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31
DRDO CSE 2022 Paper 2 | Question: 25
Assume when encrypting $3$-bit plaintext with a block cipher with key $\text{K},$ ... with key $\mathrm{K}$ in counter mode (with initial counter value $=0):$ $\text{C}=100110000$ What was the plaintext?
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Computer Networks
Dec 15, 2022
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admin
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drdocse-2022-paper2
computer-networks
cryptography
7-marks
descriptive
1
vote
0
answers
32
DRDO CSE 2022 Paper 2 | Question: 26
Suppose $\mathrm{A}$ and $\mathrm{B}$ use Diffie-Hellnian key exchange. Let the commonly agreed (i.e., global public) prime number $(q)=13$ and the primitive root $(\alpha)=6$. If $\text{A}$ chose the private value $\left(X_{A}\right)=5$ ... value $\left(X_{B}\right)=4$. Find the shared secret key $(\mathrm{K})$ between $\mathrm{A}$ and $\mathrm{B}$
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in
Computer Networks
Dec 15, 2022
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admin
371
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drdocse-2022-paper2
computer-networks
cryptography
5-marks
descriptive
1
vote
1
answer
33
DRDO CSE 2022 Paper 2 | Question: 27
A transposition cipher (but not a rail-fence cipher) was used to produce the following ciphertext: $\text{X 2! H M E S S S E 2 Y T A 2 I I A}$ The key used was: $5 \; 2 \; 6 \; 3 \; 4 \; 1.$ What was the plaintext used (in English)?
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asked
in
Computer Networks
Dec 15, 2022
by
admin
437
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drdocse-2022-paper2
computer-networks
cryptography
7-marks
descriptive
1
vote
0
answers
34
DRDO CSE 2022 Paper 2 | Question: 30
Given an input image of size $230 \times 230$ with convolution filter of size $5 \times 5$ and stride $3$. What would be the size of the output?
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asked
in
Computer Graphics
Dec 15, 2022
by
admin
358
views
drdocse-2022-paper2
computer-graphics
5-marks
descriptive
2
votes
2
answers
35
DRDO CSE 2022 Paper 2 | Question: 31
What is the State $\mathrm{X}$ called for the following machine learning model?
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asked
in
Artificial Intelligence
Dec 15, 2022
by
admin
680
views
drdocse-2022-paper2
artificial-intelligence
2-marks
descriptive
1
vote
1
answer
36
DRDO CSE 2022 Paper 2 | Question: 32
A perceptron consists of weights $\left[w_{1}, w_{2}, w_{3}, w_{4}\right]=[0.5,2,1,-3]$. The activation function is provided as $y=f(z)=1$ if $z \geq 2$ otherwise $0,$ where $z= \sum(w . d)$. What is the output $y$ ...
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asked
in
Artificial Intelligence
Dec 15, 2022
by
admin
396
views
drdocse-2022-paper2
artificial-intelligence
activation-function
5-marks
descriptive
1
vote
0
answers
37
DRDO CSE 2022 Paper 2 | Question: 12 (b)
Let $L_{1}$ and $L_{2}$ be two languages decidable by Non-deterministic Turing machines $M_{1}$ and $M_{2}$. Using $M_{1}$ and $M_{2}$, construct a Non-deterministic Turing machine for the following languages. $L=\left\{a \circ b \mid a \in L_{1}, b \in L_{2}\right\}$ where $a$ o $b$ denotes the concatenation of the strings $a$ and $b$
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Theory of Computation
Dec 15, 2022
by
admin
193
views
drdocse-2022-paper2
theory-of-computation
decidability
turing-machine
2-marks
descriptive
1
vote
0
answers
38
DRDO CSE 2022 Paper 2 | Question: 12 (c)
Let $L_{1}$ and $L_{2}$ be two languages decidable by Non-deterministic Turing machines $M_{1}$ and $M_{2}$. Using $M_{1}$ and $M_{2}$, construct a Non-deterministic Turing machine for the following languages. $L_{1} \cap L_{2}$
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in
Theory of Computation
Dec 15, 2022
by
admin
267
views
drdocse-2022-paper2
theory-of-computation
decidability
turing-machine
2-marks
descriptive
1
vote
0
answers
39
DRDO CSE 2022 Paper 2 | Question: 15 (c)
Answer the following. Which of the following are not keys in the database? Compliment * Agreement Construct Supplement
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asked
in
Databases
Dec 15, 2022
by
admin
268
views
drdocse-2022-paper2
databases
database-normalization
1-mark
descriptive
1
vote
0
answers
40
DRDO CSE 2022 Paper 2 | Question: 23 (b)
Fill in the table below to create firewall rules that perform the actions described below on a local network with address $1.2.3.0$ (subnet $255.255.255.0).$ Assume that by default, all traffic will be accepted. You can refer to an entire network by its ...
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asked
in
Computer Networks
Dec 15, 2022
by
admin
280
views
drdocse-2022-paper2
computer-networks
subnetting
2-and-half-marks
descriptive
1
vote
1
answer
41
DRDO CSE 2022 Paper 1 | Question: 33 (b)
Consider the following graph. How many nodes (apart from $s$) does the Depth First Search algorithm discover before discovering $t$ when starting from $s.$
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in
Algorithms
Dec 15, 2022
by
admin
260
views
drdocse-2022-paper1
2-marks
descriptive
1
vote
0
answers
42
DRDO CSE 2022 Paper 1 | Question: 32 (b)
Let us suppose we are given an integer $\text{N}$ in binary representation. Let us consider the following algorithm to check if $\text{N}$ is a prime. For every $i$ such that $2 \leq i \leq\lceil\sqrt{\text{N}}\rceil$ ... of the running time in terms of the input size? (Assume hypothetically that division can be done in $\text{O}(1)$ time).
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in
Algorithms
Dec 15, 2022
by
admin
225
views
drdocse-2022-paper1
algorithms
time-complexity
3-marks
descriptive
1
vote
0
answers
43
DRDO CSE 2022 Paper 1 | Question: 6 (b)
Let $\oplus$ sign denote bitwise addition modulo $2$. Let $n$ and $m$ be integers. Consider the set of $m$ equations on $n$ variables as follows. \[\begin{array}{l} a_{1,1} x_{1} \oplus a_{1,2} x_{2} \oplus \ldots \ ... $\{0,1\}$. What is the expected number of equations that can be satisfied if $x_i$'s are picked uniformly and independently at random.
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in
Digital Logic
Dec 15, 2022
by
admin
302
views
drdocse-2022-paper1
digital-logic
boolean-algebra
descriptive
3-and-half-marks
1
vote
1
answer
44
DRDO CSE 2022 Paper 1 | Question: 1
Compute $\left[M M^{T}\right]^{-1}$ for an orthogonal matrix where \[M=\left[\begin{array}{lll} \frac{1}{\sqrt{2}} & \frac{2}{\sqrt{2}} & \frac{-2}{\sqrt{2}} \\ \frac{-2}{\sqrt{2}} & \frac{2}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ \frac{2}{\sqrt{2}} & \frac{1}{\sqrt{2}} & \frac{2}{\sqrt{2}} \end{array}\right] .\]
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asked
in
Linear Algebra
Dec 15, 2022
by
admin
449
views
drdocse-2022-paper1
linear-algebra
matrix
3-marks
descriptive
1
vote
0
answers
45
DRDO CSE 2022 Paper 1 | Question: 2
Calculate the eigenvalues of matrix $M, M^{-1}, M^{2}$ and $M+2 I$ where \[M=\left[\begin{array}{cc} 4 & 5 \\ 2 & -5 \end{array}\right].\]
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in
Linear Algebra
Dec 15, 2022
by
admin
230
views
drdocse-2022-paper1
linear-algebra
eigen-value
5-marks
descriptive
1
vote
1
answer
46
DRDO CSE 2022 Paper 1 | Question: 3
With no unique solution, solve for $n$ with the following system of equations $\begin{array}{r} a+b+2 c=3 \\ a+2 b+3 c=4 \\ a+4 b+n c=6 \end{array}$
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asked
in
Linear Algebra
Dec 15, 2022
by
admin
277
views
drdocse-2022-paper1
linear-algebra
system-of-equations
5-marks
descriptive
1
vote
1
answer
47
DRDO CSE 2022 Paper 1 | Question: 4
Let the function $f(x)$ be defined as follows. \[f(x)=\left\{\begin{array}{ll} x^{2} & x \leq 1 \\ 2 a x^{2}+bx + c & 1 < x \leq 2 \\ x + 2d & x>1 \end{array}\right.\] Find the values of $a, b, c$ and $d$ such that $f$ is continuous and differentiable everywhere.
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asked
in
Calculus
Dec 15, 2022
by
admin
343
views
drdocse-2022-paper1
calculus
continuity-and-differentiability
5-marks
descriptive
1
vote
0
answers
48
DRDO CSE 2022 Paper 1 | Question: 5 (a)
Consider rolling of a dice experiment. Let $\text{A}$ be the event of getting an even number and $\mathrm{B}$ be the event of getting a prime number. Write the sets representing the following events. $\mathrm{A}$ or $\mathrm{B}$
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asked
in
Probability
Dec 15, 2022
by
admin
307
views
drdocse-2022-paper1
probability
1-mark
descriptive
2
votes
0
answers
49
DRDO CSE 2022 Paper 1 | Question: 6 (a)
Let $\oplus$ sign denote bitwise addition modulo $2$. Let $n$ and $m$ be integers. Consider the set of $m$ equations on $n$ variables as follows. \[\begin{array}{l} a_{1,1} x_{1} \oplus a_{1,2} x_{2} \oplus \ldots \oplus a_{1, n} x_{n}=b_{ ... $a_{1, n} x_{n}=b_{1}$ if all $x_{i}$'s are picked uniformly and independently at random from $\{0,1\}$.
admin
asked
in
Digital Logic
Dec 15, 2022
by
admin
327
views
drdocse-2022-paper1
digital-logic
boolean-algebra
probability
independent-events
3-and-half-marks
descriptive
1
vote
0
answers
50
DRDO CSE 2022 Paper 1 | Question: 7
Let $T$ be a subset of $\{1,2, \ldots, n\}$ of size $\frac{n}{2}$, sampled uniformly at random from all subsets of size $\frac{n}{2}$ of the same set $\{1,2, \ldots, n\}$. Let $S \subseteq\{1,2, \ldots, n\}$ be an arbitrary subset of size $\frac{n}{2}$. What is the probability that $|S \cap T|=\frac{n}{4}$.
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asked
in
Probability
Dec 15, 2022
by
admin
351
views
drdocse-2022-paper1
probability
uniform-distribution
6-marks
descriptive
1
vote
0
answers
51
DRDO CSE 2022 Paper 1 | Question: 8
Given a powerset $S$ of $\{1,2,3\}$, its partial order $\leq$ is given by set inclusion. That is, for any subsets $T_{1} \neq T_{2}$ of $\{1,2,3\}$ we have $T_{1} \leq T_{2}$ if and only if $T_{1} \subset T_{2}$. Construct the Hasse diagram on $S$ under this partial order definition.
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in
Set Theory & Algebra
Dec 15, 2022
by
admin
235
views
drdocse-2022-paper1
set-theory&algebra
partial-order
4-marks
descriptive
3
votes
0
answers
52
DRDO CSE 2022 Paper 1 | Question: 9
Count the number of perfect matchings in the bipartite graph whose adjacency matrix $\text{A}$ is as follows. \[\left[\begin{array}{lll} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right]\]
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asked
in
Graph Theory
Dec 15, 2022
by
admin
380
views
drdocse-2022-paper1
graph-theory
bipartite-graph
graph-matching
4-marks
descriptive
1
vote
0
answers
53
DRDO CSE 2022 Paper 1 | Question: 10
Given a tree $\text{T}$ and $\lambda \geq 2$ colours $\left(c_{1}, c_{2}, \ldots, c_{\lambda}\right),$ how many proper colourings of the tree $\text{T}$ are possible?
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asked
in
Graph Theory
Dec 15, 2022
by
admin
285
views
drdocse-2022-paper1
graph-theory
graph-coloring
4-marks
descriptive
1
vote
0
answers
54
DRDO CSE 2022 Paper 1 | Question: 11
Consider the following graph. Find closeness centrality of $\text{‘A’}$ node.
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asked
in
Graph Theory
Dec 15, 2022
by
admin
267
views
drdocse-2022-paper1
graph-theory
graph-connectivity
5-marks
descriptive
1
vote
0
answers
55
DRDO CSE 2022 Paper 1 | Question: 13
Consider the following graph. Which nodes form the cliques of size $3?$
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asked
in
Graph Theory
Dec 15, 2022
by
admin
274
views
drdocse-2022-paper1
graph-theory
graph-connectivity
5-marks
descriptive
1
vote
0
answers
56
DRDO CSE 2022 Paper 1 | Question: 14
Derangements are permutations $\pi$ of the set $\{1,2, \ldots, n\}$ such that $\pi(i) \neq i.$ Compute the number of derangements on the set $1,2, \ldots, n$.
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in
Combinatory
Dec 15, 2022
by
admin
178
views
drdocse-2022-paper1
combinatory
counting
7-marks
descriptive
1
vote
1
answer
57
DRDO CSE 2022 Paper 1 | Question: 15
What is the generating function corresponding to Fibonacci series. \[F_{n}=F_{n-1}+F_{n-2} .\] Note that $F_{0}=F_{1}=1$.
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in
Combinatory
Dec 15, 2022
by
admin
485
views
drdocse-2022-paper1
combinatory
generating-functions
6-marks
descriptive
1
vote
0
answers
58
DRDO CSE 2022 Paper 1 | Question: 16
Let us say we have a supply of $1$ rupee and $2$ rupee coins in large quantities. What is the generating function for the number of ways of giving change with $1$ rupee and $2$ rupee coins.
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asked
in
Combinatory
Dec 15, 2022
by
admin
382
views
drdocse-2022-paper1
combinatory
generating-functions
5-marks
descriptive
2
votes
1
answer
59
DRDO CSE 2022 Paper 1 | Question: 18
A gardener wants to buy $3$ neem plants, $5$ rose plants and $1$ banyan plant from a nursery having $7$ neem, $10$ rose and $6$ banyan plants. How many choices does a gardener have?
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in
Combinatory
Dec 15, 2022
by
admin
314
views
drdocse-2022-paper1
combinatory
counting
5-marks
descriptive
1
vote
1
answer
60
DRDO CSE 2022 Paper 1 | Question: 19
How many seven digit numbers are possible with exactly four $4 \mathrm{s}?$
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in
Combinatory
Dec 15, 2022
by
admin
348
views
drdocse-2022-paper1
combinatory
counting
5-marks
descriptive
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