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Recent questions and answers in Engineering Mathematics
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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
878
views
Lakshmi Narayana404
answered
6 hours
ago
Calculus
gate-ds-ai-2024
numerical-answers
limits
engineering-mathematics
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0
votes
0
answers
2
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
21
views
Priyam Garg
asked
17 hours
ago
Probability
probability
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0
votes
0
answers
3
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
18
views
ENTJ007
asked
1 day
ago
6
votes
3
answers
4
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
313
views
pinaksh10
answered
1 day
ago
Mathematical Logic
goclasses_2025_cs_dm_tw_1
goclasses
mathematical-logic
first-order-logic
multiple-selects
easy
1-mark
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9
votes
2
answers
5
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
386
views
pinaksh10
answered
1 day
ago
Mathematical Logic
goclasses_2025_cs_dm_tw_1
goclasses
mathematical-logic
first-order-logic
difficult
2-marks
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–
13
votes
2
answers
6
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
463
views
https_guru
answered
1 day
ago
Mathematical Logic
goclasses_2025_cs_dm_tw_1
goclasses
mathematical-logic
propositional-logic
multiple-selects
moderate
2-marks
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–
44
votes
11
answers
7
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
18.0k
views
yudhistar
answered
2 days
ago
Combinatory
gatecse-2016-set2
modular-arithmetic
normal
numerical-answers
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34
votes
6
answers
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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
8.8k
views
arunimaaa15
answered
2 days
ago
Set Theory & Algebra
gate1996
set-theory&algebra
functions
normal
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3
votes
3
answers
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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
2 days
ago
Set Theory & Algebra
ugcnetcse-dec2013-paper2
algebra
function-composition
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0
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0
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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
35
views
jaydip74
asked
4 days
ago
Set Theory & Algebra
finite-automata
relations
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–
10
votes
2
answers
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GATE CSE 2023 | Question: 41
Let $X$ be a set and $2^{X}$ denote the powerset of $X$. Define a binary operation $\Delta$ on $2^{X}$ as follows: \[ A \Delta B=(A-B) \cup(B-A) \text {. } \] Let $H=\left(2^{X}, \Delta\right)$. Which of the following statements about $H$ is/are correct? ... $A \in 2^{X},$ the inverse of $A$ is the complement of $A$. For every $A \in 2^{X},$ the inverse of $A$ is $A$.
Let $X$ be a set and $2^{X}$ denote the powerset of $X$.Define a binary operation $\Delta$ on $2^{X}$ as follows:\[A \Delta B=(A-B) \cup(B-A) \text {. }\]Let $H=\left(2^{...
Bhaskar_Saini
5.7k
views
Bhaskar_Saini
answered
5 days
ago
Set Theory & Algebra
gatecse-2023
set-theory&algebra
group-theory
multiple-selects
2-marks
+
–
6
votes
2
answers
12
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 1
Let $A$ be an $n \times n$ matrix of real or complex numbers. Which of the following statements are equivalent to: “the matrix $A$ is invertible”? The columns of $A$ are linearly independent. The rows of $A$ are linearly independent. The only solution of the homogeneous equations $Ax = 0$ is $x = 0$. The rank of $A$ is $n$.
Let $A$ be an $n \times n$ matrix of real or complex numbers. Which of the following statements are equivalent to: “the matrix $A$ is invertible”?The columns of $A$ a...
Teet Makor
126
views
Teet Makor
answered
5 days
ago
Linear Algebra
goclasses2025_csda_wq5
multiple-selects
goclasses
linear-algebra
matrix
easy
1-mark
+
–
35
votes
4
answers
13
GO Classes CS 2025 | Weekly Quiz 2 | Propositional Logic | Question: 12
Two compound propositions are logically equivalent if they have the same truth table. For example, the following two compound propositions are logically equivalent: $\mathrm{p} \rightarrow \mathrm{q}$ ... propositional variables, how many compound propositions are there that are Not logically equivalent to each other?
Two compound propositions are logically equivalent if they have the same truth table.For example, the following two compound propositions are logically equivalent: $\math...
AjithAddala
1.3k
views
AjithAddala
answered
5 days
ago
Mathematical Logic
goclasses2025_cs_wq2
numerical-answers
goclasses
mathematical-logic
propositional-logic
2-marks
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–
0
votes
1
answer
14
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?
tajammulbasheer
95
views
tajammulbasheer
answered
6 days
ago
Set Theory & Algebra
discrete-mathematics
set-theory&algebra
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–
1
votes
0
answers
15
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
50
views
yuyutsu
asked
6 days
ago
Set Theory & Algebra
discrete-mathematics
group-theory
+
–
16
votes
5
answers
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GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 11
Which of the following is(are) true for the following system of linear equations $\text{AX}=\overrightarrow{0}$ ... $\text{AX}=\overrightarrow{0}$.
Which of the following is(are) true for the following system of linear equations $\text{AX}=\overrightarrow{0}$$$\left[\begin{array}{ccc}2 & 3 & -5 \\-5 & -1 & 32 \\2 & -...
Biswajit Kumar
1.2k
views
Biswajit Kumar
answered
6 days
ago
Linear Algebra
goclasses2025_csda_wq3
goclasses
linear-algebra
vector-space
multiple-selects
2-marks
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–
0
votes
1
answer
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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...
Sahil5635
82
views
Sahil5635
answered
6 days
ago
Mathematical Logic
linear-algebra
matrix
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–
3
votes
2
answers
18
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 ...
Sahil5635
169
views
Sahil5635
answered
Apr 20
Mathematical Logic
discrete-mathematics
set-theory
partial-order
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–
78
votes
12
answers
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GATE CSE 2009 | Question: 21
An unbalanced dice (with $6$ faces, numbered from $1$ to $6$) is thrown. The probability that the face value is odd is $90\%$ of the probability that the face value is even. The probability of getting any even numbered face is the same. If the ... following options is closest to the probability that the face value exceeds $3$? $0.453$ $0.468$ $0.485$ $0.492$
An unbalanced dice (with $6$ faces, numbered from $1$ to $6$) is thrown. The probability that the face value is odd is $90\%$ of the probability that the face value is ev...
harshitraj12
16.6k
views
harshitraj12
answered
Apr 20
Probability
gatecse-2009
probability
normal
conditional-probability
+
–
2
votes
1
answer
20
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 9
Suppose that $a \neq 0$ and $a \neq b$. Which equation below is the equation relating $a, b$ and $c$ ... $4 a-3 b+c \neq 0$ $3 a-4 b-c \neq 0$ $4 a-3 b-c \neq 0$
Suppose that $a \neq 0$ and $a \neq b$. Which equation below is the equation relating $a, b$ and $c$ so that the vectors$$\left[\begin{array}{l}1 \\1 \\a\end{array}\right...
tejashmore25
51
views
tejashmore25
answered
Apr 18
Linear Algebra
goclasses2025_da_wq1
linear-algebra
1-mark
+
–
1
votes
1
answer
21
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 8
Consider a linear system $A \mathbf{x}=\mathbf{b}$, where $A$ is a $3 \times 4$ matrix with $\operatorname{Rank}(A)=2$ ... unique solution. (i) infinitely many solutions, (ii) no solution. (i) infinitely many solutions, (ii) unique solution.
Consider a linear system $A \mathbf{x}=\mathbf{b}$, where $A$ is a $3 \times 4$ matrix with $\operatorname{Rank}(A)=2$.How many solutions does this system have if $(i) \o...
tejashmore25
48
views
tejashmore25
answered
Apr 18
Linear Algebra
goclasses2025_da_wq1
linear-algebra
1-mark
+
–
1
votes
1
answer
22
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 10
Let $T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$ ... $\left(\begin{array}{lll}2 & 1 & 3 \\ 6 & 3 & 9\end{array}\right)$
Let $T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$ be a linear transformation such that $T\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right]=\left[\begin{array}{l}2 \\ 6...
tejashmore25
49
views
tejashmore25
answered
Apr 18
Linear Algebra
goclasses2025_da_wq1
linear-algebra
2-marks
+
–
4
votes
1
answer
23
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 7
Consider a $4 \times 4$ matrix $A$ and a vector $\mathbf{v} \in \mathbb{R}^{4}$ such that $A^{4} \mathbf{v}=\mathbf{0}$ but $A^{3} \mathbf{v} \neq \mathbf{0}$ ... $\mathbb{R}^{4}$. $\mathcal{B}$ is a basis of $\mathbb{R}^{4}$. $\mathcal{B}$ is not linearly independent.
Consider a $4 \times 4$ matrix $A$ and a vector $\mathbf{v} \in \mathbb{R}^{4}$ such that $A^{4} \mathbf{v}=\mathbf{0}$ but $A^{3} \mathbf{v} \neq \mathbf{0}$.Set $\mathc...
tejashmore25
58
views
tejashmore25
answered
Apr 18
Linear Algebra
goclasses2025_da_wq1
linear-algebra
multiple-selects
2-marks
+
–
5
votes
2
answers
24
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 5
Consider the linear map $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ defined by $ T(x, y)=(x-y, x-2 y), \text { for } x, y \in \mathbb{R} $ Let $\mathcal{E}$ be the standard basis for $\mathbb{R}^{2}$ ... $\left(\begin{array}{ll}0 & -1 \\ 1 & -1\end{array}\right)$
Consider the linear map $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ defined by$$T(x, y)=(x-y, x-2 y), \text { for } x, y \in \mathbb{R}$$Let $\mathcal{E}$ be the stand...
tejashmore25
62
views
tejashmore25
answered
Apr 18
Linear Algebra
goclasses2025_da_wq1
linear-algebra
2-marks
+
–
0
votes
1
answer
25
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
71
views
suvasish114
asked
Apr 16
Graph Theory
graph-theory
combinatory
isi2019-pcb-cs
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0
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1
answer
26
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
47
views
farhan777
asked
Apr 14
Mathematical Logic
self-doubt
discrete-mathematics
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–
0
votes
0
answers
27
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
61
views
RahulVerma3
asked
Apr 12
Set Theory & Algebra
discrete-mathematics
set-theory
analytical-aptitude
equivalence-class
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–
4
votes
1
answer
28
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
67
views
GO Classes
asked
Apr 11
Linear Algebra
goclasses2025_da_wq1
numerical-answers
linear-algebra
2-marks
+
–
4
votes
1
answer
29
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
77
views
GO Classes
asked
Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
easy
multiple-selects
1-mark
+
–
3
votes
1
answer
30
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
57
views
GO Classes
asked
Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
rank-of-matrix
1-mark
+
–
2
votes
1
answer
31
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 4
Let $\mathcal{B}=\left\{\mathbf{b}_{1}, \mathbf{b}_{2}, \mathbf{b}_{3}\right\}$ and $\mathcal{C}=\left\{\mathbf{c}_{1}, \mathbf{c}_{2}, \mathbf{c}_{3}\right\}$ be two bases of $\mathbb{R}^{3}$, and ... $\left[\begin{array}{r}3 \\ -1 \\ 1\end{array}\right]$
Let $\mathcal{B}=\left\{\mathbf{b}_{1}, \mathbf{b}_{2}, \mathbf{b}_{3}\right\}$ and $\mathcal{C}=\left\{\mathbf{c}_{1}, \mathbf{c}_{2}, \mathbf{c}_{3}\right\}$ be two bas...
GO Classes
57
views
GO Classes
asked
Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
2-marks
+
–
3
votes
1
answer
32
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 6
Suppose that ...
Suppose that$$\left[\left[\begin{array}{l}1 \\2\end{array}\right]\right]_{\mathcal{B}}=\left[\begin{array}{l}3 \\4\end{array}\right] \text { and }\left[\left[\begin{array...
GO Classes
52
views
GO Classes
asked
Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
2-marks
+
–
3
votes
1
answer
33
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 11
Which of the following statements are true? There exists a $3 \times 3$ matrix $A$ and vectors $b, c \in \mathbb{R}^{3}$ such that the linear system $A x=b$ has a unique solution but $A x=c$ has infinitely ... $n$, then the column space of $A$ is equal to the column space of $B$.
Which of the following statements are true?There exists a $3 \times 3$ matrix $A$ and vectors $b, c \in \mathbb{R}^{3}$ such that the linear system $A x=b$ has a unique s...
GO Classes
43
views
GO Classes
asked
Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
multiple-selects
2-marks
+
–
3
votes
2
answers
34
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 12
Consider two statements S1 and S2. S1: If $\left\{v_{1}, \ldots, v_{n}\right\}$ are linearly INDEPENDENT vectors in $V$, then $\left\{T\left(v_{1}\right), \ldots, T\left(v_{n}\right)\right\}$ are linearly ... $\mathrm{S} 2$ is true. Both S1 and S2 are true. Both S1 and S2 are false.
Consider two statements S1 and S2.S1: If $\left\{v_{1}, \ldots, v_{n}\right\}$ are linearly INDEPENDENT vectors in $V$, then $\left\{T\left(v_{1}\right), \ldots, T\left(v...
GO Classes
65
views
GO Classes
asked
Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
1-mark
+
–
5
votes
2
answers
35
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 13
Suppose $A$ is a $4 \times 3$ matrix and $B$ is a $3 \times 2$ matrix, and let $T$ be the matrix transformation $T(x)=A B x$. Which of the following must be true? The column space of $A B$ ... space of $A$. $T$ has domain $\mathbf{R}^{2}$ and codomain $\mathbf{R}^{4}$. $T$ cannot be onto.
Suppose $A$ is a $4 \times 3$ matrix and $B$ is a $3 \times 2$ matrix, and let $T$ be the matrix transformation $T(x)=A B x$. Which of the following must be true?The colu...
GO Classes
56
views
GO Classes
asked
Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
multiple-selects
1-mark
+
–
2
votes
1
answer
36
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 14
Suppose $A$ is an $11 \times 5$ matrix and $T$ is the corresponding linear transformation given by the formula $T(x)=A x$ ... the matrix equation $A x=0$ has infinitely many solutions, then $\operatorname{rank}(A) \leq 4$.
Suppose $A$ is an $11 \times 5$ matrix and $T$ is the corresponding linear transformation given by the formula $T(x)=A x$. Which of the following statements are true?$\op...
GO Classes
56
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GO Classes
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Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
1-mark
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2
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1
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37
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 15
The matrix $ \left(\begin{array}{rr} -2 & 11 \\ 4 & 2 \end{array}\right) $ represents a linear transformation $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ ... $\left(\begin{array}{rr}-2 & 11 \\ 4 & 2\end{array}\right)$
The matrix$$\left(\begin{array}{rr}-2 & 11 \\4 & 2\end{array}\right)$$represents a linear transformation $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ with respect to th...
GO Classes
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GO Classes
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Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
2-marks
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4
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1
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38
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 16
Suppose $A$ is an $11 \times 5$ matrix and $T$ is the corresponding linear transformation given by the formula $T(x)=A x$ ... the matrix equation $A x=0$ has infinitely many solutions, then $\operatorname{rank}(A) \leq 4$.
Suppose $A$ is an $11 \times 5$ matrix and $T$ is the corresponding linear transformation given by the formula $T(x)=A x$. Which of the following statements are true?$\op...
GO Classes
56
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GO Classes
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Apr 11
Linear Algebra
goclasses2025_da_wq1
linear-algebra
multiple-selects
2-marks
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1
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1
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39
GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 1
If $A$ and $B$ are two sets and $A \cup B = A \cap B$ then $A=\phi$ $B=\phi$ $A\neq B$ $A=B$
If $A$ and $B$ are two sets and $A \cup B = A \cap B$ then$A=\phi$$B=\phi$$A\neq B$$A=B$
GO Classes
79
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GO Classes
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Apr 10
Set Theory & Algebra
goclasses2025_cs_wq5
goclasses
discrete-mathematics
set-theory&algebra
set-theory
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1
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2
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40
GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 2
The cardinality of the power set of $A \cup B$, where $A=\{2,3,5,7\}$ and $B=\{2$, $5,8,9\}$, is?
The cardinality of the power set of $A \cup B$, where $A=\{2,3,5,7\}$ and $B=\{2$, $5,8,9\}$, is?
GO Classes
87
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GO Classes
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Apr 10
Set Theory & Algebra
goclasses2025_cs_wq5
numerical-answers
goclasses
discrete-mathematics
set-theory&algebra
set-theory
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