Questions by Arjun / GATE Overflow for GATE CSE

50 votes

7 answers

1581

GATE CSE 2017 Set 2 | Question: 31
For any discrete random variable $X$, with probability mass function $P(X=j)=p_j, p_j \geq 0, j \in \{0, \dots , N \}$, and $\Sigma_{j=0}^N \: p_j =1$, define the polynomial function $g_x(z) = \Sigma_{j=0}^N \: p_j \: z^j$. For a certain ... . The expectation of $Y$ is $N \beta(1-\beta)$ $N \beta$ $N (1-\beta)$ Not expressible in terms of $N$ and $\beta$ alone

For any discrete random variable $X$, with probability mass function$P(X=j)=p_j, p_j \geq 0, j \in \{0, \dots , N \}$, and $\Sigma_{j=0}^N \: p_j =1$, define the polynomi...

16.1k views

asked Feb 14, 2017

67 votes

6 answers

1582

GATE CSE 2017 Set 2 | Question: 29
In a two-level cache system, the access times of $L_1$ and $L_2$ caches are $1$ and $8$ clock cycles, respectively. The miss penalty from the $L_2$ cache to main memory is $18$ clock cycles. The miss rate of $L_1$ cache is twice that of $L_2$. The average ... respectively are $0.111$ and $0.056$ $0.056$ and $0.111$ $0.0892$ and $0.1784$ $0.1784$ and $0.0892$

In a two-level cache system, the access times of $L_1$ and $L_2$ caches are $1$ and $8$ clock cycles, respectively. The miss penalty from the $L_2$ cache to main memory i...

28.7k views

asked Feb 14, 2017

32 votes

2 answers

1583

GATE CSE 2017 Set 2 | Question: 28
Given $f(w, x, y, z) = \Sigma_m(0,1, 2, 3, 7, 8, 10) + \Sigma_d(5, 6, 11, 15)$; where $d$ represents the 'don't-care' condition in Karnaugh maps. Which of the following is a minimum product-of-sums (POS) form of $f(w, x, y, z)$? $f=(\bar{w}+\bar{z}) (\bar{x}+z)$ $f=(\bar{w}+z) (x+z)$ $f=(w+z) (\bar{x}+z)$ $f=(w+\bar{z}) (\bar{x}+z)$

Given $f(w, x, y, z) = \Sigma_m(0,1, 2, 3, 7, 8, 10) + \Sigma_d(5, 6, 11, 15)$; where $d$ represents the 'don't-care' condition in Karnaugh maps. Which of the following i...

15.6k views

asked Feb 14, 2017

66 votes

6 answers

1584

GATE CSE 2017 Set 2 | Question: 26
$P$ and $Q$ are considering to apply for a job. The probability that $P$ applies for the job is $\dfrac{1}{4},$ the probability that $P$ applies for the job given that $Q$ applies for the job is $\dfrac{1}{2},$ and the probability that $Q$ applies for the ... $\left(\dfrac{5}{6}\right)$ $\left(\dfrac{7}{8}\right)$ $\left(\dfrac{11}{12}\right)$

$P$ and $Q$ are considering to apply for a job. The probability that $P$ applies for the job is $\dfrac{1}{4},$ the probability that $P$ applies for the job given that $Q...

12.6k views

asked Feb 14, 2017

33 votes

2 answers

1585

GATE CSE 2017 Set 2 | Question: 22
Let $P = \begin{bmatrix}1 & 1 & -1 \\2 & -3 & 4 \\3 & -2 & 3\end{bmatrix}$ and $Q = \begin{bmatrix}-1 & -2 &-1 \\6 & 12 & 6 \\5 & 10 & 5\end{bmatrix}$ be two matrices. Then the rank of $ P+Q$ is ___________ .

Let $P = \begin{bmatrix}1 & 1 & -1 \\2 & -3 & 4 \\3 & -2 & 3\end{bmatrix}$ and $Q = \begin{bmatrix}-1 & -2 &-1 \\6 & 12 & 6 \\5 & 10 & 5\end{bmatrix}$ be two matrices.Th...

12.0k views

asked Feb 14, 2017

20 votes

8 answers

1586

GATE CSE 2017 Set 2 | Question: 6
Which of the following statements about parser is/are CORRECT? $\text{Canonical LR}$ is more powerful than $\text{SLR}$ $\text{SLR}$ is more powerful than $\text{LALR}$ $\text{SLR}$ is more powerful than $\text{Canonical LR}$ I only II only III only II and III only

Which of the following statements about parser is/are CORRECT?$\text{Canonical LR}$ is more powerful than $\text{SLR}$$\text{SLR}$ is more powerful than $\text{LALR}$$\te...

7.9k views

asked Feb 14, 2017

24 votes

7 answers

1587

GATE CSE 2017 Set 2 | Question: 1
The representation of the value of a $16\text{-bit}$ unsigned integer $X$ in hexadecimal number system is $\textsf{BCA9}$. The representation of the value of $X$ in octal number system is $571244$ $736251$ $571247$ $136251$

The representation of the value of a $16\text{-bit}$ unsigned integer $X$ in hexadecimal number system is $\textsf{BCA9}$. The representation of the value of $X$ in octal...

6.9k views

asked Feb 14, 2017

54 votes

4 answers

1588

GATE CSE 2017 Set 1 | Question: 49
Consider a RISC machine where each instruction is exactly $4$ bytes long. Conditional and unconditional branch instructions use PC-relative addressing mode with Offset specified in bytes to the target location of the branch instruction. Further the Offset is ... $i,$ then the decimal value of the Offset is ____________ .

Consider a RISC machine where each instruction is exactly $4$ bytes long. Conditional and unconditional branch instructions use PC-relative addressing mode with Offset sp...

14.6k views

asked Feb 14, 2017

56 votes

10 answers

1589

GATE CSE 2017 Set 1 | Question: 48
Let $A$ be an array of $31$ numbers consisting of a sequence of $0$'s followed by a sequence of $1$'s. The problem is to find the smallest index $i$ such that $A\left [i \right ]$ is $1$ by probing the minimum number of locations in $A$. The worst case number of probes performed by an optimal algorithm is ____________.

Let $A$ be an array of $31$ numbers consisting of a sequence of $0$'s followed by a sequence of $1$'s. The problem is to find the smallest index $i$ such that $A\left [i ...

21.8k views

asked Feb 14, 2017

25 votes

9 answers

1590

GATE CSE 2017 Set 1 | Question: 47
The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .

The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .

11.7k views

asked Feb 14, 2017

52 votes

5 answers

1591

GATE CSE 2017 Set 1 | Question: 46
Consider a database that has the relation schema CR(StudentName, CourseName). An instance of the schema CR is as given below. ... $T2 \leftarrow CR\div T1$ The number of rows in $T2$ is ______________ .

Consider a database that has the relation schema CR(StudentName, CourseName). An instance of the schema CR is as given below.$$\begin{array}{|c|c|} \hline \textbf{Student...

13.0k views

asked Feb 14, 2017

58 votes

7 answers

1592

GATE CSE 2017 Set 1 | Question: 45
The values of parameters for the Stop-and-Wait ARQ protocol are as given below: Bit rate of the transmission channel $= 1$ Mbps. Propagation delay from sender to receiver $= 0.75$ ms. Time to process a frame $= 0.25$ ms. Number ... (expressed in percentage) of the Stop-and-Wait ARQ protocol for the above parameters is _____________ (correct to $2$ decimal places).

The values of parameters for the Stop-and-Wait ARQ protocol are as given below:Bit rate of the transmission channel $= 1$ Mbps.Propagation delay from sender to receiver $...

33.1k views

asked Feb 14, 2017

39 votes

12 answers

1593

GATE CSE 2017 Set 1 | Question: 44
In a RSA cryptosystem, a participant $A$ uses two prime numbers $p = 13$ and $q = 17$ to generate her public and private keys. If the public key of $A$ is $35$, then the private key of $A$ is __________ .

In a RSA cryptosystem, a participant $A$ uses two prime numbers $p = 13$ and $q = 17$ to generate her public and private keys. If the public key of $A$ is $35$, then the ...

23.9k views

asked Feb 14, 2017

57 votes

11 answers

1594

GATE CSE 2017 Set 1 | Question: 43
Consider the following grammar: stmt $\rightarrow$ if expr then expr else expr; stmt | $Ò$ expr $\rightarrow$ term relop term | term term $\rightarrow$ id | number id $\rightarrow$ a | b | c number $\rightarrow [0-9]$ where relop is a relational ... program if $e_1$ then $e_2$ else $e_3$ has $2$ control flow paths. $e_1 \rightarrow e_2$ and $e_1 \rightarrow e_3$.

Consider the following grammar:stmt $\rightarrow$ if expr then expr else expr; stmt | $Ò$expr $\rightarrow$ term relop term | termterm $\rightarrow$ id | numberid $\righ...

20.5k views

asked Feb 14, 2017

83 votes

4 answers

1595

GATE CSE 2017 Set 1 | Question: 42
In a database system, unique timestamps are assigned to each transaction using Lamport's logical clock. Let $TS(T_{1})$ and $TS(T_{2})$ be the timestamps of transactions $T_{1}$ and $T_{2}$ ... -free. The database system is starvation-free, but not deadlock-free. The database system is neither deadlock-free nor starvation-free.

In a database system, unique timestamps are assigned to each transaction using Lamport's logical clock. Let $TS(T_{1})$ and $TS(T_{2})$ be the timestamps of transactions ...

27.1k views

asked Feb 14, 2017

54 votes

5 answers

1596

GATE CSE 2017 Set 1 | Question: 41
Consider a database that has the relation schemas EMP(EmpId, EmpName, DeptId), and DEPT(DeptName, DeptId). Note that the DeptId can be permitted to be NULL in the relation EMP. Consider the following queries on the database expressed in tuple relational calculus. { ... Which of the above queries are safe? I and II only I and III only II and III only I, II and III

Consider a database that has the relation schemas EMP(EmpId, EmpName, DeptId), and DEPT(DeptName, DeptId). Note that the DeptId can be permitted to be NULL in the relatio...

25.7k views

asked Feb 14, 2017

46 votes

5 answers

1597

GATE CSE 2017 Set 1 | Question: 40
Recall that Belady's anomaly is that the page-fault rate may increase as the number of allocated frames increases. Now, consider the following statements: $S_1$: Random page replacement algorithm (where a page chosen at random is replaced) suffers from Belady's ... is true, $S_2$ is false $S_1$ is false, $S_2$ is true $S_1$ is false, $S_2$ is false

Recall that Belady's anomaly is that the page-fault rate may increase as the number of allocated frames increases. Now, consider the following statements:$S_1$: Random pa...

15.3k views

asked Feb 14, 2017

86 votes

4 answers

1598

GATE CSE 2017 Set 1 | Question: 39
Let $A$ and $B$ be finite alphabets and let $\#$ be a symbol outside both $A$ and $B$. Let $f$ be a total function from $A^{*}$ to $B^{*}$. We say $f$ is computable if there exists a Turing machine $M$ which given an ... $L_{f}$ is recursive, but not conversely. If $f$ is computable then $L_{f}$ is recursively enumerable, but not conversely.

Let $A$ and $B$ be finite alphabets and let $\#$ be a symbol outside both $A$ and $B$. Let $f$ be a total function from $A^{*}$ to $B^{*}$. We say $f$ is computable if th...

18.5k views

asked Feb 14, 2017

41 votes

6 answers

1599

GATE CSE 2017 Set 1 | Question: 38
Consider the following languages over the alphabet $\Sigma = \left \{ a, b, c \right \}$. Let $L_{1} = \left \{ a^{n}b^{n}c^{m}\mid m,n \geq 0 \right \}$ and $L_{2} = \left \{ a^{m}b^{n}c^{n}\mid m,n \geq 0 \right \}$. Which of the following are context-free languages? $L_{1} \cup L_{2}$ $L_{1} \cap L_{2}$ I only II only I and II Neither I nor II

Consider the following languages over the alphabet $\Sigma = \left \{ a, b, c \right \}$. Let $L_{1} = \left \{ a^{n}b^{n}c^{m}\mid m,n \geq 0 \right \}$ and $L_{2} = \le...

13.7k views

asked Feb 14, 2017

48 votes

8 answers

1600

GATE CSE 2017 Set 1 | Question: 37
Consider the context-free grammars over the alphabet $\left \{ a, b, c \right \}$ given below. $S$ and $T$ are non-terminals. $G_{1}:S\rightarrow aSb \mid T, T \rightarrow cT \mid \epsilon$ ... is Finite Not finite but regular Context-Free but not regular Recursive but not context-free

Consider the context-free grammars over the alphabet $\left \{ a, b, c \right \}$ given below. $S$ and $T$ are non-terminals.$G_{1}:S\rightarrow aSb \mid T, T \rightarrow...

12.3k views

asked Feb 14, 2017

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author	user:martin
title	title:apple
content	content:apple
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force match	+apple
views	views:100
score	score:10
answers	answers:2
is accepted	isaccepted:true
is closed	isclosed:true