Recent questions in Engineering Mathematics / GATE Overflow for GATE CSE

5 votes

3 answers

8821

Boolean Algebra
Consider a Hasse Diagram for a Boolean Algebra of Order 3 What can we comment about it? How is it successfully able to represent the Boolean Algebra System? Is there an easy way to check for distributive lattice, or any other properties of a lattice? ... that one should provide a complete answer to all parts of the question. Whatever one can supply to support its answer is welcomed.

Consider a Hasse Diagram for a Boolean Algebra of Order 3What can we comment about it? How is it successfully able to represent the Boolean Algebra System?Is there an eas...

amarVashishth

4.4k views

amarVashishth asked Nov 11, 2015

2 votes

2 answers

8822

Number of edges in the Hasse Diagram of a boolean algebra with 8 elements.

LeenSharma

2.4k views

LeenSharma asked Nov 10, 2015

0 votes

2 answers

8823

probability
India plays two matches each with West Indies and Australia. In any match, the probabilities of India getting, points 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is

India plays two matches each with West Indies and Australia. In any match, the probabilities of India getting, points 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Ass...

Soumyashree

1.3k views

Soumyashree asked Nov 10, 2015

9 votes

6 answers

8824

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

27 votes

5 answers

8825

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

3.5k views

makhdoom ghaya asked Nov 9, 2015

24 votes

3 answers

8826

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

17 votes

2 answers

8827

TIFR CSE 2014 | Part A | Question: 3
The Fibonacci sequence is defined as follows: $F_{0} = 0, F_{1} = 1,$ and for all integers $n \geq 2, F_{n} = F_{n−1} + F_{n−2}$. Then which of the following statements is FALSE? $F_{n+2} = 1 + \sum ^{n}_{i=0} F_{i}$ ... $3$, for every integer $n \geq 0$. $F_{5n}$ is a multiple of $4$, for every integer $n \geq 0$.

The Fibonacci sequence is defined as follows: $F_{0} = 0, F_{1} = 1,$ and for all integers $n \geq 2, F_{n} = F_{n−1} + F_{n−2}$. Then which of the following statemen...

makhdoom ghaya

1.6k views

makhdoom ghaya asked Nov 9, 2015

2 votes

1 answer

8828

injection and surjection

Shefali

816 views

Shefali asked Nov 8, 2015

13 votes

4 answers

8829

TIFR CSE 2013 | Part B | Question: 16
Consider a function $T_{k, n}: \left\{0, 1\right\}^{n}\rightarrow \left\{0, 1\right\}$ which returns $1$ if at least $k$ of its $n$ inputs are $1$. Formally, $T_{k, n}(x)=1$ if $\sum ^{n}_{1} x_{i}\geq k$. Let $y \in \left\{0, 1\right\}^{n}$ ... $y_{i}$ is omitted) is equivalent to $T_{k-1}, n(y)$ $T_{k, n}(y)$ $y_{i}$ $\neg y_{i}$ None of the above

Consider a function $T_{k, n}: \left\{0, 1\right\}^{n}\rightarrow \left\{0, 1\right\}$ which returns $1$ if at least $k$ of its $n$ inputs are $1$. Formally, $T_{k, n}(x)...

makhdoom ghaya

1.4k views

makhdoom ghaya asked Nov 8, 2015

4 votes

1 answer

8830

probability question
For the three events A, B, and C, P (exactly one of the events A or B occurs) = P (exactly one of the two events B or C occurs) = P(exactly one of the events C or A occurs) = $p$ and P (all the three events occur simultaneously) = $p^2$, where $0 < p < \frac{1}{2}$. Then the probability of at least one of the three events A, B and C occuring is

For the three events A, B, and C, P (exactly one of the events A or B occurs) = P (exactly one of the two events B or C occurs) = P(exactly one of the events C or A occur...

Soumyashree

557 views

Soumyashree asked Nov 8, 2015

5 votes

1 answer

8831

TIFR CSE 2013 | Part B | Question: 10
Let $m, n$ be positive integers with $m$ a power of $2$. Let $s= 100 n^{2} \log m$. Suppose $S_{1}, S_{2},\dots ,S_{m}$ are subsets of ${1, 2, \dots, s}$ such that $ \mid S_{i} \mid= 10 n \log m$ and $ \mid S_{i} \cap S_{j} \mid \leq \log m$ ... $x ∉ T$. $1$ if $x \in T$ and at least $0.9$ if $x ∉ T$. At least $0.9$ if $x \in T$ and $1$ if $x ∉ T$.

Let $m, n$ be positive integers with $m$ a power of $2$. Let $s= 100 n^{2} \log m$. Suppose $S_{1}, S_{2},\dots ,S_{m}$ are subsets of ${1, 2, \dots, s}$ such that $ \mid...

makhdoom ghaya

825 views

makhdoom ghaya asked Nov 7, 2015

17 votes

5 answers

8832

TIFR CSE 2013 | Part B | Question: 4
A set $S$ together with partial order $\ll$ is called a well order if it has no infinite descending chains, i.e. there is no infinite sequence $x_1, x_2,\ldots$ of elements from $S$ such that $x_{i+1} \ll x_i$ and $x_{i+1} \neq x_i$ for all $i$. ... $2^{24}$ words. $W$ is not a partial order. $W$ is a partial order but not a well order. $W$ is a well order.

A set $S$ together with partial order $\ll$ is called a well order if it has no infinite descending chains, i.e. there is no infinite sequence $x_1, x_2,\ldots$ of elemen...

makhdoom ghaya

3.1k views

makhdoom ghaya asked Nov 6, 2015

24 votes

3 answers

8833

TIFR CSE 2013 | Part B | Question: 3
How many $4 \times 4$ matrices with entries from ${0, 1}$ have odd determinant? Hint: Use modulo $2$ arithmetic. $20160$ $32767$ $49152$ $57343$ $65520$

How many $4 \times 4$ matrices with entries from ${0, 1}$ have odd determinant?Hint: Use modulo $2$ arithmetic.$20160$$32767$$49152$$57343$$65520$

makhdoom ghaya

4.5k views

makhdoom ghaya asked Nov 6, 2015

1 votes

1 answer

8834

probability
from a well shuffled pack of 52 cards. Three cards are drawn at random. Find the probability of drawing an ace, a king and a jack, a) 16/5525 b) 16/625

from a well shuffled pack of 52 cards. Three cards are drawn at random. Find the probability of drawing an ace, a king and a jack,a) 16/5525b) 16/625

Tendua

611 views

Tendua asked Nov 6, 2015

26 votes

4 answers

8835

TIFR CSE 2013 | Part B | Question: 1
Let $G= (V, E)$ be a simple undirected graph on $n$ vertices. A colouring of $G$ is an assignment of colours to each vertex such that endpoints of every edge are given different colours. Let $\chi (G)$ denote the chromatic number of $G$, i.e. the minimum ... $a\left(G\right)\leq \frac{n}{\chi \left(G\right)}$ None of the above

Let $G= (V, E)$ be a simple undirected graph on $n$ vertices. A colouring of $G$ is an assignment of colours to each vertex such that endpoints of every edge are given di...

makhdoom ghaya

4.3k views

makhdoom ghaya asked Nov 5, 2015

6 votes

1 answer

8836

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...

makhdoom ghaya

1.3k views

makhdoom ghaya asked Nov 5, 2015

9 votes

5 answers

8837

TIFR CSE 2013 | Part A | Question: 17
A stick of unit length is broken into two at a point chosen at random. Then, the larger part of the stick is further divided into two parts in the ratio $4:3$. What is the probability that the three sticks that are left CANNOT form a triangle? $1/4$ $1/3$ $5/6$ $1/2$ $\log_{e}(2)/2$

A stick of unit length is broken into two at a point chosen at random. Then, the larger part of the stick is further divided into two parts in the ratio $4:3$. What is th...

makhdoom ghaya

1.9k views

makhdoom ghaya asked Nov 5, 2015

8 votes

2 answers

8838

TIFR CSE 2013 | Part A | Question: 16
The minimum of the function $f(x) = x \log_{e}(x)$ over the interval $[\frac{1}{2}, \infty )$ is $0$ $-e$ $\frac{-\log_{e}(2)}{2}$ $\frac{-1}{e}$ None of the above

The minimum of the function $f(x) = x \log_{e}(x)$ over the interval $[\frac{1}{2}, \infty )$ is$0$$-e$$\frac{-\log_{e}(2)}{2}$$\frac{-1}{e}$None of the above

makhdoom ghaya

1.4k views

makhdoom ghaya asked Nov 5, 2015

18 votes

5 answers

8839

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...

makhdoom ghaya

1.6k views

makhdoom ghaya asked Nov 4, 2015

12 votes

3 answers

8840

TIFR CSE 2013 | Part A | Question: 13
Doctors $A$ and $B$ perform surgery on patients in stages $III$ and $IV$ of a disease. Doctor $A$ has performed a $100$ surgeries (on $80$ stage $III$ and $20$ stage $IV$ patients) and $80$ out of her $100$ patients ... she appears to be more successful There is not enough data since the choice depends on the stage of the disease the patient is suffering from.

Doctors $A$ and $B$ perform surgery on patients in stages $III$ and $IV$ of a disease. Doctor $A$ has performed a $100$ surgeries (on $80$ stage $III$ and $20$ stage $IV$...

makhdoom ghaya

1.4k views

makhdoom ghaya asked Nov 4, 2015

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