Recent questions in Engineering Mathematics / GATE Overflow for GATE CSE

2 votes

1 answer

8481

group
Which of following is true? 1)A group can have only two disjoint subgroups 2)A group can have more than two disjoint subgroups 3)a group cannot have two disjoint subgroups 4)none

Which of following is true?1)A group can have only two disjoint subgroups2)A group can have more than two disjoint subgroups3)a group cannot have two disjoint subgroups...

Pooja Palod

683 views

Pooja Palod asked Nov 13, 2015

1 votes

0 answers

8482

how many ways can we form a team of 2 men and 2 women such that no couple is a part of team ?
There are 10 couples at party .In this question I have only doubt that if I chose 2 husbands first ,now for wives remaining choice will be 8 so it will be 10C2 *8C2 ,Now I could have done it other way around ... no of ways in which team can be formed is 10C2*8C2 ,now why can't we add these two cases ?

There are 10 couples at party .In this question I have only doubt that if I chose 2 husbands first ,now for wives remaining choice will be 8 so it will be 10C2 *8C2 ,Now ...

radha gogia

730 views

radha gogia asked Nov 12, 2015

2 votes

1 answer

8483

From the word ASSASSINATION ,now in how many ways can we form 4 letter word from it ?
My confusion is how to deal with the case when I have 2 same and 2 different ,now since I have 3A's ,4 S so why can't I chose 2A's like 3C2 , what 's the problem in this ?

My confusion is how to deal with the case when I have 2 same and 2 different ,now since I have 3A's ,4 S so why can't I chose 2A's like 3C2 , what 's the problem in this ...

radha gogia

9.2k views

radha gogia asked Nov 12, 2015

4 votes

2 answers

8484

sets
Let S={1,2,3,4}.Total no of unordered pairs of disjoint subsets of S is equal to 1)25 2)34 3)42 4)41

Let S={1,2,3,4}.Total no of unordered pairs of disjoint subsets of S is equal to1)25 2)34 3)42 4)41

Pooja Palod

893 views

Pooja Palod asked Nov 12, 2015

3 votes

3 answers

8485

how many ways 10 persons can be divided into 5 teams of 2 each ?

radha gogia

6.2k views

radha gogia asked Nov 11, 2015

0 votes

1 answer

8486

From 2,3,4,4,5,how many numbers can be formed such that even digits are at odd places ?
Now I have 2 even positions and 2 odd positions and I have 3 even numbers 2 ,4 ,4 and 2 odd numbers so one odd position will be occupied by an even number but then even no can't be at odd position so then how to approach this question ?

Now I have 2 even positions and 2 odd positions and I have 3 even numbers 2 ,4 ,4 and 2 odd numbers so one odd position will be occupied by an even number but then even n...

radha gogia

1.4k views

radha gogia asked Nov 11, 2015

5 votes

3 answers

8487

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

8488

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

8489

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

8490

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

8491

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

24 votes

3 answers

8492

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

8493

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

8494

injection and surjection

Shefali

821 views

Shefali asked Nov 8, 2015

13 votes

4 answers

8495

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

8496

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

558 views

Soumyashree asked Nov 8, 2015

5 votes

1 answer

8497

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

830 views

makhdoom ghaya asked Nov 7, 2015

17 votes

5 answers

8498

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

3.2k views

makhdoom ghaya asked Nov 6, 2015

24 votes

3 answers

8499

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

4.6k views

makhdoom ghaya asked Nov 6, 2015

1 votes

1 answer

8500

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

614 views

Tendua asked Nov 6, 2015

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