Recent questions and answers in Engineering Mathematics / GATE Overflow for GATE CSE

13 votes

2 answers

1

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 7
Power set of empty set has exactly _______ subsets. One Two Zero Three

Power set of empty set has exactly _______ subsets.OneTwoZeroThree

Himashis Biswas

328 views

Himashis Biswas answered 4 hours ago

9 votes

2 answers

2

Discrete Mathematics question

Bharadwaja1557

3.6k views

Bharadwaja1557 answered 7 hours ago

0 votes

1 answer

3

Function Composition Question Oscar Levin Qn. 20
Let $f : X \rightarrow Y$ and $g : Y \rightarrow Z$ be functions. We can define the composition of $f$ and $g$ to be the function $g \circ f : X \rightarrow Z$ for which the image of each $x \in X$ is $g( f (x))$. That is, plug ... $f$ and $g$? Explain. (d) Suppose $g \circ f$ is surjective. What, if anything, can you say about $f$ and $g$? Explain.

Let $f : X \rightarrow Y$ and $g : Y \rightarrow Z$ be functions. We can define the composition of $f$ and $g$ to be the function $g \circ f : X \rightarrow Z$ for which ...

Deepak Poonia

22 views

Deepak Poonia answered 15 hours ago

46 votes

12 answers

4

GATE CSE 2016 Set 2 | Question: 05
Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than $100$ hours given that it is of Type $1$ is $0.7$, and given that it is of Type $2$ is $0.4$. The probability that an LED bulb chosen uniformly at random lasts more than $100$ hours is _________.

Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than $100$ hours given that it is of Type $1$ is ...

ananya_23

9.7k views

ananya_23 answered 1 day ago

13 votes

4 answers

5

GATE CSE 2024 | Set 1 | Question: 39
Let $A$ be any $n \times m$ matrix, where $m>n$. Which of the following statements is/are TRUE about the system of linear equations $Ax=0$? There exist at least $m-n$ linearly independent solutions to this system There exist $m-n$ ... solution in which at least $m-n$ variables are $0$ There exists a solution in which at least $n$ variables are non-zero

Let $A$ be any $n \times m$ matrix, where $m>n$. Which of the following statements is/are TRUE about the system of linear equations $Ax=0$?There exist at least $m-n...

Just.Prathmesh

3.7k views

Just.Prathmesh answered 1 day ago

5 votes

2 answers

6

GATE CSE 2024 | Set 2 | Question: 6
Let $f(x)$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ such that \[ f(x)=1-f(2-x) \] Which one of the following options is the CORRECT value of $\int_{0}^{2} f(x) d x$ ? $0$ $1$ $2$ $-1$

Let $f(x)$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ such that\[f(x)=1-f(2-x)\]Which one of the following options is the CORRECT value of ...

skypaul101

2.5k views

skypaul101 answered 2 days ago

4 votes

1 answer

7

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 9
Which of the following statements is $\textbf{TRUE}$? For all sets $A, B$, and $C, A-(B-C)=(A-B)-C$. For all sets $A, B$, and $C,(A-B) \cap(C-B)=(A \cap C)-B$. For all sets $A, B$, and $C,(A-B) \cap(C-B)=A-(B \cup C)$. For all sets $A, B$, and $C$, if $A \cap C=B \cap C$ then $A=B$.

Which of the following statements is $\textbf{TRUE}$?For all sets $A, B$, and $C, A-(B-C)=(A-B)-C$.For all sets $A, B$, and $C,(A-B) \cap(C-B)=(A \cap C)-B$.For all sets ...

Srken

119 views

Srken answered 3 days ago

1 votes

2 answers

8

Permutation and combination
Your mother-in-law buys 1000 small gifts to give to relatives for Christmas. Each of the 1000 things in different. There are 25 relatives to give gifts to. How many ways are there to distribute the gifts? The correct answer is $25^{1000}$. I ... ? I know some people may feel its silly question but please trust me many people like me are confused with this doubt.

Your mother-in-law buys 1000 small gifts to give to relatives for Christmas. Each of the 1000 things in different. There are 25 relatives to give gifts to. How many ways ...

hypnotized

134 views

hypnotized answered 5 days ago

0 votes

1 answer

9

IIT Madras MS DSAI Written Test 2024
Given, that the eigen values of a 2 x 2 matrix are -1,1 and its singular values are 1,0. What is the rank of the matrix? a) rank is 0 b) rank is 1 c) Such a matrix can't exist d) rank is 2

Given, that the eigen values of a 2 x 2 matrix are -1,1 and its singular values are 1,0. What is the rank of the matrix?a) rank is 0b) rank is 1c) Such a matrix can't exi...

꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂

69 views

꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂ answered 5 days ago

0 votes

1 answer

10

ISI PCB 2023 Q1
Suppose there are three types of people in the world. A person is honest if the person always speaks the truth. A person is a liar if the person always lies. A person is normal if the person sometimes speaks the truth and sometimes lies. In a city ... . C: B is not normal. Based on the above, deduce with appropriate justifications who among A, B and C has committed the crime.

Suppose there are three types of people in the world.A person is “honest” if the person always speaks the truth. A person is a “liar” if the person always lies. A...

Kaustubh Parmar

79 views

Kaustubh Parmar answered 5 days ago

0 votes

0 answers

11

ISI PCB 2023 Q3

vbsurya

40 views

vbsurya asked 5 days ago

1 votes

0 answers

12

ISI PCB 2023 Q2

vbsurya

26 views

vbsurya asked 5 days ago

0 votes

1 answer

13

IIT Madras MS DSAI Written Test 2024
If the determinant and sum of eigen values of a 2 x 2 matrix are -1 and 0 then, what can you say about the rank of the given matrix? a) rank is 0 b) rank is 1 c) Insufficient information d) rank is 2

If the determinant and sum of eigen values of a 2 x 2 matrix are -1 and 0 then, what can you say about the rank of the given matrix?a) rank is 0b) rank is 1c) Insufficien...

꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂

102 views

꧁༒☬ĿọŗԀ 🆂🅷🅸🆅🅰☬༒꧂ answered 6 days ago

0 votes

0 answers

14

IIT Madras MS DSAI Written Test 2024
Two fair 6-face diced are tossed independently. Let X be the random variable of the sum of two numbers on dices and let Y be the absolute difference of two numbers on dices. What is the value of P( X $\geq$ 2Y)? a) 22/36 b) 24/36 c) 26/36 c) 28/36 d) 32/36

Two fair 6-face diced are tossed independently. Let X be the random variable of the sum of two numbers on dices and let Y be the absolute difference of two numbers on dic...

harshrajhrj

75 views

harshrajhrj asked 6 days ago

1 votes

2 answers

15

GO Classes 2023 | IIITH Mock Test 1 | Question: 1
Let $\text{R}$ be a relation from a set $\text{A}$ to a set $\text{B}.$ The inverse relation from $\text{B}$ to $\text{A},$ denoted by $\text{R}^{-1},$ is the set of ordered pairs $\{(b,a) \mid (a,b) \in R\}$ ... $\text{S1}$ Only $\text{S2}$ Both $\text{S1}$ and $\text{S2}$ None of the above

Let $\text{R}$ be a relation from a set $\text{A}$ to a set $\text{B}.$ The inverse relation from $\text{B}$ to $\text{A},$ denoted by $\text{R}^{-1},$ is the set of orde...

rachna-2000

1.1k views

rachna-2000 answered Apr 28

0 votes

1 answer

16

Kenneth Rosen Edition 7 Exercise 6.1 Question 50 (Page No. 398)
How many bit strings of length $10$ contain either five consecutive $0s$ or five consecutive $1s?$

How many bit strings of length $10$ contain either five consecutive $0s$ or five consecutive $1s?$

LostAdmin

310 views

LostAdmin answered Apr 28

3 votes

2 answers

17

GATE CSE 2024 | Set 1 | Question: 4
Consider a permutation sampled uniformly at random from the set of all permutations of $\{1,2,3, \cdots, n\}$ for some $n \geq 4$. Let $X$ be the event that $1$ occurs before $2$ in the permutation, and $Y$ the event that $3$ occurs before ... The events $X$ and $Y$ are independent Either event $X$ or $Y$ must occur Event $X$ is more likely than event $Y$

Consider a permutation sampled uniformly at random from the set of all permutations of $\{1,2,3, \cdots, n\}$ for some $n \geq 4$. Let $X$ be the event that $1$ occurs be...

Bhaskar_Saini

2.5k views

Bhaskar_Saini answered Apr 28

7 votes

2 answers

18

GATE CSE 2024 | Set 1 | Question: 17
Let $A$ and $B$ be two events in a probability space with $P(A)=0.3, P(B)=0.5$, and $P(A \cap B)=0.1$. Which of the following statements is/are TRUE? The two events $A$ and $B$ are independent $P(A \cup B)=0.7$ ... $B$ $P\left(A^c \cap B^c\right)=0.4$, where $A^c$ and $B^c$ are the complements of the events $A$ and $B$, respectively

Let $A$ and $B$ be two events in a probability space with $P(A)=0.3, P(B)=0.5$, and $P(A \cap B)=0.1$. Which of the following statements is/are TRUE?The two events $A$ an...

Bhaskar_Saini

2.2k views

Bhaskar_Saini answered Apr 28

1 votes

2 answers

19

GATE CSE 2024 | Set 2 | Question: 8
When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers $(i.e., 1, 2, 3, 4, 5, \text{and } 6)$ is $\frac{1}{324}$ $\frac{5}{324}$ $\frac{7}{324}$ $\frac{11}{324}$

When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers $(i.e., 1, 2, 3, 4, 5, \text{and } 6)$ is$\frac{1}{3...

Bhaskar_Saini

2.3k views

Bhaskar_Saini answered Apr 28

1 votes

2 answers

20

GATE CSE 2024 | Set 1 | Question: 22
Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions $\text{(i)}$ from $A$ to $B$ and $\text{(ii)}$ from $A \times A$ to $A \cup B$. The number of possible values of $\text{|A|}$ is ___________.

Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions $\text{(i)}$ from $A$ to $B$ and $\text{(ii)}$ from $A \times A$ to $A \cup B...

Bhaskar_Saini

2.0k views

Bhaskar_Saini answered Apr 28

14 votes

4 answers

21

GATE CSE 2023 | Question: 39
Let $f: A \rightarrow B$ be an onto (or surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on the set $A$ as \[ a_{1} \sim a_{2} \text { if } f\left(a_{1}\right)=f\left(a_{2}\right), \] ... is NOT well-defined. $F$ is an onto (or surjective) function. $F$ is a one-to-one (or injective) function. $F$ is a bijective function.

Let $f: A \rightarrow B$ be an onto (or surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on the set $A$ as\[a_{1} \sim a_{...

Bhaskar_Saini

6.1k views

Bhaskar_Saini answered Apr 28

1 votes

3 answers

22

GATE DS&AI 2024 | Question: 50
Evaluate the following limit: \[ \lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]

Evaluate the following limit:\[\lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]

Lakshmi Narayana404

926 views

Lakshmi Narayana404 answered Apr 27

1 votes

0 answers

23

David Stirzaker, Elementary Probability, Chapter 1, Example 1.9 Urn
An urn contains $n$ heliotrope and $n$ tangerine balls. A fair die with $n$ sides is rolled. If the $r^{th}$ face is shown, $r$ balls are removed from the urn and placed in a bag. What is the probability that a ball removed at random from the bag is tangerine?

An urn contains $n$ heliotrope and $n$ tangerine balls. A fair die with $n$ sides is rolled. If the $r^{th}$ face is shown, $r$ balls are removed from the urn and placed ...

Priyam Garg

78 views

Priyam Garg asked Apr 26

0 votes

0 answers

24

Kenneth H. Rosen, Chapter 1
When three professors are seated in a restaurant, the hostess asks them: Does everyone want coffee? The first professor says: I do not know. The second professor then says: I do not know. Finally, the third professor says: No, not ... wants coffee. The hostess comes back and gives coffee to the professors who want it. How did she figure out who wanted coffee?

When three professors are seated in a restaurant, the hostess asks them: “Does everyone want coffee?” The first professor says: “I do not know.” The second profe...

ENTJ007

53 views

ENTJ007 asked Apr 26

6 votes

3 answers

25

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 5
Consider the statement $\text{S} :$ "For all natural numbers $n,$ if $n$ is prime, then $n$ is antisocial." You do not need to know what antisocial means for this problem, just that it is a property ... $10$ is antisocial. $10$ is not antisocial. $7$ is antisocial. $7$ is not antisocial.

Consider the statement $\text{S} :$ "For all natural numbers $n,$ if $n$ is prime, then $n$ is antisocial."You do not need to know what antisocial means for this problem,...

pinaksh10

386 views

pinaksh10 answered Apr 26

9 votes

2 answers

26

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 15
Let's make a trip to a new world called "Never Never Land". Regular, ordinary first-order logic has two quantifiers: $\forall$ and $\exists$. Now, let's imagine we lived in a world in which these quantifiers ... $\mathrm{Nx}(\neg A(x) \wedge B(x))$

Let's make a trip to a new world called "Never Never Land".Regular, ordinary first-order logic has two quantifiers: $\forall$ and $\exists$.Now, let's imagine we lived in...

pinaksh10

424 views

pinaksh10 answered Apr 25

13 votes

2 answers

27

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1 | Question: 9
Many programming languages support a ternary conditional operator. For example, in $\text{C, C++},$ and $\text{Java}$, the expression $x ? y : z$ means evaluate the boolean expression $x.$ If it's true, the entire expression ... $p ? p : (\neg p)$ is tautology. $(\neg p) ? p : (\neg p)$ is tautology.

Many programming languages support a ternary conditional operator. For example, in $\text{C, C++},$ and $\text{Java}$, the expression $x ? y : z$ means “evaluate the bo...

https_guru

498 views

https_guru answered Apr 25

44 votes

11 answers

28

GATE CSE 2016 Set 2 | Question: 29
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.

The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.

yudhistar

18.1k views

yudhistar answered Apr 25

34 votes

6 answers

29

GATE CSE 1996 | Question: 1.3
Suppose $X$ and $Y$ are sets and $|X| \text{ and } |Y|$ are their respective cardinality. It is given that there are exactly $97$ functions from $X$ to $Y$. From this one can conclude that $|X| =1, |Y| =97$ $|X| =97, |Y| =1$ $|X| =97, |Y| =97$ None of the above

Suppose $X$ and $Y$ are sets and $|X| \text{ and } |Y|$ are their respective cardinality. It is given that there are exactly $97$ functions from $X$ to $Y$. From this one...

arunimaaa15

8.9k views

arunimaaa15 answered Apr 25

3 votes

3 answers

30

UGC NET CSE | December 2013 | Part 2 | Question: 37
Let f and g be the functions from the set of integers defined by $f(x) = 2x+3$ and $g(x) =3x+2$. Then the composition of f and g and g and f is given as 6x+7, 6x+11 6x+11, 6x+7 5x+5, 5x+5 None of the above

Let f and g be the functions from the set of integers defined by $f(x) = 2x+3$ and $g(x) =3x+2$. Then the composition of f and g and g and f is given as6x+7, 6x+116x+11, ...

Deepak Poonia

6.8k views

Deepak Poonia answered Apr 24

0 votes

0 answers

31

Finite Automata Combined with Relation
Let DFA , M = (Q, ∑, δ, q$_0$, F) and Relation R is defined on Q as R:Q$\rightarrow$Q such that pRq iff $\forall$ w ∈ $\Sigma$* [ δ*(p,w) ∈ F $\leftrightarrow$ δ*(p,w) ∈ F OR δ* (p, w) ∉ F $\leftrightarrow$ δ* (q, w) ∉ F] then ____________ A) R is Reflexive B) R is Symmetric C) R is transitive D) None

Let DFA , M = (Q, ∑, δ, q$_0$, F) and Relation R is defined on Q as R:Q$\rightarrow$Q such that pRq iff $\forall$ w ∈ $\Sigma$* [ δ*(p,w) ∈ F $\leftrightarrow$ δ...

jaydip74

56 views

jaydip74 asked Apr 23

1 votes

0 answers

32

Charles C Pinter Abstract Algebra
If G is a group, G=(F(R), +), F(R) set of all real valued functions. H={f€F(R) ; f(-x)=-f(x)} Is H a subgroup of G? My solution.(Click on link..I have not shown th associative prt coz addition is always associative) please let me know if iam correct. https://ibb.co/sPzHg6m https://ibb.co/sPzHg6m

If G is a group, G=(F(R), +), F(R) set of all real valued functions.H={f€F(R) ; f(-x)=-f(x)}Is H a subgroup of G?My solution.(Click on link..I have not shown th associa...

yuyutsu

67 views

yuyutsu asked Apr 20

3 votes

2 answers

33

Poset
Consider the poset ({3,5,9,15,24,45},|). Which of the following is correct for the given poset? A. There exists a least element but not a greatest element B. There exists a greatest element but not a least element C. There exists a greatest element and a least element D. There does not exist a greatest element and a least element

Consider the poset ({3,5,9,15,24,45},|). Which of the following is correct for the given poset? A. There exists a least element but not a greatest elementB. There exists ...

akhilroom001

244 views

akhilroom001 asked Apr 20

0 votes

1 answer

34

Linear Algebra AX=B
Consider a matrix A (n×m) ,X(m×n) and B(n×n) such that AX=B . If A has k linearly independent columns then what conclusions can we nake about the number of linearly independent columns of B.

Consider a matrix A (n×m) ,X(m×n) and B(n×n) such that AX=B . If A has k linearly independent columns then what conclusions can we nake about the number of linearly in...

Soumya04

93 views

Soumya04 asked Apr 16

0 votes

1 answer

35

ISI kolkata MTech CS 2019
Let $K_n$ denote the complete graph on $n$ vertices, with $n ≥ 3$, and let $u$, $v$, $w$ be three distinct vertices of $K_n$. Determine the number of distinct paths from $u$ to $v$ that do not contain the vertex $w$.

Let $K_n$ denote the complete graph on $n$ vertices, with $n ≥ 3$, and let $u$, $v$, $w$ be three distinct vertices of $K_n$. Determine the number of distinct paths fro...

suvasish114

115 views

suvasish114 asked Apr 16

0 votes

1 answer

36

self doubt
how to check the validity of an a argument using laws of logics

how to check the validity of an a argument using laws of logics

farhan777

55 views

farhan777 asked Apr 14

0 votes

0 answers

37

Discrete Mathematics | Set Theory | Relation | Equivalance Relation
which if the following statement is True for every set? a. $\exists$ a equivalence class that is also a partition set. b. Every equivalence relation on a set defines a partition of that set. c. $\exists$ a partition of a set that is also equal to equivalence class of the set on some equivalence relation.

which if the following statement is True for every set?a. $\exists$ a equivalence class that is also a partition set.b. Every equivalence relation on a set defines a part...

RahulVerma3

76 views

RahulVerma3 asked Apr 12

4 votes

1 answer

38

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 1
Let $T_{1}, T_{2}: R^{5} \rightarrow R^{3}$ be linear transformations s.t $\operatorname{rank}\left(T_{1}\right)=3$ and nullity $\left(T_{2}\right)=3$. Let $T_{3}: R^{3} \rightarrow R^{3}$ be linear transformation s.t $T_{3}\left(T_{1}\right)=T_{2}$. Then find rank of $T_{3}$

Let $T_{1}, T_{2}: R^{5} \rightarrow R^{3}$ be linear transformations s.t $\operatorname{rank}\left(T_{1}\right)=3$ and nullity $\left(T_{2}\right)=3$. Let $T_{3}: R^{3} ...

GO Classes

87 views

GO Classes asked Apr 11

4 votes

1 answer

39

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 2
Suppose that $\left\{\mathbf{v}_{\mathbf{1}}, \mathbf{v}_{\mathbf{2}}, \mathbf{v}_{\mathbf{3}}\right\}$ is a linearly independent set of vectors in $\mathbb{R}^{6}$ ... is linearly independent $\left\{\mathbf{v}_{2}, \mathbf{v}_{3}, \mathbf{w}\right\}$ is linearly independent

Suppose that $\left\{\mathbf{v}_{\mathbf{1}}, \mathbf{v}_{\mathbf{2}}, \mathbf{v}_{\mathbf{3}}\right\}$ is a linearly independent set of vectors in $\mathbb{R}^{6}$.Furth...

GO Classes

93 views

GO Classes asked Apr 11

3 votes

1 answer

40

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 3
Let the linear transformation $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{3}$ be defined by $T\left(x_{1}, x_{2}\right)=\left(x_{1}, x_{1}+x_{2}, x_{2}\right)$. Then the nullity of $T$ is: 0 1 2 3

Let the linear transformation $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{3}$ be defined by $T\left(x_{1}, x_{2}\right)=\left(x_{1}, x_{1}+x_{2}, x_{2}\right)$. Then the n...

GO Classes

78 views

GO Classes asked Apr 11

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