Recent questions in Engineering Mathematics / GATE Overflow for GATE CSE

3 votes

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141

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

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GO Classes asked Jan 28

4 votes

1 answer

142

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...

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GO Classes asked Jan 28

9 votes

2 answers

143

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 ...

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GO Classes asked Jan 28

4 votes

1 answer

144

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...

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GO Classes asked Jan 28

3 votes

0 answers

145

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...

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GO Classes asked Jan 28

4 votes

1 answer

146

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...

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GO Classes asked Jan 28

3 votes

1 answer

147

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 ...

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453 views

GO Classes asked Jan 28

8 votes

2 answers

148

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...

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839 views

GO Classes asked Jan 21

7 votes

2 answers

149

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...

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656 views

GO Classes asked Jan 21

6 votes

2 answers

150

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...

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912 views

GO Classes asked Jan 21

5 votes

2 answers

151

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:$$\left\{\begin{array}{c}10 \\3\end{array}\right\}=9330$$...

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929 views

GO Classes asked Jan 21

2 votes

1 answer

152

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...

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472 views

GO Classes asked Jan 21

6 votes

1 answer

153

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....

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882 views

GO Classes asked Jan 21

3 votes

2 answers

154

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...

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676 views

GO Classes asked Jan 21

10 votes

1 answer

155

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...

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644 views

GO Classes asked Jan 21

4 votes

1 answer

156

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 ...

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659 views

GO Classes asked Jan 21

6 votes

1 answer

157

GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 47
An involution is a function $f: A \rightarrow A$ where $f(f(x))=x$. A fixed point of any function $f: A \rightarrow A$ is an element $x \in A$ for which $f(x)$ $=x$. Which of the following statement(s) ... $f: \mathrm{A} \rightarrow \mathrm{A}$ is a bijective function.

An involution is a function $f: A \rightarrow A$ where $f(f(x))=x$.A fixed point of any function $f: A \rightarrow A$ is an element $x \in A$ for which $f(x)$ $=x$.Which ...

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464 views

GO Classes asked Jan 21

0 votes

0 answers

158

Madeeasy test 45, question 48
Can anyone please explain the statements II and III?

Can anyone please explain the statements II and III?

VinayBhojwani

161 views

VinayBhojwani asked Jan 15

0 votes

1 answer

159

Made easy mock test questions from Functions
Can you explain the procedure and if possible can you share some links to any youtube playlist from where I can study this particular subject(Functions).

Can you explain the procedure and if possible can you share some links to any youtube playlist from where I can study this particular subject(Functions).

Rohit Chakraborty

163 views

Rohit Chakraborty asked Jan 15

3 votes

1 answer

160

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 11
The figure above shows an undirected graph with six vertices. Enough edges are to be deleted from the graph in order to leave a spanning tree, which is a connected subgraph having the same six vertices and no cycles. How many edges must be deleted?

The figure above shows an undirected graph with six vertices. Enough edges are to be deleted from the graph in order to leave a spanning tree, which is a connected subgra...

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455 views

GO Classes asked Jan 13

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