Most answered questions in Engineering Mathematics / GATE Overflow for GATE CSE

19 votes

7 answers

121

GATE CSE 1989 | Question: 3-v
Which of the following well-formed formulas are equivalent? $P \rightarrow Q$ $\neg Q \rightarrow \neg P$ $\neg P \vee Q$ $\neg Q \rightarrow P$

Which of the following well-formed formulas are equivalent?$P \rightarrow Q$$\neg Q \rightarrow \neg P$$\neg P \vee Q$$\neg Q \rightarrow P$

makhdoom ghaya

3.7k views

makhdoom ghaya asked Nov 27, 2016

2 votes

7 answers

122

is D36 distributive ?
In one text I read that , if n is square free it is DISTRIBUTIVE in other text I read that if n is square free it is BOOLEAN ALGEBRA . Which is most correct ? Here D36 is not square free then... what conclusion can I make ?

In one text I read that , if n is square free it is DISTRIBUTIVEin other text I read that if n is square free it is BOOLEAN ALGEBRA .Which is most correct ?Here D36 is n...

pC

13.8k views

pC asked Jun 23, 2016

56 votes

7 answers

123

GATE CSE 2016 Set 2 | Question: 04
Consider the systems, each consisting of $m$ linear equations in $n$ variables. If $m < n$, then all such systems have a solution. If $m > n$, then none of these systems has a solution. If $m = n$, then there exists a system which has a solution. ... $\text{II}$ and $\text{III}$ are true. Only $\text{III}$ is true. None of them is true.

Consider the systems, each consisting of $m$ linear equations in $n$ variables.If $m < n$, then all such systems have a solution.If $m n$, then none of these systems has...

Akash Kanase

15.9k views

Akash Kanase asked Feb 12, 2016

28 votes

7 answers

124

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

19 votes

7 answers

125

TIFR CSE 2013 | Part A | Question: 6
You are lost in the National park of Kabrastan. The park population consists of tourists and Kabrastanis. Tourists comprise two-thirds of the population the park and give a correct answer to requests for directions with probability $\dfrac{3}{4}$. The air of Kabrastan has an ... $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{2}{3}\right)$ $\left(\dfrac{3}{4}\right)$

You are lost in the National park of Kabrastan. The park population consists of tourists and Kabrastanis. Tourists comprise two-thirds of the population the park and give...

makhdoom ghaya

3.3k views

makhdoom ghaya asked Nov 4, 2015

25 votes

7 answers

126

TIFR CSE 2011 | Part A | Question: 19
Three dice are rolled independently. What is the probability that the highest and the lowest value differ by $4$? $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{9}\right)$ $\left(\dfrac{5}{18}\right)$ $\left(\dfrac{2}{9}\right)$

Three dice are rolled independently. What is the probability that the highest and the lowest value differ by $4$? $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\righ...

Arjun

2.9k views

Arjun asked Oct 19, 2015

29 votes

7 answers

127

TIFR CSE 2010 | Part A | Question: 12
The coefficient of $x^{3}$ in the expansion of $(1 + x)^{3} (2 + x^{2})^{10}$ is. $2^{14}$ $31$ $\left ( \frac{3}{3} \right ) + \left ( \frac{10}{1} \right )$ $\left ( \frac{3}{3} \right ) + 2\left ( \frac{10}{1} \right )$ $\left ( \frac{3}{3} \right ) \left ( \frac{10}{1} \right ) 2^{9}$

The coefficient of $x^{3}$ in the expansion of $(1 + x)^{3} (2 + x^{2})^{10}$ is.$2^{14}$$31$$\left ( \frac{3}{3} \right ) + \left ( \frac{10}{1} \right )$$\left ( \frac{...

makhdoom ghaya

3.3k views

makhdoom ghaya asked Oct 3, 2015

43 votes

7 answers

128

GATE CSE 2015 Set 3 | Question: 41
Let $R$ be a relation on the set of ordered pairs of positive integers such that $((p,q),(r,s)) \in R$ if and only if $p-s=q-r$. Which one of the following is true about $R$? Both reflexive and symmetric Reflexive but not symmetric Not reflexive but symmetric Neither reflexive nor symmetric

Let $R$ be a relation on the set of ordered pairs of positive integers such that $((p,q),(r,s)) \in R$ if and only if $p-s=q-r$. Which one of the following is true about ...

go_editor

12.9k views

go_editor asked Feb 15, 2015

51 votes

7 answers

129

GATE CSE 2015 Set 2 | Question: 26
Let $f(x)=x^{-\left(\frac{1}{3}\right)}$ and $A$ denote the area of region bounded by $f(x)$ and the X-axis, when $x$ varies from $-1$ to $1$. Which of the following statements is/are TRUE? $f$ is continuous in $[-1, 1]$ $f$ is not bounded in $[-1, 1]$ $A$ is nonzero and finite II only III only II and III only I, II and III

Let $f(x)=x^{-\left(\frac{1}{3}\right)}$ and $A$ denote the area of region bounded by $f(x)$ and the X-axis, when $x$ varies from $-1$ to $1$. Which of the following stat...

go_editor

17.3k views

go_editor asked Feb 12, 2015

31 votes

7 answers

130

GATE IT 2005 | Question: 34
Let $n =$ $p^{2}q$, where $p$ and $q$ are distinct prime numbers. How many numbers m satisfy $1 ≤ m ≤ n$ and $gcd$ $(m, n) = 1?$ Note that $gcd$ $(m, n)$ is the greatest common divisor of $m$ and $n$. $p(q - 1)$ $pq$ $\left ( p^{2}-1 \right ) (q - 1)$ $p(p - 1) (q - 1)$

Let $n =$ $p^{2}q$, where $p$ and $q$ are distinct prime numbers. How many numbers m satisfy $1 ≤ m ≤ n$ and $gcd$ $(m, n) = 1?$ Note that $gcd$ $(m, n)$ is the great...

Ishrat Jahan

8.1k views

Ishrat Jahan asked Nov 3, 2014

63 votes

7 answers

131

GATE IT 2006 | Question: 21
Consider the following first order logic formula in which $R$ is a binary relation symbol. $∀x∀y (R(x, y) \implies R(y, x))$ The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable

Consider the following first order logic formula in which $R$ is a binary relation symbol.$∀x∀y (R(x, y) \implies R(y, x))$The formula issatisfiable and validsatisfia...

Ishrat Jahan

13.4k views

Ishrat Jahan asked Oct 31, 2014

37 votes

7 answers

132

GATE IT 2006 | Question: 11
If all the edge weights of an undirected graph are positive, then any subset of edges that connects all the vertices and has minimum total weight is a Hamiltonian cycle grid hypercube tree

If all the edge weights of an undirected graph are positive, then any subset of edges that connects all the vertices and has minimum total weight is aHamiltonian cyclegri...

Ishrat Jahan

8.9k views

Ishrat Jahan asked Oct 31, 2014

32 votes

7 answers

133

GATE IT 2007 | Question: 23
A partial order $P$ is defined on the set of natural numbers as follows. Here $\frac{x}{y}$ denotes integer division. $(0, 0) \in P.$ $(a, b) \in P$ if and only if $(a \% 10) \leq (b \% 10$) and $(\frac{a}{10},\frac{b}{10})\in P.$ ... $P$? (i) and (iii) (ii) and (iv) (i) and (iv) (iii) and (iv)

A partial order $P$ is defined on the set of natural numbers as follows. Here $\frac{x}{y}$ denotes integer division.$(0, 0) \in P.$$(a, b) \in P$ if and only if $(a \% 1...

Ishrat Jahan

11.4k views

Ishrat Jahan asked Oct 29, 2014

38 votes

7 answers

134

GATE IT 2008 | Question: 29
If $M$ is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct? S1: Each row of $M$ can be represented as a linear combination of the other rows S2: Each column of $M$ can be represented as a linear combination of the other columns S3 ... solution S4: $M$ has an inverse $S3$ and $S2$ $S1$ and $S4$ $S1$ and $S3$ $S1, S2$ and $S3$

If $M$ is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct?S1: Each row of $M$ can be represented as a linear combination of...

Ishrat Jahan

9.6k views

Ishrat Jahan asked Oct 28, 2014

58 votes

7 answers

135

GATE IT 2008 | Question: 4
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes? $5$ $4$ $3$ $2$

What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes?$5$$4$$3$$2$

Ishrat Jahan

59.0k views

Ishrat Jahan asked Oct 27, 2014

50 votes

7 answers

136

GATE CSE 1996 | Question: 1.7
Let $Ax = b$ be a system of linear equations where $A$ is an $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is an $n \times1$ column vector of unknowns. Which of the following is false? The system has a solution if and ... a unique solution. The system will have only a trivial solution when $m=n$, $b$ is the zero vector and $\text{rank}(A) =n$.

Let $Ax = b$ be a system of linear equations where $A$ is an $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is an $n \times1$ column vector of unknow...

Kathleen

21.5k views

Kathleen asked Oct 9, 2014

24 votes

7 answers

137

GATE CSE 1995 | Question: 1.24
The rank of the following $(n+1) \times (n+1)$ matrix, where $a$ ... $1$ $2$ $n$ Depends on the value of $a$

The rank of the following $(n+1) \times (n+1)$ matrix, where $a$ is a real number is $$ \begin{bmatrix} 1 & a & a^2 & \dots & a^n \\ 1 & a & a^2 & \dots & a^n \\ \vdots ...

Kathleen

5.0k views

Kathleen asked Oct 8, 2014

23 votes

7 answers

138

GATE CSE 1997 | Question: 4.2
Let $A=(a_{ij})$ be an $n$-rowed square matrix and $I_{12}$ be the matrix obtained by interchanging the first and second rows of the $n$-rowed Identity matrix. Then $AI_{12}$ is such that its first Row is the same as its second row Row is the same as the second row of $A$ Column is the same as the second column of $A$ Row is all zero

Let $A=(a_{ij})$ be an $n$-rowed square matrix and $I_{12}$ be the matrix obtained by interchanging the first and second rows of the $n$-rowed Identity matrix. Then $AI_{...

Kathleen

4.9k views

Kathleen asked Sep 29, 2014

49 votes

7 answers

139

GATE CSE 2011 | Question: 34
A deck of $5$ cards (each carrying a distinct number from $1$ to $5$) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number ... $\left(\dfrac{4}{25}\right)$ $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{2}{5}\right)$

A deck of $5$ cards (each carrying a distinct number from $1$ to $5$) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probabil...

go_editor

18.2k views

go_editor asked Sep 29, 2014

25 votes

7 answers

140

GATE CSE 2011 | Question: 31
Given $i = \sqrt{-1}$, what will be the evaluation of the definite integral $\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx$ ? $0$ $2$ $-i$ $i$

Given $i = \sqrt{-1}$, what will be the evaluation of the definite integral $\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx$ ?$0$$2$$-i$$i$

go_editor

10.9k views

go_editor asked Sep 29, 2014

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