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153
ISI2020-PCB-CS: 7
Consider two hosts, A and B, which may belong to the same network or two different networks connected through a router. Recall the Internet protocol where a sender host sends packets directly to a destination if the sender finds the network ID of the destination host same as that of its ...
Consider two hosts, A and B, which may belong to the same network or two different networks connected through a router. Recall the Internet protocol where a sender host s...
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1 votes
1 answer
154
ISI2020-PCB-CS: 8.1
Simplify the following Boolean function in product-of-sums form: $ F(A, B, C, D)=\sum(0,1,2,5,8,9,10) . $
Simplify the following Boolean function in product-of-sums form: $$ F(A, B, C, D)=\sum(0,1,2,5,8,9,10) . $$
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155
ISI2020-PCB-CS: 9
Consider a $\textsf{RISC}$ ... in the above $\textsf{RISC}$ machine? Explain your answer (no marks will be awarded if justification is not given).
Consider a $\textsf{RISC}$ machine where page tables of the virtual memory system may be swapped to disk from memory and neither machine instructions nor page-table entri...
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157
CMI-2021-DataScience-B: 5
Show that every selection of $503$ numbers from $\{1,2,3, \dots,987\}$ has two numbers with g.c.d. $1$. Recall that the g.c.d. of two positive integers $x, y$ is the largest positive integer smaller than $x, y$ which divides both $x$ and $y$.
Show that every selection of $503$ numbers from $\{1,2,3, \dots,987\}$ has two numbers with g.c.d. $1$. Recall that the g.c.d. of two positive integers $x, y$ is the larg...
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158
CMI-2021-DataScience-B: 10
Let $A$ be the $3 \times 3$ real matrix $\left(\begin{array}{lll} a & b & c \\ d & e & f \\ g & h & I \end{array}\right)$. Suppose $x^{T} Ax \geq 0$ for every $x \in \mathbb{R}^{3}$. Then show that all of $a, e$ and $i$ are non-negative.
Let $A$ be the $3 \times 3$ real matrix $\left(\begin{array}{lll} a & b & c \\ d & e & f \\ g & h & I \end{array}\right)$. Suppose $x^{T} Ax \geq 0$ for every $x \in \mat...
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159
CMI2022-B: 1
A Muller automaton is defined as a tuple $\text{M} = (\text{Q}, \text{I}, \Sigma, \rightarrow, \text{T})$ where: $\text{Q}$ is a finite set of states; $\text{I} \subseteq \text{Q}$ is the set of initial states; $\Sigma$ ... $a^{\ast}?$
A Muller automaton is defined as a tuple $\text{M} = (\text{Q}, \text{I}, \Sigma, \rightarrow, \text{T})$ where:$\text{Q}$ is a finite set of states;$\text{I} \subseteq \...
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164
CMI2021-B: 4
For a language $\text{L}$ over an alphabet $\Sigma$, define $\text{SW(L)}:= \left \{ y \in \Sigma^{\ast} \mid \exists x \in \Sigma^{\ast}\; \text{s.t.}\; xyx \in \text{L} \right \}$ Prove that if $\text{L}$ is regular, $\text{SW(L)}$ is also regular.
For a language $\text{L}$ over an alphabet $\Sigma$, define$$\text{SW(L)}:= \left \{ y \in \Sigma^{\ast} \mid \exists x \in \Sigma^{\ast}\; \text{s.t.}\; xyx \in \text{L}...
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166
In my mind
#include<stdio.h> Int main(void){ Int a=printf("%d",printf("%d %d",printf("GATE"),printf("OVERFLOW"))); printf("%d",a); return 0; } What is the reason for different output? Explain ideas.
#include<stdio.h>Int main(void){Int a=printf("%d",printf("%d %d",printf("GATE"),printf("OVERFLOW")));printf("%d",a);return 0;}What is the reason for different output?Expl...
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3 votes
1 answer
168
GATE CSE 1994 | Question: 17b
State whether the following statements are True or False with reasons for your answer: A two pass assembler uses its machine opcode table in the first pass of assembly.
State whether the following statements are True or False with reasons for your answer:A two pass assembler uses its machine opcode table in the first pass of assembly.
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5 votes
1 answer
169
GATE CSE 1994 | Question: 18b
State whether the following statements are True or False with reasons for your answer A symbol declared as ‘external’ in an assembly language program is assigned an address outside the program by the assembler itself.
State whether the following statements are True or False with reasons for your answerA symbol declared as ‘external’ in an assembly language program is assigned an ad...
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5 votes
5 answers
170
GATE CSE 1994 | Question: 14b
For a $B^+$ - tree of order $d$ with $n$ leaf nodes, the number of nodes accessed during a search is $O(\_)$.
For a $B^+$ - tree of order $d$ with $n$ leaf nodes, the number of nodes accessed during a search is $O(\_)$.
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1 votes
2 answers
171
CMI-2020-DataScience-B: 2
Consider the matrix $A=\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$. Find $A^n,$ in terms of $n,$ for $n\geq2.$
Consider the matrix $A=\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$. Find $A^n,$ in terms of $n,$ for $n\geq2.$
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5 votes
1 answer
173
Counting number of pairs whose sum is less than k
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k > 0$. Solve by summation rules. Solve by combinatorial argument.
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k 0$.Solve by summation rules.Solve by combinatorial argument.
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1 answer
177
Kenneth Rosen Edition 7 Exercise 8.3 Question 13 (Page No. 535)
Give a big-O estimate for the function $f$ given below if $f$ is an increasing function. $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$
Give a big-O estimate for the function $f$ given below if $f$ is an increasing function.$f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$
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1 votes
2 answers
178
Kenneth Rosen Edition 7 Exercise 8.3 Question 12 (Page No. 535)
Find $f (n)$ when $n = 3k,$ where $f$ satisfies the recurrence relation $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$
Find $f (n)$ when $n = 3k,$ where $f$ satisfies the recurrence relation $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$
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180
Kenneth Rosen Edition 7 Exercise 8.3 Question 10 (Page No. 535)
Find $f (n)$ when $n = 2^{k},$ where $f$ satisfies the recurrence relation $f (n) = f (n/2) + 1 \:\text{with}\: f (1) = 1.$
Find $f (n)$ when $n = 2^{k},$ where $f$ satisfies the recurrence relation $f (n) = f (n/2) + 1 \:\text{with}\: f (1) = 1.$
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