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

23 votes

9 answers

61

GATE CSE 2003 | Question: 34
$m$ identical balls are to be placed in $n$ distinct bags. You are given that $m \geq kn$, where $k$ is a natural number $\geq 1$. In how many ways can the balls be placed in the bags if each bag must contain at least $k$ ... $\left( \begin{array}{c} m - kn + n + k - 2 \\ n - k \end{array} \right)$

$m$ identical balls are to be placed in $n$ distinct bags. You are given that $m \geq kn$, where $k$ is a natural number $\geq 1$. In how many ways can the balls be place...

Kathleen

11.2k views

Kathleen asked Sep 16, 2014

40 votes

9 answers

62

GATE CSE 2009 | Question: 22
For the composition table of a cyclic group shown below: ... $a,b$ are generators $b,c$ are generators $c,d$ are generators $d,a$ are generators

For the composition table of a cyclic group shown below:$$\begin{array}{|c|c|c|c|c|} \hline \textbf{*} & \textbf{a}& \textbf{b} &\textbf{c} & \textbf{d}\\\hline \textbf{a...

gatecse

8.9k views

gatecse asked Sep 15, 2014

38 votes

9 answers

63

GATE CSE 2001 | Question: 2.1
How many $4$-digit even numbers have all $4$ digits distinct? $2240$ $2296$ $2620$ $4536$

How many $4$-digit even numbers have all $4$ digits distinct?$2240$$2296$$2620$$4536$

Kathleen

12.8k views

Kathleen asked Sep 14, 2014

40 votes

9 answers

64

GATE CSE 1991 | Question: 03,xii
If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim F_3$ are both tautologies, then which of the following is true: Both $F_1$ and $F_2$ are tautologies The conjunction $F_1 \land F_2$ is not satisfiable Neither is tautologous Neither is satisfiable None of the above

If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim F_3$ are both tautologies, then which ...

Kathleen

9.0k views

Kathleen asked Sep 12, 2014

113 votes

9 answers

65

GATE CSE 2012 | Question: 38
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to $15$ $30$ $90$ $360$

Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to$15$$30$$90$$36...

gatecse

35.0k views

gatecse asked Sep 12, 2014

25 votes

9 answers

66

GATE CSE 2008 | Question: 1
$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals $1$ $-1$ $\infty$ $-\infty$

$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals$1$$-1$$\infty$$-\infty$

Kathleen

10.1k views

Kathleen asked Sep 11, 2014

5 votes

8 answers

67

GATE CSE 2024 | Set 1 | Question: 2
The product of all eigenvalues of the matrix $\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ is $-1$ $0$ $1$ $2$

The product of all eigenvalues of the matrix $\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ is$-1$$0$$1$$2$

Arjun

3.0k views

Arjun asked Feb 16

57 votes

8 answers

68

GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 14
Consider the following popular puzzle. When asked for the ages of her three children, Mrs. Baker says that Alice is her youngest child if Bill is not her youngest child, and that Alice is not her youngest child ... is her youngest child. Carl is her youngest child. Information is not sufficient to find out the youngest child.

Consider the following popular puzzle.When asked for the ages of her three children, Mrs. Baker says that “Alice is her youngest child if Bill is not her youngest child...

GO Classes

3.7k views

GO Classes asked Mar 30, 2022

14 votes

8 answers

69

GATE CSE 2021 Set 1 | Question: 7
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic. $S_1: (\neg p\wedge(p\vee q))\rightarrow q$ $S_2: q\rightarrow(\neg p\wedge(p\vee q))$ Which one of the following choices is correct? Both $S_1$ and ... but $S_2$ is not a tautology $S_1$ is not a tautology but $S_2$ is a tautology Neither $S_1$ nor $S_2$ is a tautology

Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic.$S_1: (\neg p\wedge(p\vee q))\rightarrow q$$S_2: q\rightarrow(\neg p\wedge...

Arjun

8.4k views

Arjun asked Feb 18, 2021

28 votes

8 answers

70

GATE CSE 2020 | Question: 42
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.

The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.

Arjun

16.6k views

Arjun asked Feb 12, 2020

10 votes

8 answers

71

ISI2017-MMA-29
Suppose the rank of the matrix $\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$ is $2$ for some real numbers $a$ and $b$. Then $b$ equals $1$ $3$ $1/2$ $1/3$

Suppose the rank of the matrix$$\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$$is $2$ for some real numbers $a$ and $b$. Then $b$ equals$1$$3$$1/2$$1/3$

jjayantamahata

2.8k views

jjayantamahata asked Mar 29, 2018

35 votes

8 answers

72

GATE CSE 2018 | Question: 15
Two people, $P$ and $Q$, decide to independently roll two identical dice, each with $6$ faces, numbered $1$ to $6$. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a ... and that all trials are independent. The probability (rounded to $3$ decimal places) that one of them wins on the third trial is ____

Two people, $P$ and $Q$, decide to independently roll two identical dice, each with $6$ faces, numbered $1$ to $6$. The person with the lower number wins. In case of a ti...

gatecse

11.0k views

gatecse asked Feb 14, 2018

73 votes

8 answers

73

GATE CSE 2017 Set 1 | Question: 02
Consider the first-order logic sentence $F:\forall x(\exists yR(x,y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$? $\exists y(\exists xR(x,y))$ $\exists y(\forall xR(x,y))$ $\forall y(\exists xR(x,y))$ $¬\exists x(\forall y¬R(x,y))$ IV only I and IV only II only II and III only

Consider the first-order logic sentence $F:\forall x(\exists yR(x,y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$?$\exists y(\ex...

khushtak

17.3k views

khushtak asked Feb 14, 2017

30 votes

8 answers

74

GATE CSE 2017 Set 1 | Question: 01
The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below? $p \Rightarrow q$ $q \Rightarrow p$ $\left ( ¬q \right ) \vee p$ $\left ( ¬p \right ) \vee q$ I only I and IV only II only II and III only

The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below?$p \Rightarrow q$$q \Rightarrow p$$\left ( ...

khushtak

9.1k views

khushtak asked Feb 14, 2017

47 votes

8 answers

75

GATE CSE 2017 Set 2 | Question: 52
If the characteristic polynomial of a $3 \times 3$ matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \mathbb{R}$, and one eigenvalue of $M$ is $2,$ then the largest among the absolute values of the eigenvalues of $M$ is _______

If the characteristic polynomial of a $3 \times 3$ matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \ma...

Madhav

15.6k views

Madhav asked Feb 14, 2017

36 votes

8 answers

76

GATE CSE 1987 | Question: 10b
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?

What is the generating function $G(z)$ for the sequence of Fibonacci numbers?

makhdoom ghaya

9.9k views

makhdoom ghaya asked Nov 14, 2016

43 votes

8 answers

77

GATE CSE 2006 | Question: 73
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of connected components in $G$ is: $n$ $n + 2$ $2^{\frac{n}{2}}$ $\frac{2^{n}}{n}$

The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding set...

go_editor

8.8k views

go_editor asked Apr 24, 2016

75 votes

8 answers

78

GATE CSE 2016 Set 1 | Question: 1
Let $p, q, r, s$ represents the following propositions. $p:x\in\left\{8, 9, 10, 11, 12\right\}$ $q:$ $x$ is a composite number. $r:$ $x$ is a perfect square. $s:$ $x$ is a prime number. The integer $x\geq2$ which satisfies $\neg\left(\left(p\Rightarrow q\right) \wedge \left(\neg r \vee \neg s\right)\right)$ is ____________.

Let $p, q, r, s$ represents the following propositions.$p:x\in\left\{8, 9, 10, 11, 12\right\}$$q:$ $x$ is a composite number.$r:$ $x$ is a perfect square.$s:$ $x$ is a pr...

Sandeep Singh

13.1k views

Sandeep Singh asked Feb 12, 2016

50 votes

8 answers

79

GATE CSE 2016 Set 2 | Question: 26
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions: $P:$ $R$ is reflexive. $Q:$ $R$ is transitive. Which one of the following statements is TRUE? ... and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.

A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions:$P:$ $R$ ...

Akash Kanase

14.7k views

Akash Kanase asked Feb 12, 2016

85 votes

8 answers

80

GATE CSE 2016 Set 2 | Question: 28
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. Consider the following statements: Each compound in U \ S reacts ... \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.

Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. ...

Akash Kanase

16.7k views

Akash Kanase asked Feb 12, 2016

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