Recent questions tagged normal / GATE Overflow for GATE CSE

36 votes

7 answers

2101

GATE CSE 2006 | Question: 21
For each element in a set of size $2n$, an unbiased coin is tossed. The $2n$ coin tosses are independent. An element is chosen if the corresponding coin toss was a head. The probability that exactly $n$ elements are chosen is $\frac{^{2n}\mathrm{C}_n}{4^n}$ $\frac{^{2n}\mathrm{C}_n}{2^n}$ $\frac{1}{^{2n}\mathrm{C}_n}$ $\frac{1}{2}$

For each element in a set of size $2n$, an unbiased coin is tossed. The $2n$ coin tosses are independent. An element is chosen if the corresponding coin toss was a head. ...

Rucha Shelke

8.2k views

Rucha Shelke asked Sep 17, 2014

70 votes

9 answers

2102

GATE CSE 2006 | Question: 20, ISRO2015-17
Consider the following log sequence of two transactions on a bank account, with initial balance $12000,$ that transfer $2000$ to a mortgage payment and then apply a $5\%$ interest. T1 start T1 B old $=12000$ new $=10000$ ... $3$ because transaction T1 has committed We can apply redo and undo operations in arbitrary order because they are idempotent

Consider the following log sequence of two transactions on a bank account, with initial balance $12000,$ that transfer $2000$ to a mortgage payment and then apply a $5\%$...

Rucha Shelke

28.1k views

Rucha Shelke asked Sep 17, 2014

51 votes

6 answers

2103

GATE CSE 2006 | Question: 19
Let $L_1=\{0^{n+m}1^n0^m\mid n,m\geq 0 \}$, $L_2=\{0^{n+m}1^{n+m}0^m\mid n,m\geq 0\}$ and $L_3=\{0^{n+m}1^{n+m}0^{n+m}\mid n,m\geq 0\} $. Which of these languages are NOT context free? $L_1$ only $L_3$ only $L_1$ and $L_2$ $L_2$ and $L_3$

Let$L_1=\{0^{n+m}1^n0^m\mid n,m\geq 0 \}$,$L_2=\{0^{n+m}1^{n+m}0^m\mid n,m\geq 0\}$ and$L_3=\{0^{n+m}1^{n+m}0^{n+m}\mid n,m\geq 0\} $. Which of these languages are NOT c...

Rucha Shelke

15.5k views

Rucha Shelke asked Sep 17, 2014

41 votes

5 answers

2104

GATE CSE 2006 | Question: 18
We are given a set $X = \{X_1,\ldots,X_n\}$ where $X_i=2^i$. A sample $S\subseteq X$ is drawn by selecting each $X_i$ independently with probability $P_i = \frac{1}{2}$ . The expected value of the smallest number in sample $S$ is: $\left(\frac{1}{n}\right)$ $2$ $\sqrt n$ $n$

We are given a set $X = \{X_1,\ldots,X_n\}$ where $X_i=2^i$. A sample $S\subseteq X$ is drawn by selecting each $X_i$ independently with probability $P_i = \frac{1}{2...

Rucha Shelke

16.1k views

Rucha Shelke asked Sep 17, 2014

59 votes

7 answers

2105

GATE CSE 2006 | Question: 17
An element in an array $X$ is called a leader if it is greater than all elements to the right of it in $X$. The best algorithm to find all leaders in an array solves it in linear time using a left to right pass of the array solves it in linear time using ... pass of the array solves it using divide and conquer in time $\Theta (n\log n)$ solves it in time $\Theta( n^2)$

An element in an array $X$ is called a leader if it is greater than all elements to the right of it in $X$. The best algorithm to find all leaders in an array solves it i...

Rucha Shelke

18.0k views

Rucha Shelke asked Sep 17, 2014

21 votes

5 answers

2106

GATE CSE 2006 | Question: 16, ISRO-DEC2017-27
Let S be an NP-complete problem and Q and R be two other problems not known to be in NP. Q is polynomial time reducible to S and S is polynomial-time reducible to R. Which one of the following statements is true? R is NP-complete R is NP-hard Q is NP-complete Q is NP-hard

Let S be an NP-complete problem and Q and R be two other problems not known to be in NP. Q is polynomial time reducible to S and S is polynomial-time reducible to R. Whic...

Rucha Shelke

18.1k views

Rucha Shelke asked Sep 17, 2014

35 votes

10 answers

2107

GATE CSE 2006 | Question: 15
Consider the following C-program fragment in which $i$, $j$ and $n$ are integer variables. for( i = n, j = 0; i > 0; i /= 2, j +=i ); Let $val(j)$ denote the value stored in the variable $j$ after termination of the for loop. Which one of the following is true? $val(j)=\Theta(\log n)$ $val(j)=\Theta (\sqrt{n})$ $val(j)=\Theta( n)$ $val(j)=\Theta (n\log n)$

Consider the following C-program fragment in which $i$, $j$ and $n$ are integer variables. for( i = n, j = 0; i 0; i /= 2, j +=i );Let $val(j)$ denote the value stored i...

Rucha Shelke

19.5k views

Rucha Shelke asked Sep 17, 2014

67 votes

4 answers

2108

GATE CSE 2006 | Question: 13
A scheme for storing binary trees in an array $X$ is as follows. Indexing of $X$ starts at $1$ instead of $0$. the root is stored at $X[1]$. For a node stored at $X[i]$, the left child, if any, is stored in $X[2i]$ and the right child, if any, in $X[2i+1]$. To be able to store any binary tree on n vertices the minimum size of $X$ should be $\log_2 n$ $n$ $2n+1$ $2^n-1$

A scheme for storing binary trees in an array $X$ is as follows. Indexing of $X$ starts at $1$ instead of $0$. the root is stored at $X $. For a node stored at $X[i]$, th...

Rucha Shelke

17.3k views

Rucha Shelke asked Sep 17, 2014

56 votes

6 answers

2109

GATE CSE 2003 | Question: 90
Consider the function $f$ defined below. struct item { int data; struct item * next; }; int f(struct item *p) { return ((p == NULL) || (p->next == NULL)|| ((p->data <= p ->next -> data) && f(p- ... order of data value the elements in the list are sorted in non-increasing order of data value not all elements in the list have the same data value

Consider the function $f$ defined below.struct item { int data; struct item * next; }; int f(struct item *p) { return ((p == NULL) || (p->next == NULL)|| ((p->data <= p -...

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