Answers by srestha / GATE Overflow for GATE CSE

4 votes

41

GATE CSE 2014 Set 2 | Question: 47
The product of the non-zero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$

The product of the non-zero eigenvalues of the matrix is ____$\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & ...

37.3k views

answered Jul 24, 2019

0 votes

42

Michael Sipser Edition 3 Exercise 1 Question 55 (Page No. 91)
The pumping lemma says that every regular language has a pumping length $p,$ such that every string in the language can be pumped if it has length $p$ or more. If $p$ is a pumping length for language $A,$ so is any length $p^{'}\geq p.$ The minimum pumping ... $\epsilon$ $1^{*}01^{*}01^{*}$ $10(11^{*}0)^{*}0$ $1011$ $\sum^{*}$

The pumping lemma says that every regular language has a pumping length $p,$ such that every string in the language can be pumped if it has length $p$ or more. If $p$ is ...

2.3k views

answered Jul 14, 2019

0 votes

43

Kenneth Rosen Edition 6 Question 45 (Page No. 346)
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?

How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?

9.2k views

answered Jul 14, 2019

0 votes

44

Michael Sipser Edition 3 Exercise 2 Question 30 (Page No. 157)
Use the pumping lemma to show that the following languages are not context free$.$ $\{0^{n}1^{n}0^{n}1^{n}\mid n\geq 0\}$ $\{0^{n}\#0^{2n}\#0^{3n}\mid n\geq 0\}$ $\{w\#t\mid w$ $\text{ is a substring of}$ $ t,$ $\text{where}$ ... $\text{each}$ $ t_{i}\in\{a,b\}^{*},$ $\text{and}$ $ t_{i}=t_{j}$ $\text{ for some}$ $ i\neq j\}$

Use the pumping lemma to show that the following languages are not context free$.$$\{0^{n}1^{n}0^{n}1^{n}\mid n\geq 0\}$$\{0^{n}\#0^{2n}\#0^{3n}\mid n\geq 0\}$$\{w\#t\mid...

1.1k views

answered Jul 12, 2019

0 votes

45

MADEEASY
Consider a set S={1000,1001,1002........,9999}. The numbers in set S having atleast one digit as 2 and atleast one digit as 5 are?

Consider a set S={1000,1001,1002........,9999}. The numbers in set S having atleast one digit as 2 and atleast one digit as 5 are?

1.4k views

answered Jul 11, 2019

0 votes

46

Kenneth Rosen Edition 6th Exercise 7.5 Question 3 e (Page No. 507)
Which of these relations on the set of all functions from Z to Z are equivalence relations? Determine the properties of an equivalence relation that the others lack. {(f, g) | f(0) = g(1) and f(1) = g(0)} In ... made to check the reflexive property. Why can't we check f(0)=f(0) to confirm the reflexive property. Please help.

Which of these relations on the set of all functions from Z to Z are equivalence relations? Determine the properties of an equivalence relation that the others lack. {(f,...

557 views

answered Jul 5, 2019

3 votes

47

UGC NET CSE | June 2019 | Part 2 | Question: 22
Consider the following C-code fragment running on a $32$-bit $X86$ machine: typedef struct { union { unsigned char a; unsigned short b; } U; unsigned char c; }S; S B[10]; S*p=&B[4]; S*q=&B[5]; p → U.b=0x1234; /* structure S takes 32-bits */ If M is the ... $(M,N)$ is $(1,1)$ $(3,2)$ $(1,2)$ $(4,4)$

Consider the following C-code fragment running on a $32$-bit $X86$ machine:typedef struct { union { unsigned char a; unsigned short b; } U; unsigned char c; }S; S B[10...

2.9k views

answered Jul 2, 2019

1 votes

48

UGC NET CSE | June 2019 | Part 2 | Question: 24
Consider the following C++ function f(): unsigned int f(unsigned int n) { unsigned int b=0; while (n) { b+=n & 1; n>>1; } return b; } The function f() returns the int that represents the ____P____ in the binary representation of positive integer n, where P is number of $0$’s number of bits number of consecutive $1$’s number of $1$’s

Consider the following C++ function f():unsigned int f(unsigned int n) { unsigned int b=0; while (n) { b+=n & 1; n>>1; } return b; }The function f() returns the int that ...

2.4k views

answered Jul 2, 2019

4 votes

49

UGC NET CSE | June 2019 | Part 2 | Question: 20
Suppose that a computer program takes $100$ seconds of execution time on a computer with multiplication operation responsible for $80$ seconds of this time. How much do you have to improve the speed of the multiplication operation if you are ... this program four times faster? $14$ times faster $15$ times faster $16$ times faster $17$ times faster

Suppose that a computer program takes $100$ seconds of execution time on a computer with multiplication operation responsible for $80$ seconds of this time. How much do y...

6.0k views

answered Jul 2, 2019

1 votes

50

Kenneth Rosen Edition 7 Exercise 2.1 Question 23 (Page No. 126)
How many elements does each of these sets have where $a$ and $b$ are distinct elements? $P (\left \{a,b, \left \{a,b \right \} \right \})$ $P\left \{ \phi, a, \left \{ a \right \},\left \{ \left \{ a \right \} \right \}\right \}$ $P(P(\phi ))$

How many elements does each of these sets have where $a$ and $b$ are distinct elements? $P (\left \{a,b, \left \{a,b \right \} \right \})$$P\left \{ \phi, a, \left \{ a \...

2.3k views

answered Jul 1, 2019

2 votes

51

Kenneth Rosen Edition 7 Exercise 2.1 Question 24 (Page No. 126)
Determine whether each of these sets is the power set of a set, where $a$ and $b$ are distinct elements. $\phi$ $\left \{ \phi ,\left \{ a \right \} \right \}$ $\left \{ \phi ,\left \{ a \right \},\left \{ \phi ,a \right \} \right \}$ $\left \{ \phi ,\left \{ a \right \},\left \{ b \right \},\left \{ a,b \right \} \right \}$

Determine whether each of these sets is the power set of a set, where $a$ and $b$ are distinct elements.$\phi$$\left \{ \phi ,\left \{ a \right \} \right \}$$\left \{ \ph...

524 views

answered Jul 1, 2019

4 votes

52

Cormen Edition 3 Exercise 8.3 Question 4 (Page No. 200)
Show how to sort $n$ integers in the range $0$ to $n^3-1$ in $O(n)$ time.

Show how to sort $n$ integers in the range $0$ to $n^3-1$ in $O(n)$ time.

1.1k views

answered Jun 30, 2019

0 votes

53

Kenneth Rosen: Counting-13
How many bit strings with length not exceeding $n$ ,where n is a positive integer ,consist entirely of $1's?$

How many bit strings with length not exceeding $n$ ,where n is a positive integer ,consist entirely of $1's?$

2.4k views

answered Jun 25, 2019

0 votes

54

ISI2018-MMA-17
There are eight coins, seven of which have the same weight and the other one weighs more. In order to find the coin having more weight, a person randomly chooses two coins and puts one coin on each side of a common balance. If these two coins are found to have the same ... as before. The probability that the coin will be identified at the second draw is $1/2$ $1/3$ $1/4$ $1/6$

There are eight coins, seven of which have the same weight and the other one weighs more. In order to find the coin having more weight, a person randomly chooses two coin...

1.2k views

answered Jun 20, 2019

0 votes

55

ISI2018-MMA-18
Let $A_1 = (0, 0), A_2 = (1, 0), A_3 = (1, 1)\ $and$\ A_4 = (0, 1)$ be the four vertices of a square. A particle starts from the point $A_1$ at time $0$ and moves either to $A_2$ or to $A_4$ with equal probability. Similarly, in each of the subsequent ... $T$ be the minimum number of steps required to cover all four vertices. The probability $P(T = 4)$ is $0$ $1/16$ $1/8$ $1/4$

Let $A_1 = (0, 0), A_2 = (1, 0), A_3 = (1, 1)\ $and$\ A_4 = (0, 1)$ be the four vertices of a square. A particle starts from the point $A_1$ at time $0$ and moves either ...

1.0k views

answered Jun 20, 2019

0 votes

56

ISI2019-MMA-22
A coin with probability $p (0 < p < 1)$ of getting head, is tossed until a head appears for the first time. If the probability that the number of tosses required is even is $2/5$, then the value of $p$ is $2/7$ $1/3$ $5/7$ $2/3$

A coin with probability $p (0 < p < 1)$ of getting head, is tossed until a head appears for the first time. If the probability that the number of tosses required is even ...

896 views

answered Jun 20, 2019

4 votes

57

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...

1.9k views

answered Jun 19, 2019

0 votes

58

TIFR CSE 2013 | Part A | Question: 5
The late painter Maqbool Fida Husain once coloured the surface of a huge hollow steel sphere, of radius $1$ metre, using just two colours, Red and Blue. As was his style however, both the red and blue areas were a bunch of highly irregular disconnected ... $11 sq. metres$; None of the above.

The late painter Maqbool Fida Husain once coloured the surface of a huge hollow steel sphere, of radius $1$ metre, using just two colours, Red and Blue. As was his style ...

2.8k views

answered Jun 17, 2019

3 votes

59

TIFR CSE 2015 | Part A | Question: 15
Let $A$ and $B$ be non-empty disjoint sets of real numbers. Suppose that the average of the numbers in the first set is $\mu_{A}$ and the average of the numbers in the second set is $\mu_{B}$; let the corresponding variances be $v_{A}$ and $v_{B}$ respectively. If the average of the ... $p.v_{A}+ (1 - p). v_{B} + (\mu_{A}- \mu_{B})^{2}$

Let $A$ and $B$ be non-empty disjoint sets of real numbers. Suppose that the average of the numbers in the first set is $\mu_{A}$ and the average of the numbers in the se...

1.1k views

answered Jun 16, 2019

0 votes

60

Michael Sipser Edition 3 Exercise 1 Question 38 (Page No. 89)
An $\text{all-NFA}$ $M$ is a $\text{5-tuple}$ $(Q, Σ, δ, q_{0}, F)$ that accepts $x\in\sum^{*}$ if every possible state that $M$ could be in after reading input $x$ is a state from $F.$ Note ... string if some state among these possible states is an accept state$.$ Prove that $\text{all-NFAs}$ recognize the class of regular languages$.$

An $\text{all-NFA}$ $M$ is a $\text{5-tuple}$ $(Q, Σ, δ, q_{0}, F)$ that accepts $x\in\sum^{*}$ if every possible state that $M$ could be in after reading input $x$ is...

2.0k views

answered Jun 14, 2019

0 votes

61

Lexical Analysis: Self Doubt
The above diagram is Transition Diagrams for identifiers. As we can see that the identifier is said to be accepted if it starts with a letter and ends with a valid delimiter, which includes blank symbol, arithmetic, logical operator, left parenthesis, right ... with a delimiter and + is a valid delimiter and the error in declaration will not be detected at this stage...

The above diagram is Transition Diagrams for identifiers. As we can see that the identifier is said to be accepted if it starts with a letter and ends with a valid delimi...

1.9k views

answered Jun 9, 2019

0 votes

62

Algorithm-Self Doubt
How in a heap there are at most $\lceil \frac{n}{2^{h+1}} \rceil$ nodes of height h.

How in a heap there are at most $\lceil \frac{n}{2^{h+1}} \rceil$ nodes of height h.

415 views

answered Jun 6, 2019

0 votes

63

Stallings 6e Exercise-11.10 (page number-539) I/O Management
A 32-bit computer has two selector channels and one multiplexor channel. Each selector channel supports two magnetic disk and two magnetic tape units. The multiplexor channel has two line printers, two card readers, and ten VDT terminals ... reader 1.2 Kbytes/s VDT 1 Kbytes/s Estimate the maximum aggregate I/O transfer rate in this system

A 32-bit computer has two selector channels and one multiplexor channel. Each selector channel supports two magnetic disk and two magnetic tape units. The multiplexor cha...

2.0k views

answered Jun 5, 2019

0 votes

64

GATE 2019:EC
The value of integral $\int_{0}^{\pi }\int_{y}^{\pi }\frac{\sin x}{x}dxdy$ is equal to_________

The value of integral $\int_{0}^{\pi }\int_{y}^{\pi }\frac{\sin x}{x}dxdy$ is equal to_________

820 views

answered Jun 2, 2019

6 votes

65

Compiler design Self doubt
S → aSbS /bSaS / ϵ S → aABb A→ c/ ϵ B → d/ ϵ Which of the following is LL1. Explain in details.

S → aSbS /bSaS / ϵS → aABb A→ c/ ϵ B → d/ ϵWhich of the following is LL1. Explain in details.

2.1k views

answered Jun 1, 2019

2 votes

66

TIFR CSE 2011 | Part A | Question: 1
If either wages or prices are raised, there will be inflation. If there is inflation, then either the government must regulate it or the people will suffer. If the people suffer, the government will be unpopular. Government will not be ... raised Prices are not raised If the inflation is not regulated, then the prices are not raised Wages are not raised

If either wages or prices are raised, there will be inflation.If there is inflation, then either the government must regulate it or the people will suffer.If the people s...

3.0k views

answered May 31, 2019

2 votes

67

TIFR CSE 2010 | Part A | Question: 4
If the bank receipt is forged, then Mr. M is liable. If Mr. M is liable, he will go bankrupt. If the bank will loan him money, he will not go bankrupt. The bank will loan him money. Which of the following can be concluded from the above statements? Mr. M is liable The receipt is not forged Mr. M will go bankrupt The bank will go bankrupt None of the above

If the bank receipt is forged, then Mr. M is liable.If Mr. M is liable, he will go bankrupt.If the bank will loan him money, he will not go bankrupt.The bank will loan hi...

2.0k views

answered May 31, 2019

1 votes

68

Kenneth Rosen Edition 7 Exercise 1.4 Question 47 (Page No. 56)
Establish these logical equivalences, where $x$ does not occur as a free variable in $A$. Assume that the domain is nonempty. $(\forall x P(x)) \wedge A \equiv \forall x (P(x) \wedge A)$ $(\exists x P(x)) \wedge A \equiv \exists x (P(x) \wedge A)$

Establish these logical equivalences, where $x$ does not occur as a free variable in $A$. Assume that the domain is nonempty.$(\forall x P(x)) \wedge A \equiv \forall x (...

406 views

answered May 30, 2019

5 votes

69

GateForum Question Bank :Graph Theory
What is the probability that there is an edge in an undirected random graph having 8 vertices? 1 1/8

What is the probability that there is an edge in an undirected random graph having 8 vertices?1 1/8

2.1k views

answered May 19, 2019

0 votes

70

#probability(self doubt)
An automobile showroom has 10 cars, 2 of which are defective. If you are going to buy the 6th car sold that day at random, then the probability of selecting a defective car is??

An automobile showroom has 10 cars, 2 of which are defective. If you are going to buy the 6th car sold that day at random, then the probability of selecting a defective c...

258 views

answered May 13, 2019

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