. At any round, a player arbitrarily chooses two numbers $a, b$ from the list and generates a new number $c$ by subtracting the smaller number from the larger one. The numbers $a$ and $b$ are put ... $273$. What is the score of the best player for this game? $40$ $16$ $33$ $91$ $123$

Consider the following game. There is a list of distinct numbers. At any round, a player arbitrarily chooses two numbers $a, b$ from the list and generates a new number $...

makhdoom ghaya

3.3k views

makhdoom ghaya asked Nov 20, 2015

17 votes

5 answers

7

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...

makhdoom ghaya

5.2k views

makhdoom ghaya asked Nov 20, 2015

13 votes

3 answers

8

TIFR CSE 2014 | Part A | Question: 11
A large community practices birth control in the following peculiar fashion. Each set of parents continues having children until a son is born; then they stop. What is the ratio of boys to girls in the community if, in the absence of birth control, $51\%$ of the babies are born male? $51:49$ $1:1$ $49:51$ $51:98$ $98:51$

A large community practices birth control in the following peculiar fashion. Each set of parents continues having children until a son is born; then they stop. What is th...

makhdoom ghaya

1.6k views

makhdoom ghaya asked Nov 13, 2015

27 votes

5 answers

9

TIFR CSE 2014 | Part A | Question: 8
All that glitters is gold. No gold is silver. Claims: No silver glitters. Some gold glitters. Then, which of the following is TRUE? Only claim $1$ follows. Only claim $2$ follows. Either claim $1$ or claim $2$ follows but not both. Neither claim $1$ nor claim $2$ follows. Both claim $1$ and claim $2$ follow.

All that glitters is gold. No gold is silver.Claims:No silver glitters.Some gold glitters.Then, which of the following is TRUE?Only claim $1$ follows.Only claim $2$ follo...

makhdoom ghaya

3.6k views

makhdoom ghaya asked Nov 9, 2015

9 votes

6 answers

10

TIFR CSE 2014 | Part A | Question: 9
Solve min $x^{2}+y^{2}$ subject to $\begin {align*} x + y &\geq 10,\\ 2x + 3y &\geq 20,\\ x &\geq 4,\\ y &\geq 4. \end{align*}$ $32$ $50$ $52$ $100$ None of the above

Solve min $x^{2}+y^{2}$ subject to$$\begin {align*} x + y &\geq 10,\\2x + 3y &\geq 20,\\x &\geq 4,\\y &\geq 4.\end{align*}$$$32$$50$$52$$100$None of the above

makhdoom ghaya

1.8k views

makhdoom ghaya asked Nov 9, 2015

31 votes

3 answers

11

TIFR CSE 2014 | Part B | Question: 6
Consider the problem of computing the minimum of a set of $n$ distinct numbers. We choose a permutation uniformly at random (i.e., each of the n! permutations of $\left \langle 1,....,n \right \rangle$ is chosen with probability $(1/n!)$ and we inspect the numbers in the order ... of times MIN is updated? $O (1)$ $H_{n}=\sum ^{n}_{i=1} 1/i$ $\sqrt{n}$ $n/2$ $n$

Consider the problem of computing the minimum of a set of $n$ distinct numbers. We choose a permutation uniformly at random (i.e., each of the n! permutations of $\left \...

makhdoom ghaya

2.7k views

makhdoom ghaya asked Nov 19, 2015

19 votes

5 answers

12

TIFR CSE 2014 | Part B | Question: 7
Which of the following statements is TRUE for all sufficiently large $n$? $\displaystyle \left(\log n\right)^{\log\log n} < 2^{\sqrt{\log n}} < n^{1/4}$ $\displaystyle 2^{\sqrt{\log n}} < n^{1/4} < \left(\log n\right)^{\log\log n}$ ... $\displaystyle 2^{\sqrt{\log n}} < \left(\log n\right)^{\log\log n} < n^{1/4}$

Which of the following statements is TRUE for all sufficiently large $n$?$\displaystyle \left(\log n\right)^{\log\log n} < 2^{\sqrt{\log n}} < n^{1/4}$ $\displaystyle 2^{...

makhdoom ghaya

4.0k views

makhdoom ghaya asked Nov 19, 2015

32 votes

4 answers

13

TIFR CSE 2014 | Part B | Question: 11
Consider the following recurrence relation: $T\left(n\right)= \begin{cases} T\left(\frac{n}{k}\right)+ T\left(\frac{3n}{4}\right)+ n & \text{if } n \geq 2 \\ 1& \text{if } n=1 \end{cases}$ Which of the following statements is FALSE? $T(n)$ is $O(n^{3/2})$ ... $k=4$. $T(n)$ is $O(n \log n)$ when $k=5$. $T(n)$ is $O(n)$ when $k=5$.

Consider the following recurrence relation:$T\left(n\right)=\begin{cases}T\left(\frac{n}{k}\right)+ T\left(\frac{3n}{4}\right)+ n & \text{if } n \geq 2 \\ 1& \text{if }...

makhdoom ghaya

5.6k views

makhdoom ghaya asked Nov 20, 2015

24 votes

3 answers

14

TIFR CSE 2014 | Part A | Question: 5
The rules for the University of Bombay five-a-side cricket competition specify that the members of each team must have birthdays in the same month. What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students? $23$ $91$ $60$ $49$ None of the above

The rules for the University of Bombay five-a-side cricket competition specify that the members of each team must have birthdays in the same month. What is the minimum nu...

makhdoom ghaya

3.6k views

makhdoom ghaya asked Nov 9, 2015

35 votes

4 answers

15

TIFR CSE 2014 | Part B | Question: 4
Consider the following undirected graph with some edge costs missing. Suppose the wavy edges form a Minimum Cost Spanning Tree for $G$. Then, which of the following inequalities NEED NOT hold? cost$(a, b) \geq 6$. cost$(b, e) \geq 5$. cost$(e, f) \geq 5$. cost$(a, d) \geq 4$. cost$(b, c) \geq 4$.

Consider the following undirected graph with some edge costs missing.Suppose the wavy edges form a Minimum Cost Spanning Tree for $G$. Then, which of the following inequa...

makhdoom ghaya

5.1k views

makhdoom ghaya asked Nov 19, 2015

32 votes

6 answers

16

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...

makhdoom ghaya

6.1k views

makhdoom ghaya asked Oct 4, 2015

6 votes

2 answers

17

TIFR CSE 2014 | Part A | Question: 2
A body at a temperature of $30$ Celsius is immersed into a heat bath at $0$ Celsius at time $t = 0$. The body starts cooling at a rate proportional to the temperature difference. Assuming that the heat bath does not change in temperature throughout the process, calculate the ... $\dfrac{\log 29}{\log 25}$ $\large e^{5}$ $1 + \log_{6} 5$ None of the above

A body at a temperature of $30$ Celsius is immersed into a heat bath at $0$ Celsius at time $t = 0$. The body starts cooling at a rate proportional to the temperature dif...

makhdoom ghaya

862 views

makhdoom ghaya asked Nov 9, 2015

3 votes

2 answers

18

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\...

makhdoom ghaya

997 views

makhdoom ghaya asked Nov 19, 2015

4 votes

1 answer

19

TIFR CSE 2014 | Part A | Question: 13
Let $L$ be a line on the two dimensional plane. $L'$s intercepts with the $X$ and $Y$ axes are respectively $a$ and $b$. After rotating the co-ordinate system (and leaving $L$ untouched), the new intercepts are $a'$ and $b'$ respectively. Which ... $\frac{b}{a}+\frac{a}{b}=\frac{b'}{a'}+\frac{a'}{b'}$. None of the above.

Let $L$ be a line on the two dimensional plane. $L'$s intercepts with the $X$ and $Y$ axes are respectively $a$ and $b$. After rotating the co-ordinate system (and leavin...

makhdoom ghaya

1.5k views

makhdoom ghaya asked Nov 14, 2015

12 votes

3 answers

20

TIFR CSE 2014 | Part B | Question: 17
Let $f: \left\{0, 1\right\}^{n} \rightarrow \left\{0, 1\right\}$ ... $f$ is the MAJORITY function. $f$ is the PARITY function. $f$ outputs $1$ at exactly one assignment of the input bits.

Let $f: \left\{0, 1\right\}^{n} \rightarrow \left\{0, 1\right\}$ be a boolean function computed by a logical circuit comprising just binary AND and binary OR gates (assum...

makhdoom ghaya

3.2k views

makhdoom ghaya asked Nov 20, 2015

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