Recent questions in Engineering Mathematics / GATE Overflow for GATE CSE

20 votes

2 answers

8381

TIFR CSE 2015 | Part B | Question: 11
Let $K_{n}$ be the complete graph on $n$ vertices labeled $\left\{1, 2,\dots ,n\right\}$ with $m=\frac{n (n - 1)}{2}$ edges. What is the number of spanning trees of $K_{n}$? $\frac{m}{n - 1}$ $m^{n - 1}$ $n^{n - 2}$ $n^{n - 1}$ None of the above

Let $K_{n}$ be the complete graph on $n$ vertices labeled $\left\{1, 2,\dots ,n\right\}$ with $m=\frac{n (n - 1)}{2}$ edges. What is the number of spanning trees of $K_{n...

makhdoom ghaya

2.2k views

makhdoom ghaya asked Dec 8, 2015

28 votes

7 answers

8382

TIFR CSE 2015 | Part B | Question: 5
Suppose $\begin{pmatrix} 0&1 &0&0&0&1 \\ 1&0&1&0&0&0 \\ 0&1&0&1&0&1 \\ 0&0&1&0&1&0 \\ 0&0&0&1&0&1 \\ 1&0&1&0&1&0 \end{pmatrix}$ is the adjacency ... the above adjacency matrix? Only $(i)$ Only $(ii)$ Only $(iii)$ Only $(iv)$ $(i)$ and $(ii)$

Suppose $\begin{pmatrix}0&1 &0&0&0&1 \\1&0&1&0&0&0 \\0&1&0&1&0&1 \\0&0&1&0&1&0 \\0&0&0&1&0&1 \\1&0&1&0&1&0\end{pmatrix}$is the adjacency matrix of an undirected graph...

makhdoom ghaya

4.3k views

makhdoom ghaya asked Dec 7, 2015

2 votes

0 answers

8383

bijection, surjection please confirm the ans

Jay Singh

259 views

Jay Singh asked Dec 7, 2015

14 votes

1 answer

8384

TIFR CSE 2015 | Part A | Question: 14
Consider the following $3 \times 3$ matrices. $M_{1}=\begin{pmatrix} 0&1&1 \\ 1&0&1 \\ 1&1&0 \end{pmatrix} $ $M_{2}=\begin{pmatrix} 1&0&1 \\ 0&0&0 \\ 1&0&1 \end{pmatrix} $ How may $0-1$ column vectors of the ... are done modulo $2$, i.e, $3 = 1$ (modulo $2$), $4 = 0$ (modulo $2$)). None Two Three Four Eight

Consider the following $3 \times 3$ matrices.$M_{1}=\begin{pmatrix} 0&1&1 \\1&0&1 \\1&1&0 \end{pmatrix} $$M_{2}=\begin{pmatrix} 1&0&1 \\0&0&0 \\1&0&1 \end{pmatrix} ...

makhdoom ghaya

1.6k views

makhdoom ghaya asked Dec 5, 2015

7 votes

2 answers

8385

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...

makhdoom ghaya

1.9k views

makhdoom ghaya asked Dec 5, 2015

15 votes

5 answers

8386

TIFR CSE 2015 | Part A | Question: 11
Suppose that $f(x)$ is a continuous function such that $0.4 \leq f(x) \leq 0.6$ for $0 \leq x \leq 1$. Which of the following is always true? $f(0.5) = 0.5$. There exists $x$ between $0$ and $1$ such that $f(x) = 0.8x$. There exists $x$ between $0$ and $0.5$ such that $f(x) = x$. $f(0.5) > 0.5$. None of the above statements are always true.

Suppose that $f(x)$ is a continuous function such that $0.4 \leq f(x) \leq 0.6$ for $0 \leq x \leq 1$. Which of the following is always true?$f(0.5) = 0.5$.There exists $...

makhdoom ghaya

2.8k views

makhdoom ghaya asked Dec 5, 2015

5 votes

0 answers

8387

TIFR CSE 2015 | Part A | Question: 10
Let $f(x), x\in \left[0, 1\right]$, be any positive real valued continuous function. Then $\displaystyle \lim_{n \rightarrow \infty} (n + 1) \int_{0}^{1} x^{n} f(x) \text{d}x$ equals. $\max_{x \in \left[0, 1\right]} f(x)$ $\min_{x \in \left[0, 1\right]} f(x)$ $f(0)$ $f(1)$ $\infty$

Let $f(x), x\in \left[0, 1\right]$, be any positive real valued continuous function. Then $\displaystyle \lim_{n \rightarrow \infty} (n + 1) \int_{0}^{1} x^{n} f(...

makhdoom ghaya

706 views

makhdoom ghaya asked Dec 5, 2015

32 votes

4 answers

8388

TIFR CSE 2015 | Part A | Question: 8
There is a set of $2n$ people: $n$ male and $n$ female. A good party is one with equal number of males and females (including the one where none are invited). The total number of good parties is. $2^{n}$ $n^{2}$ $\binom{n}{⌊n/2⌋}^{2}$ $\binom{2n}{n}$ None of the above

There is a set of $2n$ people: $n$ male and $n$ female. A good party is one with equal number of males and females (including the one where none are invited). The total n...

makhdoom ghaya

4.1k views

makhdoom ghaya asked Dec 5, 2015

20 votes

8 answers

8389

TIFR CSE 2015 | Part A | Question: 7
A $1 \times 1$ chessboard has one square, a $2 \times 2$ chessboard has five squares. Continuing along this fashion, what is the number of squares on the regular $8 \times 8$ chessboard? $64$ $65$ $204$ $144$ $256$

A $1 \times 1$ chessboard has one square, a $2 \times 2$ chessboard has five squares. Continuing along this fashion, what is the number of squares on the regular $8 \time...

makhdoom ghaya

3.2k views

makhdoom ghaya asked Dec 5, 2015

20 votes

5 answers

8390

TIFR CSE 2015 | Part A | Question: 6
Ram has a fair coin, i.e., a toss of the coin results in either head or tail and each event happens with probability exactly half $(1/2)$. He repeatedly tosses the coin until he gets heads in two consecutive tosses. The expected number of coin tosses that Ram does is. $2$ $4$ $6$ $8$ None of the above

Ram has a fair coin, i.e., a toss of the coin results in either head or tail and each event happens with probability exactly half $(1/2)$. He repeatedly tosses the coin u...

makhdoom ghaya

5.1k views

makhdoom ghaya asked Dec 5, 2015

1 votes

0 answers

8391

math
(Z- , >=) whereZ- is the negative integers is this woset expalin.? and also tell the least element.??

(Z- , >=) whereZ- is the negative integers is this woset expalin.? and also tell the least element.??

focus _GATE

301 views

focus _GATE asked Dec 5, 2015

18 votes

4 answers

8392

TIFR CSE 2015 | Part A | Question: 5
What is logically equivalent to "If Kareena and Parineeti go to the shopping mall then it is raining": If Kareena and Parineeti do not go to the shopping mall then it is not raining. If Kareena and Parineeti do not go to the shopping ... shopping mall. If it is not raining then Kareena and Parineeti do not go to the shopping mall. None of the above.

What is logically equivalent to "If Kareena and Parineeti go to the shopping mall then it is raining":If Kareena and Parineeti do not go to the shopping mall then it is n...

makhdoom ghaya

2.2k views

makhdoom ghaya asked Dec 4, 2015

1 votes

2 answers

8393

Find absolute minimum

Himanshu1

724 views

Himanshu1 asked Dec 4, 2015

2 votes

1 answer

8394

How many integers are there between 1 and 10^6 such that sum of digits is 12 ?

radha gogia

2.1k views

radha gogia asked Dec 4, 2015

8 votes

6 answers

8395

In how many ways can the entrepreneur assign 5 different tasks to 3 employees if each should get atleast 1 task ?

For this I considered cases1. 1 job each to 2 people and then jobs to a single person2. 2 jobs each to 2 people and then 1 job to a single person For the first case I di...

radha gogia

5.9k views

radha gogia asked Dec 3, 2015

1 votes

0 answers

8396

Find the Coefficient
Find the coefficient of $x^4$ in the series expansion of $(1+x+x^2)^{-4}$? How do you expand $(1+x+x^2)^{-4}$? Using Taylor series?

Find the coefficient of $x^4$ in the series expansion of $(1+x+x^2)^{-4}$?How do you expand $(1+x+x^2)^{-4}$? Using Taylor series?

amarVashishth

457 views

amarVashishth asked Dec 3, 2015

4 votes

2 answers

8397

statistics
Q) Let $x$ be normal variable with mean $8$ and standard deviation $4$ then $p(X\leq5)$ is A). Greater than zero but less than $0.5$ B). Greater than $0.75$ C). Greater than $0.5$ but less than $1$ D). Equal to $0.5$

Q) Let $x$ be normal variable with mean $8$ and standard deviation $4$ then $p(X\leq5)$ is A). Greater than zero but less than $0.5$B). Greater than $0.75$C). Greater tha...

richa116

1.1k views

richa116 asked Dec 3, 2015

14 votes

5 answers

8398

TIFR CSE 2015 | Part A | Question: 1
Consider a $6$-sided die with all sides not necessarily equally likely such that probability of an even number is $P (\left \{2, 4, 6 \right \}) =\dfrac{1}{2}$, probability of a multiple of $3$ is $P (\left \{3, 6 \right \}) = 1/3$ and probability of $1$ is ... $P(\left \{ 5 \right \}) \leq \dfrac{1}{3}$ None of the above

Consider a $6$-sided die with all sides not necessarily equally likely such that probability of an even number is $P (\left \{2, 4, 6 \right \}) =\dfrac{1}{2}$, probabil...

makhdoom ghaya

2.1k views

makhdoom ghaya asked Dec 2, 2015

2 votes

0 answers

8399

recurrence relation
for the recurrence relation an=6an-1-9an-2 + F n , what will be the particular solution if case 1; F n = 3n 5n+1 case 2; F n = 2n 5n+1

for the recurrence relation an=6an-1-9an-2 + F n , what will be the particular solutionif case 1; F n = 3n 5n+1 case 2; F n = 2n 5n+1

Banti Arya

358 views

Banti Arya asked Dec 2, 2015

5 votes

2 answers

8400

recurrence relation
the solution to the recurrence relation T(n)= T(n-1) +n, T(0)=2 is.. what is approach to solve it??

the solution to the recurrence relation T(n)= T(n-1) +n, T(0)=2 is..what is approach to solve it??

Banti Arya

1.4k views

Banti Arya asked Dec 2, 2015

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