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operating sysytem
a system has four processes and five allocable resources the current allocation and maximum needs are as follows Allocated Maximum Available process A 10211 11213 00x11 process B 20110 22210 process C 11010 21310 process D 11110 11221
Skarma Angmo
asked
in
Operating System
Sep 16
by
Skarma Angmo
77
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operating-system
deadlock-prevention-avoidance-detection
descriptive
0
votes
0
answers
2
ISI 2020 | PCB Mathematics | Question: 5.2
Deduce that if $N, H, K$ are normal subgroups of a group $G$ such that $ N \bigcap H=N \bigcap K=H \bigcap K=\left\{e_{G}\right\} $ and $G=H K$, then $N$ is an Abelian group.
Lakshman Patel RJIT
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Others
Aug 25
by
Lakshman Patel RJIT
16
views
isi2020-pcb-mathematics
descriptive
0
votes
0
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3
ISI2020-PCB-CS: 8.2
Consider the following state diagram of a sequential circuit, where each of a, b, c, d, e, f and g represents a state. Represent the state diagram with minimum number of states without altering the input-output relationships. Justify your answer.
Lakshman Patel RJIT
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in
Others
Aug 25
by
Lakshman Patel RJIT
17
views
isi2020-pcb-cs
descriptive
0
votes
1
answer
4
ISI 2021 | PCB CS | Question: 7.b
Consider a $4$-way set associative cache mapping, in which the cache blocks are grouped into sets and each set has $4$ blocks. There are $16$ cache blocks in total. The following memory block requests arrive in order when ... . Show the cache configuration (along with intermediate configurations) on meeting the above memory requirements. What is the hit ratio?
Lakshman Patel RJIT
asked
in
CO and Architecture
Aug 24
by
Lakshman Patel RJIT
45
views
isi2021-pcb-cs
descriptive
co-and-architecture
cache-memory
1
vote
3
answers
5
ISI2020-PCB-CS: 1.3
What does the following function compute for $x \neq 0?$ float isi1(float x, int y){ if (y==0){ return 1 ;} else if (y>0) {return isi1(x,-y);} else { return isi1(x, y+1)/x;} }
Lakshman Patel RJIT
asked
in
Programming
Aug 18
by
Lakshman Patel RJIT
176
views
isi2020-pcb-cs
identify-function
descriptive
0
votes
1
answer
6
ISI2020-PCB-CS: 1.2
What will be the output of the following C program? Justify your answer. Negative numbers are represented in $2$'s complement, #include<stdio.h> int main() { if (-~-1) printf("COVID"); if ((~7 & Ox000f ) == 8) printf (“19”); printf ("*"); }
Lakshman Patel RJIT
asked
in
Programming
Aug 18
by
Lakshman Patel RJIT
139
views
isi2020-pcb-cs
programming
programming-in-c
number-representation
descriptive
0
votes
0
answers
7
ISI 2019 | PCB Mathematics | Question: 1
Let $\left\{a_{n}\right\}$ be a decreasing sequence such that $\displaystyle{}\sum_{n=1}^{\infty} a_{n}$ is convergent. Prove that the sequence $\left\{n a_{n}\right\}$ goes to zero as $n \rightarrow \infty$.
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
29
views
isi2019-pcb-mathematics
descriptive
0
votes
1
answer
8
ISI 2019 | PCB Mathematics | Question: 2
Consider an $n \times n$ matrix $A=I_{n}-\alpha \alpha^{T}$, where $I_{n}$ is the identity matrix of order $n$ and $\alpha$ is an $n \times 1$ column vector such that $\alpha^{T} \alpha=1$. Prove that $A^{2}=A.$
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
27
views
isi2019-pcb-mathematics
descriptive
1
vote
0
answers
9
ISI 2019 | PCB Mathematics | Question: 3
Let $A$ and $B$ be two invertible real matrices of order $n$. Show that $\det(x A+(1-x) B)=0$ has finitely many solutions for $x.$
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
90
views
isi2019-pcb-mathematics
descriptive
0
votes
0
answers
10
ISI 2019 | PCB Mathematics | Question: 4
Show that for every $\theta \in\left(0, \frac{\pi}{2}\right),$ there exists a unique real number $x_{\theta}$ such that $ (\sin \theta)^{x_{\theta}}+(\cos \theta)^{x_{\theta}}=\frac{3}{2} . $
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
18
views
isi2019-pcb-mathematics
descriptive
0
votes
0
answers
11
ISI 2019 | PCB Mathematics | Question: 5
Suppose $f$ and $g$ are continuous real valued functions on $[a, b]$ and are differentiable on $(a, b)$. Assume that $g^{\prime}(x) \neq 0$ for any $x \in(a, b)$. Prove that there exists $\xi \in(a, b)$ such that $ \frac{f^{\prime}(\xi)}{g^{\prime}(\xi)}=\frac{f(b)-f(a)}{g(b)-g(a)} $
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
18
views
isi2019-pcb-mathematics
descriptive
0
votes
0
answers
12
ISI 2019 | PCB Mathematics | Question: 6
Consider the function $f: \mathbb{R}^{2} \rightarrow \mathbb{R}$ defined by $ f(0,0)=0, \quad f(x, y)=\frac{x y}{x^{2}+y^{2}}, \quad(x, y) \neq(0,0) . $ Prove that the directional derivative of $f$ at $(0,0)$ exists in all directions. Is $f$ continuous at $(0,0)$ ? Justify your answer.
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
12
views
isi2019-pcb-mathematics
descriptive
0
votes
0
answers
13
ISI 2019 | PCB Mathematics | Question: 7
Solve the differential equation $ x^{2}\left(x^{2}-1\right) \frac{d y}{d x}+x\left(x^{2}+1\right) y=x^{2}-1 . $
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
19
views
isi2019-pcb-mathematics
descriptive
0
votes
0
answers
14
ISI 2019 | PCB Mathematics | Question: 8
Let $f$ be a real valued function on $\mathbb{R}$. If for all real $x$, $ f(x)+3 f(1-x)=5 $ holds, then show that $f$ is a constant function.
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
16
views
isi2019-pcb-mathematics
descriptive
0
votes
0
answers
15
ISI 2019 | PCB Mathematics | Question: 9
Let $f:[0,1] \rightarrow[0, \infty)$ be a continuous function. Let $ a=\inf _{0 \leq x \leq 1} f(x) \text { and } b=\sup _{0 \leq x \leq 1} f(x) . $ For every positive integer $m$ ... $c_{m} \in[a, b]$, for all $m \geq 1$, $\displaystyle{}\lim _{m \rightarrow \infty} c_{m}$ exists and find its value.
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
13
views
isi2019-pcb-mathematics
descriptive
0
votes
0
answers
16
ISI 2019 | PCB Mathematics | Question: 10
Let $f_{1}:[0,4] \rightarrow[0,4]$ be defined by $f_{1}(x)=3-(x / 2)$. Define $f_{n}(x)=$ $f_{1}\left(f_{n-1}(x)\right)$ for $n \geq 2$. Prove that $\displaystyle{}\lim _{n \rightarrow \infty} f_{n}(0)$ exists. Find the set of all $x$ such that $\displaystyle{}\lim _{n \rightarrow \infty} f_{n}(x)$ exists and also find the corresponding limits.
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
12
views
isi2019-pcb-mathematics
descriptive
0
votes
0
answers
17
ISI 2019 | PCB Mathematics | Question: 11
Let $m$ be a fixed integer greater than $2.$ Prove that all simple graphs having $n\;(n \geq 3)$ vertices and with $m$ edges are connected if and only if $m>\left(\begin{array}{c}n-1 \\ 2\end{array}\right)$.
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
12
views
isi2019-pcb-mathematics
descriptive
0
votes
0
answers
18
ISI 2019 | PCB Mathematics | Question: 12
Suppose the collection $\left\{A_{1}, \cdots, A_{k}\right\}$ forms a group under matrix multiplication, where each $A_{i}$ is an $n \times n$ real matrix. Let $\displaystyle{}A=\sum_{i=1}^{k} A_{i}$. Show that $A^{2}=k A$. If the trace of $A$ is zero, then show that $A$ is the zero matrix.
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
17
views
isi2019-pcb-mathematics
descriptive
0
votes
0
answers
19
ISI 2019 | PCB Mathematics | Question: 13
Let $A$ be an $n \times n$ integer matrix whose entries are all even. Show that the determinant of $A$ is divisible by $2^{n}$. Hence or otherwise, show that if $B$ is an $n \times n$ matrix whose entries are $\pm 1$, then the determinant of $B$ is divisible by $2^{n-1}$.
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
14
views
isi2019-pcb-mathematics
descriptive
0
votes
0
answers
20
ISI 2019 | PCB Mathematics | Question: 15
Let $n, r, s$ be positive integers, each greater than $2.$ Prove that $n^{r}-1$ divides $n^{s}-1$ if and only if $r$ divides $s.$
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
12
views
isi2019-pcb-mathematics
descriptive
0
votes
1
answer
21
ISI 2019 | PCB Mathematics | Question: 17
Show that $5|x|+x(x-2) \geq 0$ for every real number $x.$
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
30
views
isi2019-pcb-mathematics
descriptive
0
votes
0
answers
22
ISI 2019 | PCB Mathematics | Question: 19
Let $G$ be a finite group and $H$ the only subgroup of $G$ of order $|H|$. Prove that $H$ is normal in $G.$
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
13
views
isi2019-pcb-mathematics
descriptive
0
votes
0
answers
23
ISI 2019 | PCB Mathematics | Question: 20
Let $H$ and $K$ be subgroups of a group $G$ of finite indices $(\text{i.e.}, [G: H]<$ $\infty$ and $[G: K]<\infty).$ Prove that $H \cap K$ is also of finite index $(\text{i.e.}, [G: H \cap K]<\infty).$
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
16
views
isi2019-pcb-mathematics
descriptive
1
vote
1
answer
24
ISI 2019 | PCB Mathematics | Question: 22
If $\alpha, \beta, \gamma$ are the roots of the equation $x^{3}+6 x+1=0$, then prove that $ \frac{\alpha}{\beta}+\frac{\beta}{\alpha}+\frac{\beta}{\gamma}+\frac{\gamma}{\beta}+\frac{\gamma}{\alpha}+\frac{\alpha}{\gamma}=-3. $
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
19
views
isi2019-pcb-mathematics
descriptive
0
votes
0
answers
25
ISI 2019 | PCB Mathematics | Question: 23
Let $X \sim \operatorname{Bin}(n, p)$, and $Y \sim \operatorname{Poisson}\; (\lambda)$. Let $ T=X_{1}+X_{2}+\cdots+X_{Y}, $ with $X_{i} \text{'s i. i. d}.\; \operatorname{Bin}(n, p)\;($and independent to $Y),$ ... $X).$ Compare Expectations of $T$ and $S$ and Variances of $T$ and $S.$
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
13
views
isi2019-pcb-mathematics
descriptive
1
vote
0
answers
26
ISI 2019 | PCB CS | Question: 1
Let $A$ be a sorted array containing $n$ distinct integers, such that, for all $1 \leq i<j \leq n$, we have $A[i]<A[j]$. Note that the integers stored in the array $A$ ... time of the algorithm should be asymptotically better than $O(n)$. Prove the correctness of your algorithm and state its asymptotic time complexity.
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
25
views
isi2019-pcb-cs
descriptive
0
votes
0
answers
27
ISI 2019 | PCB CS | Question: 3
When we add a pair of two-bit binary numbers, say $a b$ and $c d$, we get a number of at most three bits, say $p q r$. Using standard operators of Boolean algebra, namely $\operatorname{AND}\;(\wedge), \operatorname{OR}\; (\vee)$ and $\operatorname{NOT}\;(\neg)$, derive the Boolean expressions of $p, q$ and $r$ in terms of $a, b, c$ and $d$.
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
15
views
isi2019-pcb-cs
descriptive
0
votes
0
answers
28
ISI 2019 | PCB CS | Question: 4
In a binary tree $T$, for a node $v$, the $\text{LEFT-HEIGHT} (v)$ is the length of the longest path from $v$ to any leaf in the left subtree of $v$. If $v$ has no left child then $\text{LEFT-HEIGHT} (v)=0$ ... Design an efficient algorithm that, given a binary tree, enumerates all the nodes which are properly balanced.
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
12
views
isi2019-pcb-cs
descriptive
1
vote
0
answers
29
ISI 2019 | PCB CS | Question: 5
Consider a stack machine where the only available workspace is a stack whose elements are unsigned integers. We will denote the configuration of the stack by a sequence. For example $[a, b, c, d]$ represents a stack with $a$ being the ... $a b$.
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
22
views
isi2019-pcb-cs
descriptive
0
votes
0
answers
30
ISI 2019 | PCB CS | Question: 6
Consider the alphabet $\Sigma=\{0,1,2, \ldots, 9, \#\}$, and the language of strings of the form $x \# y \# z$, where $x, y$ and $z$ are strings of digit such that when viewed as numbers, satisfy the equation $x+y=z$. For example, the string $123 \# 45 \# 168$ is in this language because $123+45=168$. Is this language regular? Justify your answer.
Lakshman Patel RJIT
asked
in
Others
Aug 9
by
Lakshman Patel RJIT
9
views
isi2019-pcb-cs
descriptive
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