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

47 votes

2 answers

2521

GATE IT 2005 | Question: 46
A line $L$ in a circuit is said to have a $stuck-at-0$ fault if the line permanently has a logic value $0$. Similarly a line $L$ in a circuit is said to have a $stuck-at-1$ fault if the line permanently has a logic value $1$. A circuit is said to have a ... number of distinct multiple $stuck-at$ faults possible in a circuit with $N$ lines is $3^N$ $3^N - 1$ $2^N - 1$ $2$

A line $L$ in a circuit is said to have a $stuck-at-0$ fault if the line permanently has a logic value $0$. Similarly a line $L$ in a circuit is said to have a $stuck-at-...

Ishrat Jahan

7.6k views

Ishrat Jahan asked Nov 3, 2014

34 votes

2 answers

2522

GATE IT 2004 | Question: 37
What is the number of vertices in an undirected connected graph with $27$ edges, $6$ vertices of degree $2, 3$ vertices of degree $4$ and remaining of degree $3$? $10$ $11$ $18$ $19$

What is the number of vertices in an undirected connected graph with $27$ edges, $6$ vertices of degree $2, 3$ vertices of degree $4$ and remaining of degree $3$?$10$$11$...

Ishrat Jahan

13.0k views

Ishrat Jahan asked Nov 2, 2014

28 votes

2 answers

2523

GATE IT 2004 | Question: 3
Let $a(x, y), b(x, y,)$ and $c(x, y)$ be three statements with variables $x$ and $y$ chosen from some universe. Consider the following statement: $\qquad(\exists x)(\forall y)[(a(x, y) \wedge b(x, y)) \wedge \neg c(x, y)]$ ... $\neg (\forall x)(\exists y)[(a(x, y) \vee b(x, y)) \to c(x, y)]$

Let $a(x, y), b(x, y,)$ and $c(x, y)$ be three statements with variables $x$ and $y$ chosen from some universe. Consider the following statement:$\qquad(\exists x)(\foral...

Ishrat Jahan

6.3k views

Ishrat Jahan asked Nov 1, 2014

27 votes

2 answers

2524

GATE IT 2004 | Question: 1
In a population of $N$ families, $50 \%$ of the families have three children, $30 \%$ of the families have two children and the remaining families have one child. What is the probability that a randomly picked child belongs to a family with two children? $\left(\dfrac{3}{23}\right)$ $\left(\dfrac{6}{23}\right)$ $\left(\dfrac{3}{10}\right)$ $\left(\dfrac{3}{5}\right)$

In a population of $N$ families, $50 \%$ of the families have three children, $30 \%$ of the families have two children and the remaining families have one child. What is...

Ishrat Jahan

10.5k views

Ishrat Jahan asked Nov 1, 2014

43 votes

2 answers

2525

GATE IT 2008 | Question: 22
Which of the following is the negation of $[∀ x, α → (∃y, β → (∀ u, ∃v, y))]$ $[∃ x, α → (∀y, β → (∃u, ∀ v, y))]$ $[∃ x, α → (∀y, β → (∃u, ∀ v, ¬y))]$ $[∀ x, ¬α → (∃y, ¬β → (∀u, ∃ v, ¬y))]$ $[∃ x, α \wedge (∀y, β \wedge (∃u, ∀ v, ¬y))]$

Which of the following is the negation of $[∀ x, α → (∃y, β → (∀ u, ∃v, y))]$$[∃ x, α → (∀y, β → (∃u, ∀ v, y))]$$[∃ x, α → (∀y, β → ...

Ishrat Jahan

7.8k views

Ishrat Jahan asked Oct 27, 2014

21 votes

2 answers

2526

GATE IT 2008 | Question: 2
A sample space has two events $A$ and $B$ such that probabilities $P(A\cap B) = \dfrac{1}{2}, P(A') = \dfrac{1}{3}, P(B') =\dfrac{1}{3}$. What is $P(A\cup B)$ ? $\left(\dfrac{11}{12}\right)$ $\left(\dfrac{10}{12}\right)$ $\left(\dfrac{9}{12}\right)$ $\left(\dfrac{8}{12}\right)$

A sample space has two events $A$ and $B$ such that probabilities $P(A\cap B) = \dfrac{1}{2}, P(A') = \dfrac{1}{3}, P(B') =\dfrac{1}{3}$. What is $P(A\cup B)$ ?$\left(\df...

Ishrat Jahan

4.4k views

Ishrat Jahan asked Oct 27, 2014

19 votes

2 answers

2527

On a set of n elements, how many relations are there that are both irreflexive and antisymmetric?
On a set of n elements, how many relations are there that are both irreflexive and antisymmetric? Please explain how to calculate .

On a set of n elements, how many relations are there that are both irreflexive and antisymmetric?Please explain how to calculate .

shree

26.4k views

shree asked Oct 24, 2014

27 votes

2 answers

2528

GATE CSE 1996 | Question: 3
Let $f$ be a function defined by $f(x) = \begin{cases} x^2 &\text{ for }x \leq 1\\ ax^2+bx+c &\text{ for } 1 < x \leq 2 \\ x+d &\text{ for } x>2 \end{cases}$ Find the values for the constants $a$, $b$, $c$ and $d$ so that $f$ is continuous and differentiable everywhere on the real line.

Let $f$ be a function defined by$$f(x) = \begin{cases} x^2 &\text{ for }x \leq 1\\ ax^2+bx+c &\text{ for } 1 < x \leq 2 \\ x+d &\text{ for } x>2 \end{cases}$$Find the va...

Kathleen

5.3k views

Kathleen asked Oct 9, 2014

6 votes

2 answers

2529

GATE CSE 1995 | Question: 7(A)
Determine the number of divisors of $600.$

Determine the number of divisors of $600.$

Kathleen

1.8k views

Kathleen asked Oct 8, 2014

12 votes

2 answers

2530

GATE CSE 1995 | Question: 2.13
A unit vector perpendicular to both the vectors $a=2i-3j+k$ and $b=i+j-2k$ is: $\frac{1}{\sqrt{3}} (i+j+k)$ $\frac{1}{3} (i+j-k)$ $\frac{1}{3} (i-j-k)$ $\frac{1}{\sqrt{3}} (i+j-k)$

A unit vector perpendicular to both the vectors $a=2i-3j+k$ and $b=i+j-2k$ is:$\frac{1}{\sqrt{3}} (i+j+k)$$\frac{1}{3} (i+j-k)$$\frac{1}{3} (i-j-k)$$\frac{1}{\sqrt{3}} (i...

Kathleen

4.1k views

Kathleen asked Oct 8, 2014

18 votes

2 answers

2531

GATE CSE 1994 | Question: 15
Use the patterns given to prove that $\sum\limits_{i=0}^{n-1} (2i+1) = n^2$ (You are not permitted to employ induction) Use the result obtained in (A) to prove that $\sum\limits_{i=1}^{n} i = \frac{n(n+1)}{2}$

Use the patterns given to prove that$\sum\limits_{i=0}^{n-1} (2i+1) = n^2$(You are not permitted to employ induction)Use the result obtained in (A) to prove that $\sum\li...

Kathleen

2.0k views

Kathleen asked Oct 5, 2014

25 votes

2 answers

2532

GATE CSE 1994 | Question: 2.8
Let $A, B,$ and $C$ be independent events which occur with probabilities $0.8, 0.5,$ and $0.3$ respectively. The probability of occurrence of at least one of the event is _______

Let $A, B,$ and $C$ be independent events which occur with probabilities $0.8, 0.5,$ and $0.3$ respectively. The probability of occurrence of at least one of the event is...

Kathleen

4.6k views

Kathleen asked Oct 4, 2014

42 votes

2 answers

2533

GATE CSE 1997 | Question: 6.1
A partial order $≤$ is defined on the set $S=\left \{ x, a_1, a_2, \ldots, a_n, y \right \}$ as $x$ $\leq _{i}$ $a_{i}$ for all $i$ and $a_{i}\leq y$ for all $i$, where $n ≥ 1$. The number of total orders on the set S which contain the partial order $≤$ is $n!$ $n+2$ $n$ $1$

A partial order $≤$ is defined on the set $S=\left \{ x, a_1, a_2, \ldots, a_n, y \right \}$ as $x$ $\leq _{i}$ $a_{i}$ for all $i$ and $a_{i}\leq y$ for all $i$, where...

Kathleen

8.9k views

Kathleen asked Sep 29, 2014

20 votes

2 answers

2534

GATE CSE 1997 | Question: 1.1
The probability that it will rain today is $0.5$. The probability that it will rain tomorrow is $0.6$. The probability that it will rain either today or tomorrow is $0.7$. What is the probability that it will rain today and tomorrow? $0.3$ $0.25$ $0.35$ $0.4$

The probability that it will rain today is $0.5$. The probability that it will rain tomorrow is $0.6$. The probability that it will rain either today or tomorrow is $0.7$...

Kathleen

6.3k views

Kathleen asked Sep 29, 2014

17 votes

2 answers

2535

GATE CSE 2011 | Question: 17
K4 and Q3 are graphs with the following structures. Which one of the following statements is TRUE in relation to these graphs? K4 is a planar while Q3 is not Both K4 and Q3 are planar Q3 is planar while K4 is not Neither K4 nor Q3 is planar

K4 and Q3 are graphs with the following structures.Which one of the following statements is TRUE in relation to these graphs?K4 is a planar while Q3 is notBoth K4 and Q3 ...

go_editor

7.0k views

go_editor asked Sep 29, 2014

19 votes

2 answers

2536

GATE CSE 2014 Set 3 | Question: 52
Let $\delta$ denote the minimum degree of a vertex in a graph. For all planar graphs on $n$ vertices with $\delta \geq 3$, which one of the following is TRUE? In any planar embedding, the number of faces is at least $\frac{n}{2}+2$ In any planar ... than $\frac{n}{2}+2$ There is a planar embedding in which the number of faces is at most $\frac {n}{\delta+1}$

Let $\delta$ denote the minimum degree of a vertex in a graph. For all planar graphs on $n$ vertices with $\delta \geq 3$, which one of the following is TRUE?In any plana...

go_editor

8.1k views

go_editor asked Sep 28, 2014

35 votes

2 answers

2537

GATE CSE 2014 Set 3 | Question: 5
If $V_1$ and $V_2$ are $4$-dimensional subspaces of a $6$-dimensional vector space $V$, then the smallest possible dimension of $V_1 \cap V_2$ is _____.

If $V_1$ and $V_2$ are $4$-dimensional subspaces of a $6$-dimensional vector space $V$, then the smallest possible dimension of $V_1 \cap V_2$ is _____.

go_editor

10.8k views

go_editor asked Sep 28, 2014

41 votes

2 answers

2538

GATE CSE 2014 Set 3 | Question: 3
Let $G$ be a group with $15$ elements. Let $L$ be a subgroup of $G$. It is known that $L \neq\ G$ and that the size of $L$ is at least $4$. The size of $L$ is __________.

Let $G$ be a group with $15$ elements. Let $L$ be a subgroup of $G$. It is known that $L \neq\ G$ and that the size of $L$ is at least $4$. The size of $L$ is __________....

go_editor

8.5k views

go_editor asked Sep 28, 2014

25 votes

2 answers

2539

GATE CSE 2013 | Question: 25
Which of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even. P only Q only Both P and Q Neither P nor Q

Which of the following statements is/are TRUE for undirected graphs?P: Number of odd degree vertices is even.Q: Sum of degrees of all vertices is even. P only Q only Both...

Arjun

16.0k views

Arjun asked Sep 24, 2014

16 votes

2 answers

2540

GATE CSE 1999 | Question: 2.1
Consider two events $E_1$ and $E_2$ such that probability of $E_1$, $P_r[E_1]=\frac{1}{2}$, probability of $E_2$, $P_r[E_{2}]=\frac{1}{3}$, and probability of $E_1$, and $E_2$, $P_r[E_1 \: and \: E_2] = \frac{1}{5}$. Which of the ... Events $E_1$ and $E_2$ are independent Events $E_1$ and $E_2$ are not independent $P_r \left[{E_1}\mid{E_2} \right] = \frac{4}{5}$

Consider two events $E_1$ and $E_2$ such that probability of $E_1$, $P_r[E_1]=\frac{1}{2}$, probability of $E_2$, $P_r[E_{2}]=\frac{1}{3}$, and probability of $E_1$, and ...

Kathleen

4.2k views

Kathleen asked Sep 23, 2014

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