Recent activity by KG / GATE Overflow for GATE CSE

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GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 3
Consider the following atomic propositions: $\text{R}$: It is Raining $\text{S}$ ... , and vice versa It is raining is equivalent to sonu is sick It is raining or sonu is sick but not both

Consider the following atomic propositions:$\text{R}$: It is Raining$\text{S}$: Sonu is SickWhich of the following is/are correct English Translation of the following log...

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commented 6 days ago

4 answers

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GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 8
A very special island, "Smullyan's island", is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You encounter two people, $\text{A}$ and $\text{B. A}$ ... respectively, if they address you in the above way described: Knight, Knight Knight, Knave Knave, Knight Knave, Knave

A very special island, "Smullyan's island", is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You encounter two people, $\tex...

1.3k views

commented Apr 14

6 answers

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GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 15
Consider the following popular puzzle. A boy and a girl are talking. One of them has black hair, another has white hair. I am a boy said the child with black hair. I am a girl said the child with white hair ... Which of them is lying? The boy only The girl only Both of them Information is not sufficient to find out the liar

Consider the following popular puzzle.A boy and a girl are talking. One of them has black hair, another has white hair.“I am a boy” said the child with black hair.“...

1.6k views

answered Apr 14

8 answers

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GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 14
Consider the following popular puzzle. When asked for the ages of her three children, Mrs. Baker says that Alice is her youngest child if Bill is not her youngest child, and that Alice is not her youngest child ... is her youngest child. Carl is her youngest child. Information is not sufficient to find out the youngest child.

Consider the following popular puzzle.When asked for the ages of her three children, Mrs. Baker says that “Alice is her youngest child if Bill is not her youngest child...

3.7k views

answered Apr 14

6 answers

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GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 10
Which of the following is(are) sufficient argument(s) to show that the vectors of set $\text{S}$ ... $7 u+(-1) v+1 w=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$

Which of the following is(are) sufficient argument(s) to show that the vectors of set $\text{S}$ are linearly dependent?$$\text{S}=\left\{u=\left[\begin{array}{c}1 \\-2 \...

1.4k views

answered Mar 21

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GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 2
If $n!$ denotes the product of the integers $1$ through $n,$ what is the remainder when $(1 !+2 !+3 !+4 !+5 !+6 !+\ldots +9 ! )$ is divided by $9 ?$

If $n!$ denotes the product of the integers $1$ through $n,$ what is the remainder when $(1 !+2 !+3 !+4 !+5 !+6 !+\ldots +9 ! )$ is divided by $9 ?$

766 views

answered Mar 21

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GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 13
What will be value of $x$ satisfying the below equation? $ \sqrt{\log _2 x^4}+4 \log _4 \sqrt{\frac{2}{x}}=2 $

What will be value of $x$ satisfying the below equation?$$\sqrt{\log _2 x^4}+4 \log _4 \sqrt{\frac{2}{x}}=2$$

824 views

answered Mar 21

4 answers

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GATE CSE 2023 | Question: 44
Consider functions $\textsf{Function_1}$ and $\textsf{Function_2}$ ... $f_{1}(n) \in \omega\left(f_{2}(n)\right)$ $f_{1}(n) \in O(n)$

Consider functions $\textsf{Function_1}$ and $\textsf{Function_2}$ expressed in pseudocode as follows:Function_1 | Function_2 while n 1 do | for i = 1 to 100 * n do for ...

11.7k views

answered Feb 24

4 answers

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GATE CSE 1994 | Question: 1.9
The rank of matrix $\begin{bmatrix} 0 & 0 & -3 \\ 9 & 3 & 5 \\ 3 & 1 & 1 \end{bmatrix}$ is: $0$ $1$ $2$ $3$

The rank of matrix $\begin{bmatrix} 0 & 0 & -3 \\ 9 & 3 & 5 \\ 3 & 1 & 1 \end{bmatrix}$ is:$0$$1$$2$$3$

5.7k views

commented Jul 24, 2023

9 answers

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GATE CSE 2020 | Question: 16
What is the worst case time complexity of inserting $n$ elements into an empty linked list, if the linked list needs to be maintained in sorted order? $\Theta(n)$ $\Theta(n \log n)$ $\Theta ( n)^{2}$ $\Theta(1)$

What is the worst case time complexity of inserting $n$ elements into an empty linked list, if the linked list needs to be maintained in sorted order?$\Theta(n)$$\Theta(n...

26.6k views

commented Jul 6, 2023

1 answer

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Combinatorics Question uOttawa (University of Ottawa)
Consider the fourteen letters: $\text{A A A B B C C C C C D E E E}$ . An ARRANGEMENT is a sequence using $\text{all}$ ... order, somewhere in the arrangement). c) How many words have all letters distinct? d) How many arrangements have no two vowels consecutive?

Consider the fourteen letters: $\text{A A A B B C C C C C D E E E}$ .An ARRANGEMENT is a sequence using $\text{all}$ of these letters.For the purposes of this question, a...

709 views

commented Jul 1, 2023

10 answers

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GATE CSE 2017 Set 1 | Question: 29
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \right )\rightarrow q$ is a tautology a contradiction always TRUE when $p$ is FALSE always TRUE when $q$ is TRUE

Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \r...

10.7k views

answered May 25, 2023

3 answers

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GATE CSE 1993 | Question: 02.1
$\displaystyle \lim_{x \to 0} \frac{x(e^x - 1) + 2(\cos x -1)}{x(1 - \cos x)}$ is __________

$\displaystyle \lim_{x \to 0} \frac{x(e^x - 1) + 2(\cos x -1)}{x(1 - \cos x)}$ is __________

3.8k views

answer edited May 25, 2023

8 answers

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GATE CSE 2010 | Question: 5
What is the value of $ \displaystyle\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ? $0$ $e^{-2}$ $e^{-1/2}$ $1$

What is the value of $ \displaystyle\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ?$0$$e^{-2}$$e^{-1/2}$$1$

9.0k views

answered May 25, 2023

9 answers

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GATE CSE 2008 | Question: 1
$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals $1$ $-1$ $\infty$ $-\infty$

$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals$1$$-1$$\infty$$-\infty$

10.1k views

answered May 25, 2023

10 answers

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GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$

Let $p, q, r$ denote the statements ”It is raining”, “It is cold”, and “It is pleasant”, respectively. Then the statement “It is not raining and it is pleas...

12.3k views

answered Apr 28, 2023

5 answers

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GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 12
Let $P$ be a compound proposition over $4$ propositional variables: $a,b,c,d$. We know that for a compound proposition over $n$ propositional variables, we have $2^n$ rows in the truth table. Every row of truth table of $P$ is called ... $P$ be $'a \rightarrow b'$. How many models are there for $P?$

Let $P$ be a compound proposition over $4$ propositional variables: $a,b,c,d$.We know that for a compound proposition over $n$ propositional variables, we have $2^n$ rows...

2.0k views

answer edited Apr 23, 2023

8 answers

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GATE CSE 2021 Set 1 | Question: 7
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic. $S_1: (\neg p\wedge(p\vee q))\rightarrow q$ $S_2: q\rightarrow(\neg p\wedge(p\vee q))$ Which one of the following choices is correct? Both $S_1$ and ... but $S_2$ is not a tautology $S_1$ is not a tautology but $S_2$ is a tautology Neither $S_1$ nor $S_2$ is a tautology

Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic.$S_1: (\neg p\wedge(p\vee q))\rightarrow q$$S_2: q\rightarrow(\neg p\wedge...

8.4k views

answered Apr 22, 2023

9 answers

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GATE CSE 2021 Set 2 | Question: 15
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$

Choose the correct choice(s) regarding the following proportional logic assertion $S$:$$S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \righta...

9.0k views

answered Apr 22, 2023

9 answers

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GATE IT 2004 | Question: 31
Let $p, q, r$ and $s$ be four primitive statements. Consider the following arguments: $P: [(¬p\vee q) ∧ (r → s) ∧ (p \vee r)] → (¬s → q)$ $Q: [(¬p ∧q) ∧ [q → (p → r)]] → ¬r$ $R: [[(q ∧ r) → p] ∧ (¬q \vee p)] → r$ $S: [p ∧ (p → r) ∧ (q \vee ¬ r)] → q$ Which of the above arguments are valid? $P$ and $Q$ only $P$ and $R$ only $P$ and $S$ only $P, Q, R$ and $S$

Let $p, q, r$ and $s$ be four primitive statements. Consider the following arguments:$P: [(¬p\vee q) ∧ (r → s) ∧ (p \vee r)] → (¬s → q)$$Q: [(¬p ∧q) �...

11.9k views

answered Apr 22, 2023

3 answers

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GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 9
Consider two statements below - Statement $1: $ If $A$ is invertible and $\lambda$ is an eigenvalue of $A$, then $\frac{1}{\lambda}$ is an eigenvalue of $A^{-1}$. Statement $2:$ Let $A$ be a real skew- ... true but Statement $2$ is false Statement $2$ is true but Statement $1$ is false Both statements are true Both statements are false

Consider two statements below -Statement $1: $ If $A$ is invertible and $\lambda$ is an eigenvalue of $A$, then $\frac{1}{\lambda}$ is an eigenvalue of $A^{-1}$.Statement...

780 views

commented Apr 20, 2023

2 answers

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Discrete Mathematics | Propositional Logic | Test 2 | Question: 6
How many assignments of truth values to distinct $P_1,P_2,P_3,...,P_n$ with $n \geq 5$ ... $\textbf{Hint}:$ Try to construct the recurrence for the given problem and then solve it)

How many assignments of truth values to distinct $P_1,P_2,P_3,...,P_n$ with $n \geq 5$ are there for which $(...(((P_1 \rightarrow P_2) \rightarrow P_3 ) \rightarrow P_4)...

682 views

comment edited Apr 19, 2023

2 answers

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Discrete Mathematics | Propositional Logic | Test 2 | Question: 11
Consider the following argument: If either wages or prices are raised, there will be inflation. If there is inflation, then either Congress must regulate it or the people will suffer. If the people suffer, Congressmen ... $P \rightarrow Q$ is a tautology. Validity of the given argument can't be determined.

Consider the following argument: If either wages or prices are raised, there will be inflation. If there is inflation, then either Congress must regulate it or ...

916 views

answered Apr 17, 2023

1 answer

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Discrete Mathematics | Propositional Logic | Test 2 | Question: 10
Premises $P_1,P_2,...,P_n$ infer/derive a conclusion $Q$ if and only if the conditional $(P_1 \wedge P_2 \wedge...\wedge P_n) \rightarrow Q$ is a tautology. Consider the following statements: From $P$ ... $P$, $Q$ and $R$ are distinct atomic sentences ) Number of correct statements are ______

Premises $P_1,P_2,...,P_n$ infer/derive a conclusion $Q$ if and only if the conditional $(P_1 \wedge P_2 \wedge...\wedge P_n) \rightarrow Q$ is a tautology. �...

1.0k views

answered Apr 17, 2023

2 answers

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Discrete Mathematics | Propositional Logic | Test 2 | Question: 1
Let $\Phi$ be a well-formed formula having atleast one occurrence of atomic variable $x.$ Consider $\Psi$ be any formula. Now, $_x\Phi_{\Psi}$ is the formula obtained by replacing each occurrence of $x$ by $\Psi$ in $\Phi$ and ... Only (i) is correct Only (ii) is correct Both (i) and (ii) are correct None of the above

Let $\Phi$ be a well-formed formula having atleast one occurrence of atomic variable $x.$ Consider $\Psi$ be any formula. Now, $_x\Phi_{\Psi}$ is the formula obtained by ...

512 views

answered Apr 17, 2023

1 answer

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Discrete Mathematics | Propositional Logic | Test 2 | Question: 3
Suppose we have to construct a formula that expresses the truth function $\phi$ ... The formula that $\phi$ expresses is $\neg p \rightarrow ((p \rightarrow \neg p) \rightarrow (\neg p \rightarrow p))$

Suppose we have to construct a formula that expresses the truth function $\phi$ given by: $$\begin{array}{c|c|c}p & q & \phi \\\hlineT & T & T \\T & F & T \\F...

437 views

answered Apr 17, 2023

1 answer

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Discrete Mathematics | Propositional Logic | Test 2 | Question: 2
Consider the following argument: Either logic is difficult, or not many students like it. If mathematics is easy, then logic is not difficult. $\textit{Therefore,}$ if many students like logic, mathematics is not ... then $P \rightarrow Q$ is a tautology Validity of the given argument can't be determined

Consider the following argument: Either logic is difficult, or not many students like it. If mathematics is easy, then logic is not difficult. $\textit{Therefor...

409 views

answered Apr 17, 2023

2 answers

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GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 2
Which of the following is/are CORRECT? If events $E_1$ and $E_2$ are statistically independent, then $ \mathrm{P}\left(E_1 \cup E_2\right)=\mathrm{P}\left(E_1\right)+\mathrm{P}\left(E_2\right) $ If events $E_1$ and $E_2$ are ...

Which of the following is/are CORRECT?If events $E_1$ and $E_2$ are statistically independent, then$$\mathrm{P}\left(E_1 \cup E_2\right)=\mathrm{P}\left(E_1\right)+\mathr...

970 views

commented Apr 15, 2023

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GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 1
Which all of the following is true for the Venn diagram shown here: $P(E \cup G)=P(E)+P(G)$ $P(E \cup G)=P(E)+P(G)-P(E \cap G)$ $P\left(E^C \cap F\right)=P\left(F^C\right)-P(E)$ $P\left(E^C \cap F\right)=1-\left(P\left(F^C\right)-P(E)\right)$

Which all of the following is true for the Venn diagram shown here:$P(E \cup G)=P(E)+P(G)$$P(E \cup G)=P(E)+P(G)-P(E \cap G)$$P\left(E^C \cap F\right)=P\left(F^C\right)-P...

963 views

answered Apr 15, 2023

0 answers

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Discrete Mathematics | Propositional Logic | Test 1 | Question: 9
Consider the following statements: "Ralph is a dog if he's not a puppet" can be formalized as $\neg$ (Ralph is a puppet) $\rightarrow$ (Ralph is a dog) "Ralph is not a dog because he's a puppet" ... correct $(i)$ and $(iii)$ are correct $(i),(ii)$ and $(iii)$ are correct

Consider the following statements: "Ralph is a dog if he’s not a puppet" can be formalized as $\neg$ (Ralph is a puppet) $\rightarrow$ (Ralph is a dog) ...

392 views

commented Apr 12, 2023

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