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Previous GATE
Featured
Questions without an upvoted answer in Engineering Mathematics
0
votes
2
answers
1
Find no of sets A and B such that A n B = {3,5} and A U B = {2,3,5,7,8)
saisri
91
views
saisri
asked
Mar 13
1
votes
1
answer
2
Why (p ∨ T) is not a tautology?
tbhaxor
141
views
tbhaxor
asked
Mar 5
Mathematical Logic
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
3
#discrete
Çșȇ ʛấẗẻ
60
views
Çșȇ ʛấẗẻ
asked
Feb 24
Mathematical Logic
discrete-mathematics
kenneth-rosen
+
–
0
votes
0
answers
4
Question on Quotient set
What will be quotient set for equivalence relation R={(x,y) ∣ x ≡ y mod 5} in set builder form?
What will be quotient set for equivalence relation R={(x,y) ∣ x ≡ y mod 5} in set builder form?
rick55
54
views
rick55
asked
Feb 23
0
votes
1
answer
5
GATE DS&AI 2024 | Question: 26
A fair six-sided die (with faces numbered $1,2,3,4,5,6$ ) is repeatedly thrown independently. What is the expected number of times the die is thrown until two consecutive throws of even numbers are seen? $2$ $4$ $6$ $8$
A fair six-sided die (with faces numbered $1,2,3,4,5,6$ ) is repeatedly thrown independently.What is the expected number of times the die is thrown until t...
Arjun
986
views
Arjun
asked
Feb 16
Probability
gate-ds-ai-2024
probability
+
–
0
votes
1
answer
6
GATE DS&AI 2024 | Question: 48
Consider two events $T$ and $S$. Let $\bar{T}$ denote the complement of the event $T$. The probability associated with different events are given as follows: \[ P(\bar{T})=0.6, \quad P(S \mid T)=0.3, \quad P(S \mid \bar{T})=0.6 \] Then, $P(T \mid S)$ is $\_\_\_\_\_\_\_\_$ (rounded off to two decimal places).
Consider two events $T$ and $S$. Let $\bar{T}$ denote the complement of the event $T$. The probability associated with different events are given as follows:\[P(\bar{T})=...
Arjun
632
views
Arjun
asked
Feb 16
Probability
gate-ds-ai-2024
numerical-answers
probability
+
–
1
votes
1
answer
7
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...
Arjun
1.8k
views
Arjun
asked
Feb 16
Probability
gatecse2024-set1
multiple-selects
probability
+
–
1
votes
1
answer
8
GATE CSE 2024 | Set 1 | Question: 42
Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE? Operator $\diamond$ ... $\square$ obeys the distributive law Operator $\square$ over the operator $\diamond$ obeys the distributive law
Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE?Ope...
Arjun
1.6k
views
Arjun
asked
Feb 16
Set Theory & Algebra
gatecse2024-set1
multiple-selects
set-theory&algebra
+
–
0
votes
0
answers
9
Regular expression to finite automata
Çșȇ ʛấẗẻ
199
views
Çșȇ ʛấẗẻ
asked
Feb 15
Mathematical Logic
finite-automata
theory-of-computation
regular-expression
+
–
0
votes
0
answers
10
COA Self doubt
Çșȇ ʛấẗẻ
83
views
Çșȇ ʛấẗẻ
asked
Feb 15
Mathematical Logic
co-and-architecture
self-doubt
+
–
1
votes
0
answers
11
Gate 2016
The minimum number of colours that is sufficient to vertex-colour any planar graph is ________. I am confused with the question's language. please correct me if I have a wrong assumption. We need to tell the minimum colors required for a planar graph. Suppose I start ... is only fixed to 4. I understand the answer not to be less than 4. What does the word "any" means here?
The minimum number of colours that is sufficient to vertex-colour any planar graph is ________.I am confused with the question's language.please correct me if I have a wr...
TusharRana
180
views
TusharRana
asked
Feb 8
0
votes
0
answers
12
Combinatorics & Probability
A rumor is spread randomly among a group of 10 people by successively having one person call someone, who calls someone, and so on. A person can pass the rumor on to anyone except the individual who just called. (a) By how many different paths can a rumor ... in $N$ calls? (c) What is the probability that if $A$ starts the rumor, then $A$ receives the third calls?
A rumor is spread randomly among a group of 10 people by successively having one person call someone, who calls someone, and so on. A person can pass the rumor on to anyo...
Debargha Mitra Roy
137
views
Debargha Mitra Roy
asked
Feb 8
Combinatory
combinatory
counting
+
–
0
votes
0
answers
13
#self doubt
Can someone please verify it ? isn't should be 8. https://www.toppr.com/ask/question/the-cardinality-of-the-power-set-of-left-phi-left-phiright-left-phi-left/ Let S={ϕ,{ϕ},{ϕ,{ϕ}}} P(s)= Power Set of set S P(s)={ϕ,{ϕ},{ϕ,{ϕ}},{ϕ,{ϕ,{ϕ}}},{{ϕ},{ϕ,{ϕ}}},{ϕ,{ϕ},{ϕ,{ϕ}}}} n(P(s))=6.
Can someone please verify it ? isn't should be 8. https://www.toppr.com/ask/question/the-cardinality-of-the-power-set-of-left-phi-left-phiright-left-phi-left/Let S={ϕ,{�...
Dknights
112
views
Dknights
asked
Feb 6
Set Theory & Algebra
discrete-mathematics
+
–
6
votes
2
answers
14
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 49
Consider a $2 \times 2$ matrix M. Which of the following are NOT POSSIBLE for the system of equations $M x=p?$ no solutions for some but not all $\vec{p}$; exactly one solution for all other $\vec{p}$ exactly one solution for ... some $\vec{p}$, exactly one solution for some $\vec{p}$ and more than one solution for some $\vec{p}$
Consider a $2 \times 2$ matrix M. Which of the following are NOT POSSIBLE for the system of equations $M x=p?$no solutions for some but not all $\vec{p}$; exactly one sol...
GO Classes
496
views
GO Classes
asked
Feb 5
Linear Algebra
goclasses2024-mockgate-14
linear-algebra
system-of-equations
multiple-selects
2-marks
+
–
0
votes
0
answers
15
Memory Based GATE DA 2024 | Question: 5
Consider a matrix \(M \in \mathbb{R}^{3 \times 3}\) and let \(U\) be a 2-dimensional subspace such that \(M\) is a projection onto \(U\). Which of the following statements are true? \(M^3 = M\) \(M^2 = M\) The nullspace of \(M\) is 1-dimensional. The nullspace of \(M\) is 2-dimensional.
Consider a matrix \(M \in \mathbb{R}^{3 \times 3}\) and let \(U\) be a 2-dimensional subspace such that \(M\) is a projection onto \(U\). Which of the following statement...
GO Classes
203
views
GO Classes
asked
Feb 4
Linear Algebra
gate2024-da-memory-based
goclasses
linear-algebra
vector-space
+
–
0
votes
0
answers
16
Memory Based GATE DA 2024 | Question: 11
Consider a dataset with a raw score \(x = 75\), a mean \(\mu = 70\), and a standard deviation \(\sigma = 5\). Calculate the Z-score using the formula \(z = \frac{x - \mu}{\sigma}\).
Consider a dataset with a raw score \(x = 75\), a mean \(\mu = 70\), and a standard deviation \(\sigma = 5\). Calculate the Z-score using the formula \(z = \frac{x - \mu}...
GO Classes
169
views
GO Classes
asked
Feb 4
Probability
gate2024-da-memory-based
goclasses
probability
normal-distribution
numerical-answers
+
–
0
votes
1
answer
17
Memory Based GATE DA 2024 | Question: 14
Consider two events $\mathrm{T}$ and $\mathrm{S}$. Let $\overline{\mathrm{T}}$ denote the complement of event $\mathrm{T}$. The probabilities associated with different events are given as follows: $\mathrm{P}({\mathrm{T}})=0.4$ ... $\mathrm{P}(\mathrm{T}|\mathrm{S})$.
Consider two events $\mathrm{T}$ and $\mathrm{S}$. Let $\overline{\mathrm{T}}$ denote the complement of event $\mathrm{T}$. The probabilities associated with different ev...
GO Classes
181
views
GO Classes
asked
Feb 4
Probability
gate2024-da-memory-based
goclasses
probability
conditional-probability
numerical-answers
+
–
1
votes
0
answers
18
Memory Based GATE DA 2024 | Question: 15
Consider the joint probability density function given by: $ f(x, y)= \begin{cases} 2xy & \text{if } 0 < x < 2 \text{ and } 0 < y < x \\ 0 & \text{otherwise} \end{cases} $ \noindent Determine the conditional expectation $E(Y | X = 1.5)$.
Consider the joint probability density function given by:$$f(x, y)=\begin{cases} 2xy & \text{if } 0 < x < 2 \text{ and } 0 < y < x \\ 0 & \text{otherwise}\e...
GO Classes
184
views
GO Classes
asked
Feb 4
Probability
gate2024-da-memory-based
goclasses
probability
expectation
numerical-answers
+
–
1
votes
0
answers
19
Memory Based GATE DA 2024 | Question: 28
Consider a function \(f\) with \(f^1(X^*) = 0\) and \(f^{1l}(X^*) > 0\). Based on these conditions, determine the nature of the critical point \(X^*\) for the function \(f(X)\). \(X^*\) is a local maximum \(X^*\) is a local minimum \(X^*\) is a global maximum \(X^*\) is a global minimum
Consider a function \(f\) with \(f^1(X^*) = 0\) and \(f^{1l}(X^*) 0\). Based on these conditions, determine the nature of the critical point \(X^*\) for the function \(f...
GO Classes
148
views
GO Classes
asked
Feb 4
Calculus
gate2024-da-memory-based
goclasses
calculus
maxima-minima
+
–
0
votes
1
answer
20
Memory Based GATE DA 2024 | Question: 29
Consider the vector \( u = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \\ 5 \end{bmatrix} \), and let \( M = uu^{\top} \). If \( \sigma_1, \sigma_2, \sigma_3, \ldots, \sigma_5 \) are the singular values of \( M \), what is the value of \( \sum_{i=1}^5 \sigma_i \)?
Consider the vector \( u = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \\ 5 \end{bmatrix} \), and let \( M = uu^{\top} \). If \( \sigma_1, \sigma_2, \sigma_3, \ldots, \sigma_5 \) ar...
GO Classes
170
views
GO Classes
asked
Feb 4
Linear Algebra
gate2024-da-memory-based
goclasses
linear-algebra
vector-space
numerical-answers
+
–
1
votes
1
answer
21
Memory Based GATE DA 2024 | Question: 33
Which of the following are tautologies? \(x \land \neg y \Rightarrow y \rightarrow x\) \(\neg x \land y \Rightarrow \neg x \rightarrow y\) \(x \land \neg y \Rightarrow \neg x \rightarrow y\) \(\neg x \land y \Rightarrow y \rightarrow x\)
Which of the following are tautologies? \(x \land \neg y \Rightarrow y \rightarrow x\)\(\neg x \land y \Rightarrow \neg x \rightarrow y\)\(x \land \neg y \Rightarrow \ne...
GO Classes
191
views
GO Classes
asked
Feb 4
Mathematical Logic
gate2024-da-memory-based
goclasses
mathematical-logic
propositional-logic
+
–
0
votes
0
answers
22
Memory Based GATE DA 2024 | Question: 35
Conditional probability \[ \begin{aligned} & \mathrm{P}(\mathrm{U}, \mathrm{V}, \mathrm{W}, \mathrm{X}, \mathrm{Y}) & = \mathrm{P}(\mathrm{U}) \cdot \mathrm{P}(\mathrm{V}) \cdot \mathrm{P}(\mathrm{W} / \mathrm{U}, \mathrm{V}) \cdot \mathrm{P}(\mathrm{X} / \mathrm{W}) \cdot \mathrm{P}(\mathrm{Y} / \mathrm{W}) \end{aligned} \]
Conditional probability\[\begin{aligned} & \mathrm{P}(\mathrm{U}, \mathrm{V}, \mathrm{W}, \mathrm{X}, \mathrm{Y}) & = \mathrm{P}(\mathrm{U}) \cdot \mathrm{P...
GO Classes
132
views
GO Classes
asked
Feb 4
Probability
gate2024-da-memory-based
goclasses
probability
conditional-probability
+
–
0
votes
0
answers
23
Memory Based GATE DA 2024 | Question: 41
Consider two random variables, $x$ and $y$, defined as follows: \[ x = \begin{cases} 1 & \text{if HH } \\ 0 & \text{otherwise} \end{cases} \] \[ y = \begin{cases} 1 & \text{if at least one head} \\ 0 & \text{otherwise} \end{cases} \] What is the covariance between $x$ and $y?$
Consider two random variables, $x$ and $y$, defined as follows:\[x =\begin{cases}1 & \text{if HH } \\0 & \text{otherwise}\end{cases}\]\[y =\begin{cases}1 & \text{if at le...
GO Classes
88
views
GO Classes
asked
Feb 4
Probability
gate2024-da-memory-based
goclasses
probability
statistics
+
–
0
votes
1
answer
24
Memory Based GATE DA 2024 | Question: 42
Consider two random variables, (x) and (y), each following a uniform distribution. Specifically, (x) is uniformly distributed over the interval ([1, 3]), and (y) is uniformly distributed over the interval ([2, 4]). What will be $P(x \geq y)$
Consider two random variables, (x) and (y), each following a uniform distribution. Specifically, (x) is uniformly distributed over the interval ([1, 3]), and (y) is uni...
GO Classes
217
views
GO Classes
asked
Feb 4
Probability
gate2024-da-memory-based
goclasses
probability
random-variable
uniform-distribution
numerical-answers
+
–
0
votes
0
answers
25
Memory Based GATE DA 2024 | Question: 44
Consider the statements below related to probability distributions: \textbf{(S1):} For a Poisson distribution, the mean and variance are equal. \textbf{(S2):} For a standard normal distribution, the mean is 0, and the variance is 1. Which of the following ... true. S1 is true, but S2 is false. S1 is false, but S2 is true. Both S1 and S2 are false.
Consider the statements below related to probability distributions:\textbf{(S1):} For a Poisson distribution, the mean and variance are equal.\textbf{(S2):} For a standar...
GO Classes
139
views
GO Classes
asked
Feb 4
Probability
gate2024-da-memory-based
goclasses
probability
poisson-distribution
normal-distribution
+
–
0
votes
0
answers
26
Memory Based GATE DA 2024 | Question: 52
Consider the function \(f(x) = \frac{x^4}{4} - \frac{2x^3}{3} - \frac{3x^2}{2}\). Which of the following statements about the critical points of \(f(x)\) are correct? Local minima at \(x = 0\) Local maxima at \(x = 0\) Local minima at \(x = 3\) Local minima at \(x = -1\)
Consider the function \(f(x) = \frac{x^4}{4} - \frac{2x^3}{3} - \frac{3x^2}{2}\).Which of the following statements about the critical points of \(f(x)\) are correct?Local...
GO Classes
138
views
GO Classes
asked
Feb 4
Calculus
gate2024-da-memory-based
goclasses
calculus
maxima-minima
+
–
0
votes
0
answers
27
Memory Based GATE DA 2024 | Question: 57
First-order logic question: All balls are round except rugby balls.
First-order logic question: All balls are round except rugby balls.
GO Classes
97
views
GO Classes
asked
Feb 4
Mathematical Logic
gate2024-da-memory-based
goclasses
mathematical-logic
first-order-logic
+
–
0
votes
0
answers
28
Memory Based GATE DA 2024 | Question: 60
Linear Algebra Question: Four options were given related to subspace R3. Something like this : A. \( \alpha \cdot x + \beta \cdot y \) B. \( \alpha^2 \cdot x + \beta^2 \cdot y \) C. \(f(x) = 4x_1 + 2x_3 + 3x_3 \) D.
Linear Algebra Question: Four options were given related to subspace R3.Something like this :A. \( \alpha \cdot x + \beta \cdot y \)B. \( \alpha^2 \cdot x + \beta^2 \cdot...
GO Classes
118
views
GO Classes
asked
Feb 4
Linear Algebra
gate2024-da-memory-based
goclasses
linear-algebra
vector-space
+
–
1
votes
0
answers
29
Memory Based GATE DA 2024 | Question: 64
Minimum Number of colors in concentric circles.
Minimum Number of colors in concentric circles.
GO Classes
117
views
GO Classes
asked
Feb 4
Graph Theory
gate2024-da-memory-based
goclasses
graph-theory
graph-coloring
+
–
0
votes
0
answers
30
madeeasy
plz explain option c
plz explain option c
nihal_chourasiya
88
views
nihal_chourasiya
asked
Feb 1
Mathematical Logic
engineering-mathematics
maxima-minima
+
–
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