Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Filter
Recent
Hot!
Most votes
Most answers
Most views
Previous GATE
Featured
Recent questions in Engineering Mathematics
5
votes
1
answer
31
GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 8
Let $A=\{0,1\} \times\{0,1\}$ and $B=\{a, b, c\}$. Suppose $A$ is listed in lexicographic order based on $0<1$ and $B$ is in alphabetic order. If $A \times B \times A$ is listed in lexicographic order, then the next element after $((1,0), c,(1,1))$ is $((1,0), a,(0,0))$ $((1,1), c,(0,0))$ $((1,1), a,(0,0))$ $((1,1), a,(1,1))$
Let $A=\{0,1\} \times\{0,1\}$ and $B=\{a, b, c\}$. Suppose $A$ is listed in lexicographic order based on $0<1$ and $B$ is in alphabetic order. If $A \times B \times A$ is...
GO Classes
94
views
GO Classes
asked
Apr 10
Set Theory & Algebra
goclasses2025_cs_wq5
goclasses
discrete-mathematics
set-theory&algebra
set-theory
2-marks
+
–
3
votes
0
answers
32
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 ...
GO Classes
66
views
GO Classes
asked
Apr 10
Set Theory & Algebra
goclasses2025_cs_wq5
goclasses
discrete-mathematics
set-theory&algebra
set-theory
2-marks
+
–
1
votes
0
answers
33
GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 10
Which of the following statements is $\textbf{FALSE}$? $C-(B \cup A)=(C-B)-A$ $A-(C \cup B)=(A-B)-C$ $B-(A \cup C)=(B-C)-A$ $A-(B \cup C)=(B-C)-A$
Which of the following statements is $\textbf{FALSE}$?$C-(B \cup A)=(C-B)-A$$A-(C \cup B)=(A-B)-C$$B-(A \cup C)=(B-C)-A$$A-(B \cup C)=(B-C)-A$
GO Classes
57
views
GO Classes
asked
Apr 10
Set Theory & Algebra
goclasses2025_cs_wq5
goclasses
discrete-mathematics
set-theory&algebra
set-theory
2-marks
+
–
0
votes
1
answer
34
Internet
A non empty set A is termed as an algebraic structure ________ a)with respect to binary operation * b)with respect to ternary operation ? c)with respect to binary operation + d)with respect to unary operation –
A non empty set A is termed as an algebraic structure ________a)with respect to binary operation *b)with respect to ternary operation ?c)with respect to binary operation ...
Tankut
86
views
Tankut
asked
Apr 4
6
votes
2
answers
35
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...
GO Classes
105
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
multiple-selects
goclasses
linear-algebra
matrix
easy
1-mark
+
–
7
votes
3
answers
36
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 2
Let $M$ be a $2 \times 2$ matrix with the property that the sum of each of the rows and also the sum of each of the columns is the same constant $c$. Which (if any) any of the vectors must be an eigenvector of $M$ ... $W = \left[\begin{array}{l}1 \\ 1 \\ \end{array}\right]$ $U$ $V$ $W$ None of the above
Let $M$ be a $2 \times 2$ matrix with the property that the sum of each of the rowsand also the sum of each of the columns is the same constant $c$. Which (if any) any of...
GO Classes
148
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
eigen-value
easy
1-mark
+
–
3
votes
1
answer
37
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 3
Let the $n \times n$ matrix $A$ have an eigenvalue $\lambda$ with corresponding eigenvector $v$. Which of the following statements are true for matrix $A$. $-v$ is an eigenvector of $-A$ with eigenvalue $- \lambda$. If $v$ is also ... $A+B$. eigenvalue of $A^3$ is $\lambda^3$ and the eigenvector is $v^3$ .
Let the $n \times n$ matrix $A$ have an eigenvalue $\lambda$ with corresponding eigenvector $v$.Which of the following statements are true for matrix $A$.$-v$ is an eigen...
GO Classes
155
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
eigen-value
medium
multiple-selects
2-marks
+
–
1
votes
2
answers
38
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 4
Consider the following matrix A: $\left[\begin{array}{lll}2 & -1 & 0 \\ 0 & 2 & 0 \\ 1 & 0 & 2\end{array}\right]$ Which of the following regarding the matrix $A$ ... $x$ is the eigenvector corresponding to eigenvalue $\lambda$ of $A$ then $x$ is also the eigenvector of $A^{-1}$.
Consider the following matrix A:$\left[\begin{array}{lll}2 & -1 & 0 \\ 0 & 2 & 0 \\ 1 & 0 & 2\end{array}\right]$Which of the following regarding the matrix $A$ is/are cor...
GO Classes
102
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
eigen-value
medium
multiple-selects
2-marks
+
–
1
votes
1
answer
39
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 5
Suppose a $3 \times 5$ matrix $A$ has rank $r = 3$. Then the equation $Ax = b$ $\textbf{BLANK 1}$ has $\textbf{BLANK 2}$ ... BLANK 2: Infinitely many solutions BLANK 1: Sometimes, BLANK 2: Unique solution BLANK 1: Sometimes, BLANK 2: Infinitely many solutions
Suppose a $3 \times 5$ matrix $A$ has rank $r = 3$. Then the equation $Ax = b$ $\textbf{BLANK 1}$ has $\textbf{BLANK 2}$.Which of the following are appropriate words ...
GO Classes
57
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
rank-of-matrix
medium
2-marks
+
–
3
votes
2
answers
40
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 6
Which of the following statements is/are $\textbf{NOT CORRECT}$? If $v1$ and $v2$ are linearly independent eigenvectors then they can correspond to the same eigenvalue. If $A$ is a nilpotent matrix, meaning that $A^k = 0$ for the ... is an eigenvalue of an invertible matrix $A$ then $\lambda ^{-1}$ is an eigenvalue of $A^{-1}$.
Which of the following statements is/are $\textbf{NOT CORRECT}$?If $v1$ and $v2$ are linearly independent eigenvectors then they can correspond to the same eigenvalue.If ...
GO Classes
102
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
eigen-value
medium
multiple-selects
2-marks
+
–
2
votes
1
answer
41
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 7
Given an $m \times n$ matrix $A$ whose rows are linearly independent. Now, consider following statements regarding $A$: $S1:$ The system of equations $Ax = b$ for any $b$ is consistent. $S2:$ $Ax = b$ always has a unique solution. ... $S2$ is FALSE. $S1$ is FALSE and $S2$ is TRUE. Both $S1$ and $S2$ are FALSE.
Given an $m \times n$ matrix $A$ whose rows are linearly independent. Now, consider following statements regarding $A$: $S1:$ The system of equations $Ax = b$ for any ...
GO Classes
74
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
medium
2-marks
+
–
3
votes
1
answer
42
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 8
Which of the following statements is/are $\textbf{FALSE}$? For $n \times n$ real-symmetric matrices $A$ and $B$, $AB$ and $BA$ always have the same eigenvalues. For $n \times n$ matrices $A$ and $B$ with $B$ ... eigenvectors. For $n \times n$ real-symmetric matrices $A$ and $B$, $AB$ and $BA$ always have the same eigenvectors.
Which of the following statements is/are $\textbf{FALSE}$?For $n \times n$ real-symmetric matrices $A$ and $B$, $AB$ and $BA$ always have the same eigenvalues.For $n \tim...
GO Classes
107
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
eigen-value
medium
multiple-selects
2-marks
+
–
4
votes
1
answer
43
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 9
Let $A$ and $B$ be two $n \times n$ matrices. If $B$ is invertible and $(I+BA)^{-1} = 2B^2$, then which of the following is the correct definition of $A$ in terms of $B$? $A = (1/2)B^{-3} - B^{-1}$ $A = 2B^{-3}- B^{-1}$ $A = 2B^3-I$ None of the above
Let $A$ and $B$ be two $n \times n$ matrices. If $B$ is invertible and $(I+BA)^{-1} = 2B^2$, then which of the following is the correct definition of $A$ in terms of $B$?...
GO Classes
75
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
easy
1-mark
+
–
3
votes
1
answer
44
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 10
A $4 \times 4$ matrix $\mathrm{A}$ has rank 3 . Which of the following is/are true? 1. $A^{-1}$ does not exist 2. $A^{-1}$ may exist, and if it does, its rank must be less than 3 3. $A^{-1}$ may ... , and it can take any rank less than 5 Only 1 is correct Only 2,3 are correct Only 4 is correct None of the statements are correct.
A $4 \times 4$ matrix $\mathrm{A}$ has rank 3 . Which of the following is/are true?1. $A^{-1}$ does not exist2. $A^{-1}$ may exist, and if it does, its rank must be less ...
GO Classes
65
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
rank-of-matrix
1-mark
+
–
1
votes
1
answer
45
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 11
The rank and nullity of a matrix $A$ are 4 and 2 , respectively. The nullity of $A^{\top}$ is 3 . What are the dimensions of $A$ ? $6 \times 7$ $4 \times 5$ $7 \times 6$ $5 \times 4$
The rank and nullity of a matrix $A$ are 4 and 2 , respectively. The nullity of $A^{\top}$ is 3 . What are the dimensions of $A$ ?$6 \times 7$$4 \times 5$$7 \times 6$$5 \...
GO Classes
57
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
2-marks
+
–
3
votes
1
answer
46
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 12
Consider two matrices $\mathrm{A}_{6 \times 3}$ and $\mathrm{B}_{3 \times 6}$, the non zero eigenvalues(EVs) of matrix $A B$ are $3,2,7,8$; see the following statements $\mathrm{S} 2$ : The EVs of BA must be all 0 for the ... false Both $\mathrm{S} 1$ and $\mathrm{S} 2$ are true Neither $\mathrm{S} 1$ nor $\mathrm{S} 2$ is true
Consider two matrices $\mathrm{A}_{6 \times 3}$ and $\mathrm{B}_{3 \times 6}$, the non zero eigenvalues(EVs) of matrix $A B$ are $3,2,7,8$; see the following statements$\...
GO Classes
92
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
eigen-value
1-mark
+
–
2
votes
1
answer
47
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 13
Which of the followings(s) is/are TRUE ? If a system of linear equations has no free variables, then it has a unique solution. If an augmented matrix $[A \mid b]$ is transformed into $[C \mid d]$ by elementary row operations, ... equation $A x=b$ has $a$ unique solution for every $b$ in the set of real numbers of dimension $m$.
Which of the followings(s) is/are TRUE ?If a system of linear equations has no free variables, then it has a unique solution.If an augmented matrix $[A \mid b]$ is transf...
GO Classes
75
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
multiple-selects
2-marks
+
–
4
votes
1
answer
48
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 14
Which of the following(s) is/are TRUE ? If none of the vectors in the set $S=\left\{\vec{v}_1, \vec{v}_2, \vec{v}_3\right\}$ in $\mathbb{R}^3$ is a multiple of one of the other vectors, then $S$ ... $\vec{v}_2$. Then $\left\{\vec{v}_1, \vec{v}_2, \vec{v}_3\right\}$ is linearly independent.
Which of the following(s) is/are TRUE ?If none of the vectors in the set $S=\left\{\vec{v}_1, \vec{v}_2, \vec{v}_3\right\}$ in $\mathbb{R}^3$ is a multiple of one of the ...
GO Classes
97
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
multiple-selects
2-marks
+
–
1
votes
1
answer
49
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 15
Consider the following two statements: $S 1$. If $A B=I$, then $A$ is invertible. $S 2$. If $A$ is a $3 \times 3$ matrix and the equation $A \vec{x}=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has a unique ... $S 2$ is false $\mathrm{S} 1$ is false but $\mathrm{S} 2$ is true Both are true Both are false
Consider the following two statements:$S 1$. If $A B=I$, then $A$ is invertible.$S 2$. If $A$ is a $3 \times 3$ matrix and the equation $A \vec{x}=\left[\begin{array}{l}1...
GO Classes
139
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
2-marks
+
–
3
votes
1
answer
50
GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 1
What is the Cardinality of the Power set of the set $\{0,1,2\}$? $8$ $6$ $7$ $9$
What is the Cardinality of the Power set of the set $\{0,1,2\}$?$8$$6$$7$$9$
GO Classes
94
views
GO Classes
asked
Apr 3
Set Theory & Algebra
goclasses2025_cs_wq4
goclasses
set-theory&algebra
set-theory
power-set
1-mark
+
–
Page:
« prev
1
2
3
4
5
6
7
...
525
next »
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register