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Proof of Correctness of Different Sorting Algorithms
State Proof of Correctness for Different Popular Sorting AlgorithmSorting AlgoBest Case TCAVg Case TCWorst Case TCStable Sorting?Inplace Sorting?1. Bubble Sort \[O(n) \]\...
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185
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ISI2022 - MCS - PCB - Math | Question: 7
Consider an operating system consisting of a pair of processes $P_{0}$ and $P_{1}$. The structure of each process $P_{\mathrm{i}}$ is shown below.while(TRUE){ j = 1-i; fl...
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341
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ISI2022 - MCS - PCB (CS) | Question: 2
A room has four walls. In how many different ways can you color the four walls, using colors from the set $\text{\{Red, Green, Blue, Yellow\}}$, such that no two adjacent...
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338
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ISI2023-MCS-PCA | Question: 39
Consider the following program fragment:1. i=1; 2. while (i <= n) do 3. begin 4. sum = sum +a[i]; 5. i=1+1; 6. endLet (i) $\boldsymbol{A}$ represent the initialization in...
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2 2 answers
764
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ISI PCA 2024 | Question : 2
Let $\mathbf{C} = \{ (1, 2), (2, 1) \}$ be a basis of $\mathbb{R}^2$ and $T: \mathbb{R}^2 \to \mathbb{R}^2$ be defined by\[T \begin{pmatrix} x \\ y \end{pmatrix} = \begin...
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1 1 answer
633
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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 thestate diagram with minimum number of s...
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1 1 answer
320
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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 $\a...
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263
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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 $\displayst...
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1 1 answer
489
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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 c...
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2 2 answers
896
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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. ...
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388
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ISI 2019 | PCB CS | Question: 10
Let $R$ be a relation with functional dependencies $\mathcal{F}$. For any subset of attributes $X \subseteq R$, the closure of $X$ is defined as the set$$ X^{+}=\{A \in R...
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224
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ISI 2019 | PCB CS | Question: 13
An $n$-variable Boolean function $f:\{0,1\}^{n} \rightarrow\{0,1\}$ is called symmetric if its value depends only on the number of $1 \text{'s}$ in the input. Let $\sigma...
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349
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ISI 2019 | PCB CS | Question: 14
Let the valid moves along a staircase be $U$ (one step up) and $D$ (one step down). For example, the string $s=U U D U$ represents the sequence of moves as two steps up, ...
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1 1 answer
397
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ISI 2019 | PCB CS | Question: 16
The following function computes an array $\textsf{SPF},$ where, for any integer $1<1<1000, \textsf{SPF[i]}$ is the smallest prime factor of $\textsf{i}.$ For example, $\t...
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524
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ISI 2019 | PCB CS | Question: 18
Consider a $5$-stage instruction pipeline. The stages and the corresponding stage delays are given below. InstructionStage delayFetch instruction (FI)3 nsDecode instruct...
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1 1 answer
324
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ISI 2019 | PCB CS | Question: 19
The data link layer uses a fixed-size sliding window protocol, where the window size for the connection is equal to twice the bandwidth-delay product of the network path....
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967
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ISI 2021 | PCB CS | Question: 2
Let $P$ be a set of $n$ real numbers. For any two real numbers $a$ and $b$ $(a<b),$ define $$ R(a, b)=|\{x \in P \mid a \leq x \leq b\}| . $$Design a suitable data struct...
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ISI 2021 | PCB CS | Question: 8
Consider the following language $L$ over the alphabet $\Sigma=\{a, b, c\}$. $$ L=\left\{a^{i} b^{j} c^{k} \mid i, j, k \geq 0 \text {, and if } i=1 \text { then } j=k\rig...
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1 1 answer
593
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ISI 2021 | PCB CS | Question: 10
Consider sending a message of $10,000$ bits from the source node $S$ to the destination node $D$ passing through the two routers $R 1$ and $R 2$ as shown in the figure. E...
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280
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ISI 2020 | PCB Mathematics | Question: 5.1
Prove that if $N$ and $K$ are normal subgroups of a group $G$ such that $N \cap K=\left\{e_{G}\right\}$, then $x y=y x, \forall x \in N, \forall y \in K$.
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451
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ISI2020-PCB-CS: 6
Let $L=\left\{s \overline{s_{R}} \mid s \in\{0,1\}^{*}\right\}$ be a language over alphabet $\{0,1\}$, where $\overline{s_{R}}$ describes the reverse complement of $s$. F...
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465
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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 s...
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523
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ISI2020-PCB-CS: 9
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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1 1 answer
567
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ISI2021-MMA: 14
Given a real number $\alpha \in (0, 1),$ define a sequence $\{ x_{n}\}_{n \geq 0}$ by the following recurrence relation:$$x_{n+1} = \alpha x_{n} + (1 – \alpha) x_{n – 1},...
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670
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ISI2021-MMA: 15
A straight line passes through the intersection of the lines given by $3x – 4y + 1 = 0$ and $5x + y = 1$ and makes equal intercepts of the same sign on the coordinate axe...
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488
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ISI2021-MMA: 27
Consider two real valued functions $f$ and $g$ given by $$f(x)=\frac{x}{x-1} \; \text{for } x>1, \quad \text{and }\quad g(x)=7-x^{3} \; \text{for } x \in \mathbb{R}.$$ Wh...
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1 1 answer
979
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ISI Kolkata | MMA | 2022 --- A lie detector determines correctly ....
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921
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ISI2021-PCB-C10
Suppose instead of a decoder with n input bits (n is even) to access a memory of size 2^n, one uses two decoders of input sizes k bits and (n-k) bits. Explain how these t...
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2.7k
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List of MTech Exams after GATE
This can be a duplicate question please give me a link of the exams along with when in the date of registration so that I don't miss the dates.I am aware that TIFR happen...
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500
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ISI CSB 2018 Question number C4.
C4. Construct a Deterministic Finite Automaton (DFA) to acceptL={s1s2.....sn | n >=1; for each i=1,2,.....n, si € {0,1}, and the number of 1's minus the number of 0's in ...
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