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Recent questions in Engineering Mathematics
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#self doubt
Can someone please explain the following case of combination I means identical D means different DOIB with boxes being empty and non empty As in this question the given value in question itself i am not able to interpret. https://gateoverflow.in/420251/go-classes-test-series-2024-mock-gate-test-12-question-17
Can someone please explain the following case of combinationI means identicalD means different DOIB with boxes being empty and non emptyAs in this question the given valu...
Dknights
226
views
Dknights
asked
Jan 28
Combinatory
discrete-mathematics
+
–
7
votes
2
answers
142
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 11
Let $f(x)$ be a real-valued function all of whose derivatives exist. Recall that a point $x_0$ in the domain is called an inflection point of $f(x)$ if the second derivative $f^{\prime \prime}(x)$ changes sign at ... only inflection point. $x_0=0$ and $x_0=6$, both are inflection points. The function does not have an inflection point.
Let $f(x)$ be a real-valued function all of whose derivatives exist. Recall that a point $x_0$ in the domain is called an inflection point of $f(x)$ if the second derivat...
GO Classes
879
views
GO Classes
asked
Jan 28
Calculus
goclasses2024-mockgate-13
goclasses
calculus
maxima-minima
1-mark
+
–
6
votes
1
answer
143
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 12
Let $x$ be a random variable possessing the probability density function $ f(x)= \begin{cases}c x & , x \in[0,10] \\ 0 & , \text { otherwise }\end{cases} $ where $c \in \mathbb{R}$. The probability that $x \in[1,2]$ is ______. $\dfrac{1}{100}$ $\dfrac{3}{100}$ $\dfrac{5}{100}$ $\dfrac{7}{100}$
Let $x$ be a random variable possessing the probability density function$$f(x)= \begin{cases}c x & , x \in[0,10] \\ 0 & , \text { otherwise }\end{cases}$$where $c \in \ma...
GO Classes
502
views
GO Classes
asked
Jan 28
Probability
goclasses2024-mockgate-13
goclasses
probability
random-variable
1-mark
+
–
7
votes
1
answer
144
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 13
If $A$ is a $3 \times 3$ matrix such that $A\left(\begin{array}{l}0 \\ 1 \\ 2\end{array}\right)=\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)$ ... $\left(\begin{array}{r}1 \\ -1 \\ 0\end{array}\right)$ $\left(\begin{array}{r}9 \\ 10 \\ 11\end{array}\right)$
If $A$ is a $3 \times 3$ matrix such that $A\left(\begin{array}{l}0 \\ 1 \\ 2\end{array}\right)=\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)$ and $A\left(\begin{ar...
GO Classes
585
views
GO Classes
asked
Jan 28
Linear Algebra
goclasses2024-mockgate-13
goclasses
linear-algebra
matrix
1-mark
+
–
3
votes
1
answer
145
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 28
A group $G$ in which $(a b)^2=a^2 b^2$ for all $a, b$ in $G$ is necessarily finite cyclic abelian none of the above
A group $G$ in which $(a b)^2=a^2 b^2$ for all $a, b$ in $G$ is necessarilyfinitecyclicabeliannone of the above
GO Classes
365
views
GO Classes
asked
Jan 28
Set Theory & Algebra
goclasses2024-mockgate-13
goclasses
set-theory&algebra
group-theory
1-mark
+
–
4
votes
1
answer
146
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 30
A university's mathematics department has $10$ professors and will offer $20$ different courses next semester. Each professor will be assigned to teach exactly $2$ of the courses, and each course will have exactly one professor assigned to teach it. If any ... $10^{20}-2^{10}$ $\dfrac{20 ! 10 !}{2^{10}}$
A university's mathematics department has $10$ professors and will offer $20$ different courses next semester. Each professor will be assigned to teach exactly $2$ of the...
GO Classes
634
views
GO Classes
asked
Jan 28
Combinatory
goclasses2024-mockgate-13
goclasses
combinatory
counting
1-mark
+
–
9
votes
2
answers
147
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 43
Let $A$ be a $2 \times 2$ matrix for which there is a constant $k$ such that the sum of the entries in each row and each column is $k$. Which of the following must be an eigenvector of $A?$ ... $\left[\begin{array}{l}1 \\ 1\end{array}\right]$. I only II only III only I and II only
Let $A$ be a $2 \times 2$ matrix for which there is a constant $k$ such that the sum of the entries in each row and each column is $k$. Which of the following must be an ...
GO Classes
516
views
GO Classes
asked
Jan 28
Linear Algebra
goclasses2024-mockgate-13
goclasses
linear-algebra
eigen-vector
2-marks
+
–
4
votes
1
answer
148
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 44
Football teams $T_1$ and $T_2$ play two games against each other in the Premier League. It is assumed that the outcomes of the two games are independent of each other. The probabilities of $T_1$ winning, drawing and losing against $T_2$ ... What will be the value of $P(X=Y)?$ $1 / 3$ $13 / 36$ $1 / 36$ $1 / 18$
Football teams $T_1$ and $T_2$ play two games against each other in the Premier League. It is assumed that the outcomes of the two games are independent of each other. Th...
GO Classes
484
views
GO Classes
asked
Jan 28
Probability
goclasses2024-mockgate-13
goclasses
probability
conditional-probability
2-marks
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–
3
votes
0
answers
149
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 61
Let $S$ be the set of all functions $f: \mathbb{R} \rightarrow \mathbb{R}$. Consider the two binary operations + and $\circ$ on $S$ ... law $(g+h) \circ f=(g \circ f)+(h \circ f)$. None III only II and III only I, II, and III
Let $S$ be the set of all functions $f: \mathbb{R} \rightarrow \mathbb{R}$. Consider the two binary operations + and $\circ$ on $S$ defined as pointwise addition and comp...
GO Classes
440
views
GO Classes
asked
Jan 28
Set Theory & Algebra
goclasses2024-mockgate-13
goclasses
set-theory&algebra
group-theory
2-marks
+
–
4
votes
1
answer
150
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 62
As a refresher, if $R$ is an equivalence relation over a set $A$ and $x \in A$, then the equivalence class of $\boldsymbol{x}$ in $\boldsymbol{R}$, denoted $[x]_R,$ is the set $ [x]_R=\{y \in A \mid x R y\} $ Let's now introduce some ... $\mathrm{I}(\mathrm{R})=n / 2$ and $\mathrm{W}(\mathrm{R})=n / 2$
As a refresher, if $R$ is an equivalence relation over a set $A$ and $x \in A$, then the equivalence class of $\boldsymbol{x}$ in $\boldsymbol{R}$, denoted $[x]_R,$ is th...
GO Classes
501
views
GO Classes
asked
Jan 28
Set Theory & Algebra
goclasses2024-mockgate-13
goclasses
set-theory&algebra
set-theory
relations
equivalence-class
2-marks
+
–
3
votes
1
answer
151
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 63
For an undirected graph $G$, let $\overline{G}$ refer to the complement (a graph on the same vertex set as $G$, with $(i, j)$ as an edge in $\overline{G}$ if and only if it is not an edge in $G$ ). Consider the following ... is equivalent to (iii) and (v). (i) is equivalent to (ii) and (iv). (i) is equivalent to (ii) and (v)
For an undirected graph $G$, let $\overline{G}$ refer to the complement (a graph on the same vertex set as $G$, with $(i, j)$ as an edge in $\overline{G}$ if and only if ...
GO Classes
456
views
GO Classes
asked
Jan 28
Graph Theory
goclasses2024-mockgate-13
goclasses
graph-theory
vertex-cover
2-marks
+
–
8
votes
2
answers
152
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 6
A college has $10$ (non-overlapping) time slots for its courses, and assigns courses to time slots randomly and independently. A student randomly chooses $3$ of the courses to enroll in. What is the probability that there is a conflict in the student's schedule? (answer upto $2$ decimals)
A college has $10$ (non-overlapping) time slots for its courses, and assigns courses to time slots randomly and independently. A student randomly chooses $3$ of the cours...
GO Classes
845
views
GO Classes
asked
Jan 21
Probability
goclasses2024-mockgate-12
goclasses
numerical-answers
probability
independent-events
1-mark
+
–
7
votes
2
answers
153
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 7
Let $\text{A}$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $\text{A}$, we get a matrix $\text{B}$ which has $12$ nonzero rows. Which of the following is/are always true? The rank of $\text{A}$ ... that $\text{A} v=0$ then $\text{B} v$ is also $0.$ The rank of $\text{B}$ is at most $11.$
Let $\text{A}$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $\text{A}$, we get a matrix $\text{B}$ which has $12$ nonzero rows. W...
GO Classes
661
views
GO Classes
asked
Jan 21
Linear Algebra
goclasses2024-mockgate-12
goclasses
linear-algebra
rank-of-matrix
multiple-selects
1-mark
+
–
6
votes
2
answers
154
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 17
The number of ways that one can divide $10$ distinguishable objects into $3$ indistinguishable non-empty piles, is: $ \left\{\begin{array}{c} 10 \\ 3 \end{array}\right\}=9330 $ In how many different ways can one do this if the piles are also distinguishable?
The number of ways that one can divide $10$ distinguishable objects into $3$ indistinguishable non-empty piles, is:$$\left\{\begin{array}{c}10 \\3\end{array}\right\}=9330...
GO Classes
918
views
GO Classes
asked
Jan 21
Combinatory
goclasses2024-mockgate-12
goclasses
numerical-answers
combinatory
counting
1-mark
+
–
5
votes
2
answers
155
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 18
The number of ways that one can divide $10$ distinguishable objects in $3$ indistinguishable non-empty piles, is: $ \left\{\begin{array}{c} 10 \\ 3 \end{array}\right\}=9330 $ In how many different ways can one do this if the objects are also indistinguishable?
The number of ways that one can divide $10$ distinguishable objects in $3$ indistinguishable non-empty piles, is:$$\left\{\begin{array}{c}10 \\3\end{array}\right\}=9330$$...
GO Classes
934
views
GO Classes
asked
Jan 21
Combinatory
goclasses2024-mockgate-12
goclasses
numerical-answers
combinatory
counting
1-mark
+
–
2
votes
1
answer
156
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 19
Let $\ast $ be the binary operation on the rational numbers given by $a \ast b=a+b+2 a b$. Which of the following are true? $\ast $ is commutative There is a rational number that is a $\ast \;-$ identity. Every rational number has a $\ast \;-$ inverse. I only I and II only I and III only I, II, and III
Let $\ast $ be the binary operation on the rational numbers given by $a \ast b=a+b+2 a b$. Which of the following are true?$\ast $ is commutativeThere is a rational numbe...
GO Classes
474
views
GO Classes
asked
Jan 21
Set Theory & Algebra
goclasses2024-mockgate-12
goclasses
set-theory&algebra
group-theory
1-mark
+
–
6
votes
1
answer
157
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 36
Let $A, B, C$ be events such that $P(A)=P(B)=P(C)=0.5, P(A \cap B)=0.3, P(A \cap C)=0$. Which of the following is/are true? $P(A \cup B)=0.75$ $P(A \cup C)=1$ $P(B \cap C)=0.23$ $P(B \cup C)=0.9$
Let $A, B, C$ be events such that $P(A)=P(B)=P(C)=0.5, P(A \cap B)=0.3, P(A \cap C)=0$.Which of the following is/are true?$P(A \cup B)=0.75$$P(A \cup C)=1$$P(B \cap C)=0....
GO Classes
889
views
GO Classes
asked
Jan 21
Probability
goclasses2024-mockgate-12
goclasses
probability
multiple-selects
2-marks
+
–
3
votes
2
answers
158
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 37
Which of the following is/are TRUE? There is a differentiable function $f(x)$ with the property that $f(1)=-2$ and $f(5)=14$ and $f^{\prime}(x)\lt 3$ for every real number $x$. There exists a function $f$ ... $a\lt c\lt b$ and $f(c)=0$. If $f$ is differentiable at the number $x$, then it is continuous at $x$.
Which of the following is/are TRUE?There is a differentiable function $f(x)$ with the property that $f(1)=-2$ and $f(5)=14$ and $f^{\prime}(x)\lt 3$ for every real number...
GO Classes
679
views
GO Classes
asked
Jan 21
Calculus
goclasses2024-mockgate-12
goclasses
calculus
differentiation
multiple-selects
2-marks
+
–
10
votes
1
answer
159
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 45
Below is a drawing(graph representation) of a binary relation $\text{R}$ over a set $\text{P}$ of elements $\{ \text{A, B, C, D, E, F}\}:$ Which of the following first-order logic statements about $\mathrm{R}$ ... $\forall x \in P . \exists y \in P . x R y$
Below is a drawing(graph representation) of a binary relation $\text{R}$ over a set $\text{P}$ of elements $\{ \text{A, B, C, D, E, F}\}:$Which of the following first-ord...
GO Classes
647
views
GO Classes
asked
Jan 21
Mathematical Logic
goclasses2024-mockgate-12
goclasses
mathematical-logic
first-order-logic
multiple-selects
2-marks
+
–
4
votes
1
answer
160
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 46
Assume the following graph is a labeled graph i.e. every vertex has a unique label. In how many ways can we color the following labeled graph $\mathrm{G}$ with six colors $\{R, G, B, W, Y, M\}$ such that no two adjacent vertices are assigned the same color?
Assume the following graph is a labeled graph i.e. every vertex has a unique label.In how many ways can we color the following labeled graph $\mathrm{G}$ with six colors ...
GO Classes
665
views
GO Classes
asked
Jan 21
Graph Theory
goclasses2024-mockgate-12
goclasses
numerical-answers
graph-theory
graph-coloring
2-marks
+
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