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Questions by soujanyareddy13

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1 answer
1
Let $L=\{0^n1^n|n\ge 0\}$ be a context free language. Which of the following is correct? $\overline L$ is context free and $L^k$ is not context free for any $k\ge1$ $\overline L$ is not context free and $L^k$ is context free for any $k\ge1$ Both $\overline L$ and $L^k$ for any $k\ge1$ are context free Both $\overline L$ and $L^k$ for any $k\ge1$ are not context free
asked 19 hours ago in Theory of Computation 14 views
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0 answers
2
A perceptron has input weights $W_1=-3.9$ and $W_2=1.1$ with threshold value $T=0.3.$ What output does it give for the input $x_1=1.3$ and $x_2=2.2?$ $-2.65$ $-2.30$ $0$ $1$
asked 19 hours ago in Artificial Intelligence 11 views
0 votes
1 answer
3
A software program that infers and manipulates existing knowledge in order to generate new knowledge is known as: Data dictionary Reference mechanism Inference engine Control strategy
asked 19 hours ago in Artificial Intelligence 8 views
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0 answers
4
Which one of the following is correct, when a class grants friend status to another class? The member functions of the class generating friendship can access the members of the friend class All member functions of the class granted friendship have unrestricted access to the members of the class granting the friendship Class friendship is reciprocal to each other There is no such concept
asked 23 hours ago in Object Oriented Programming 7 views
0 votes
1 answer
5
Let $\Sigma=\{a,b\}.$ Given a language $L\underline\subset \Sigma^{\ast}$ and a word $w\in\Sigma^{\ast}$, define the languages: $Extend(L,w) :=\{xw\:|\:x\in L\}$ $Shrink(L,w) :=\{x\:|\:xw\in L\}$Show that if $L$ is regular, both $Extend(L,w)$ and $Shrink(L,w)$ are regular.
asked 23 hours ago in Theory of Computation 12 views
0 votes
1 answer
6
A box contains $5$ red marbles, $8$ green marbles, $11$ blue marbles, and $15$ yellow marbles. We draw marbles uniformly at random without replacement from the box. What is the minimum number of marbles to be drawn to ensure that out of the marbles drawn, at least $7$ are of the same colour? $7$ $8$ $23$ $24$ $39$
asked Mar 25 in Others 209 views
0 votes
1 answer
7
What is the area of a rectangle with the largest perimeter that can be inscribed in the unit circle (i.e., all the vertices of the rectangle are on the circle with radius $1$)? $1$ $2$ $3$ $4$ $5$
asked Mar 25 in Others 135 views
1 vote
0 answers
8
Let $M$ be an $n \times m$ real matrix. Consider the following: Let $k_{1}$ be the smallest number such that $M$ can be factorized as $A \cdot B$, where $A$ is an $n \times k_{1}$ and $B$ is a $k_{1} \times m$ matrix. Let $k_{2}$ ... $k_{2}= k_{3}< k_{1}$ $k_{1}= k_{2}= k_{3}$ No general relationship exists among $k_{1}, k_{2}$ and $k_{3}$
asked Mar 25 in Others 83 views
0 votes
1 answer
9
What is the probability that at least two out of four people have their birthdays in the same month, assuming their birthdays are uniformly distributed over the twelve months? $\frac{25}{48}$ $\frac{5}{8}$ $\frac{5}{12}$ $\frac{41}{96}$ $\frac{55}{96}$
asked Mar 25 in Others 81 views
0 votes
1 answer
10
Let $n, m$ and $k$ be three positive integers such that $n \geq m \geq k$. Let $S$ be a subset of $\left \{ 1, 2,\dots, n \right \}$ of size $k$. Consider sampling a function $f$ uniformly at random from the set of all functions mapping $\left \{ 1,\dots, n \right \}$ ... $1-\frac{k!\binom{m}{k}}{m^{k}}$ $1-\frac{k!\binom{n}{k}}{n^{k}}$ $1-\frac{k!\binom{n}{k}}{m^{k}}$
asked Mar 25 in Others 59 views
0 votes
1 answer
11
A matching in a graph is a set of edges such that no two edges in the set share a common vertex. Let $G$ be a graph on $n$ $\textit{vertices}$ in which there is a subset $M$ of $m$ $\textit{edges}$ which is a matching. Consider a random process where each vertex in the graph is independently selected ... $p^{2m}$ $\left ( 1-p^{2} \right )^{m}$ $1-\left ( 1-p\left ( 1-p \right ) \right )^{m}$
asked Mar 25 in Others 49 views
0 votes
1 answer
12
Let $d$ be the positive square integers (that is, it is a square of some integer) that are factors of $20^{5} \times 21^{5}$. Which of the following is true about $d$? $50\leq d< 100$ $100\leq d< 150$ $150\leq d< 200$ $200\leq d< 300$ $300\leq d$
asked Mar 25 in Others 51 views
0 votes
0 answers
13
Consider the sequence $y_{n}=\frac{1}{\int_{1}^{n}\frac{1}{\left ( 1+x/n \right )^{3}}dx}$ for $\text{n} = 2,3,4, \dots$ Which of the following is $\text{TRUE}$? The sequence $\{y_{n}\}$ does not have a limit as $n\rightarrow \infty$. $y_{n}\leq 1$ for all ... $0$. The sequence $\{y_{n}\}$ first increases and then decreases as $\text{n}$ takes values $2, 3, 4, \dots$
asked Mar 25 in Others 40 views
0 votes
2 answers
14
Fix $n\geq 6$. Consider the set $\mathcal{C}$ of binary strings $x_{1}, x_{2} \dots x_{n}$ of length $n$ such that the bits satisfy the following set of equalities, all modulo $2$: $x_{i}+x_{i+1}+x_{i+2}=0$ for all $1\leq i\leq n-2, x_{n-1}+x_{n}+x_{1}=0,$ ... $3$ $\left | \mathcal{C} \right |=4$. If $n\geq 6$ is not divisible by $3$ then $\left | \mathcal{C} \right |=1$.
asked Mar 25 in Others 69 views
0 votes
1 answer
15
Lavanya and Ketak each flip a fair coin (i.e., both heads and tails have equal probability of appearing) $n$ times. What is the probability that Lavanya sees more heads than ketak? In the following, the binomial coefficient $\binom{n}{k}$ counts the number of $k$-element subsets of an $n$ ... $\sum_{i=0}^{n}\frac{\binom{n}{i}}{2^{n}}$
asked Mar 25 in Others 51 views
1 vote
1 answer
16
Find the following sum. $\frac{1}{2^{2}-1}+\frac{1}{4^{2}-1}+\frac{1}{6^{2}-1}+\cdots+\frac{1}{40^{2}-1}$ $\frac{20}{41}$ $\frac{10}{41}$ $\frac{10}{21}$ $\frac{20}{21}$ $1$
asked Mar 25 in Others 72 views
0 votes
1 answer
17
How many numbers in the range ${0, 1, \dots , 1365}$ have exactly four $1$'s in their binary representation? (Hint: $1365_{10}$ is $10101010101_{2}$, that is, $1365=2^{10} + 2^{8}+2^{6}+2^{4}+2^{2}+2^{0}.)$ In the following, the binomial coefficient $\binom{n}{k}$ counts the number of ... $\binom{11}{4}+\binom{9}{3}+\binom{7}{2}+\binom{5}{1}$ $1024$
asked Mar 25 in Others 46 views
0 votes
3 answers
18
What are the last two digits of $7^{2021}$? $67$ $07$ $27$ $01$ $77$
asked Mar 25 in Others 73 views
1 vote
1 answer
19
Five married couples attended a party. In the party, each person shook hands with those they did not know. Everyone knows his or her spouse. At the end of the party, Shyamal, one of the attendees, listed the number of hands that other attendees including his spouse shook. He ... $8$ once in the list. How many persons shook hands with Shyamal at the party? $2$ $4$ $6$ $8$ Insufficient information
asked Mar 25 in Others 58 views
0 votes
0 answers
20
Let $P$ be a convex polygon with sides $5, 4, 4, 3$. For example, the following: Consider the shape in the plane that consists of all points within distance $1$ from some point in $P$. If $\ell$ is the perimeter of the shape, which of the following is always correct? $\ell$ cannot be determined from the given information. $20\leq \ell < 21$ $21\leq \ell< 22$ $22\leq \ell< 23$ $23\leq \ell< 24$
asked Mar 25 in Others 36 views
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