Recent questions in Engineering Mathematics / GATE Overflow for GATE CSE

4 votes

1 answer

161

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 30
Let $A$ be a matrix defined as $A=u v^T$, where $u$ and $v$ are column vectors of dimension $3 \times 1$. The resulting matrix $A$ will be of dimension $3 \times 3$. What are the maximum number of nonzero eigenvalues possible for the matrix $A?$

Let $A$ be a matrix defined as $A=u v^T$, where $u$ and $v$ are column vectors of dimension $3 \times 1$. The resulting matrix $A$ will be of dimension $3 \times 3$. What...

GO Classes

774 views

GO Classes asked Jan 13

3 votes

1 answer

162

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 31
If $f, f^{\prime}$, and $f^{\prime \prime}$ are continuous and $f(2)=0, f^{\prime}(2)=2$, and $f^{\prime \prime}(2)=-3$, what can we say about the function $f(x)$ at $x=2?$ $f$ has a local minimum at $x=2$. $f$ has a local maximum at $x=2$. $f$ is increasing, at $x=2$ $f$ is decreasing, at $x=2$

If $f, f^{\prime}$, and $f^{\prime \prime}$ are continuous and $f(2)=0, f^{\prime}(2)=2$, and $f^{\prime \prime}(2)=-3$, what can we say about the function $f(x)$ at $x=2...

GO Classes

511 views

GO Classes asked Jan 13

5 votes

1 answer

163

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 36
Consider the system $A \mathbf{x}=\mathbf{b}$, with coefficient matrix $A$ and augmented matrix $[A \mid b]$. The sizes of $\mathbf{b}, A$, and $[A \mid \mathbf{b}]$ are $m \times 1, m \times n$ ... $\operatorname{rank}[A]>$ $\operatorname{rank}[A \mid b]$.

Consider the system $A \mathbf{x}=\mathbf{b}$, with coefficient matrix $A$ and augmented matrix $[A \mid b]$. The sizes of $\mathbf{b}, A$, and $[A \mid \mathbf{b}]$ are ...

GO Classes

511 views

GO Classes asked Jan 13

2 votes

1 answer

164

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 37
If $b$ and $c$ are elements in a group $G$, and if $b^5=c^3=e$, where $e$ is the unit element of $G$, then the inverse of $b^2 c b^4 c^2$ must be $b^4 c^2 b^2 c$ $c^2 b^4 c b^2$ $c b^2 c^2 b^4$ $c b c^2 b^3$

If $b$ and $c$ are elements in a group $G$, and if $b^5=c^3=e$, where $e$ is the unit element of $G$, then the inverse of $b^2 c b^4 c^2$ must be$b^4 c^2 b^2 c$$c^2 b^4 c...

GO Classes

432 views

GO Classes asked Jan 13

9 votes

1 answer

165

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 38
A binary relation $\mathrm{R}$ over a set $\mathrm{A}$ is called a "GO Relation" if for all $\mathrm{x}, \mathrm{y}, \mathrm{z}$ $\in A$, if $x R y$ and $x R z$, then $y R z$. Which of the following ... is transitive. If $R$ is a GO relation then $R$ is reflexive. If $R$ is an equivalence relation then $R$ is a GO relation.

A binary relation $\mathrm{R}$ over a set $\mathrm{A}$ is called a "GO Relation" if for all $\mathrm{x}, \mathrm{y}, \mathrm{z}$ $\in A$, if $x R y$ and $x R z$, then $y ...

GO Classes

567 views

GO Classes asked Jan 13

7 votes

2 answers

166

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 44
Acceptable input for a certain pocket calculator is a finite sequence of characters each of which is either a digit or a sign. The first character must be a digit, the last character must be a digit, and any character that is a sign must be followed by a digit. There ... by $N_k=a N _{k-1}+b N _{k-2}$, for $k \geq 3$. What is $a+ b?$

Acceptable input for a certain pocket calculator is a finite sequence of characters each of which is either a digit or a sign. The first character must be a digit, the la...

GO Classes

559 views

GO Classes asked Jan 13

0 votes

0 answers

167

Madeeasy 2024 full length test 3
Can anyone please help me solve this question or explain the formula used in the solution part of the same?

Can anyone please help me solve this question or explain the formula used in the solution part of the same?

VinayBhojwani

162 views

VinayBhojwani asked Jan 12

0 votes

0 answers

168

Linear Transformation of Matrix

Debargha Mitra Roy

68 views

Debargha Mitra Roy asked Jan 12

0 votes

0 answers

169

Consider a weighted undirected graph with positive edge weights and let (u, v) be an [2] edge in the graph. It is known that the shortest path from source vertex r to u has weight 53 and shortest path from r to v has weight 65. Which statement is always true?

Consider a weighted undirected graph with positive edge weights and let (u, v) be an edge in the graph. It is known that the shortest path from source vertex r to u hasw...

Malusi

108 views

Malusi asked Jan 12

0 votes

2 answers

170

Confusion between implication with its converse.
I have given two propositions p: You drive over 65 mph q: You get a speeding ticket Here are two natural language statements Driving over 65 mph is sufficient for getting a speeding ticket (answer key: $p \to q$) Whenever you get a speeding ... , anything that comes after when/whenever is the antecedent, it should be $p \to q$. Where I am wrong here?

I have given two propositionsp: You drive over 65 mphq: You get a speeding ticketHere are two natural language statementsDriving over 65 mph is sufficient for getting a s...

tbhaxor

177 views

tbhaxor asked Jan 11

0 votes

1 answer

171

Why inclusive or is used with Either...Or... here?
There are 2 propositions p: It is below freezing q: It is snowing. I want to write the symbolic form of: Either it is below freezing or it is snowing, but it is not snowing if it is freezing. This is what I came up with: ... . Second part it clear to me, but in the first shouldn't it will be exclusive or, because of Either...or...?

There are 2 propositionsp: It is below freezingq: It is snowing.I want to write the symbolic form of: Either it is below freezing or it is snowing, but it is not snowing ...

tbhaxor

147 views

tbhaxor asked Jan 11

0 votes

1 answer

172

GATE 2016 | MATHS | Q-48
Let $ M= \begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix} $ and $ e^M = Id + M + \frac{M^2}{2!} + \frac{M^3}{3!} + \frac{M^4}{4!} + \ldots $. If $ e^M = [b_{ij}]$. then \[\frac{1}{e} \sum_{i=1}^{3} \sum_{j=1}^{3} b_{ij} \] is equal to ________________________

Let $ M= \begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix} $ and $ e^M = Id + M + \frac{M^2}{2!} + \frac{M^3}{3!} + \frac{M^4}{4!} + \ldots $. If \( e...

rajveer43

165 views

rajveer43 asked Jan 11

0 votes

0 answers

173

GATE 2016 | MATHS | QUESTION-47
Let $ A = \begin{bmatrix} a & b & c \\ b& d & e\\ c& e& f\end{bmatrix} $ be a real matrix with eigenvalues 1, 0, and 3. If the eigenvectors corresponding to 1 and 0 are $\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}$ and $\begin{bmatrix} 1 \\ -1 \\ 0 \end{bmatrix}$ respectively, then the value of $3f$ is equal to ________________________

Let $ A = \begin{bmatrix} a & b & c \\ b& d & e\\ c& e& f\end{bmatrix} $ be a real matrix with eigenvalues 1, 0, and 3. If the eigenvectors corresponding to 1 and 0 are...

rajveer43

166 views

rajveer43 asked Jan 11

0 votes

1 answer

174

GATE 2016 | MATHS | Q-33
Suppose $ X $ and $ Y $ are two random variables such that $ aX + bY $ is a normal random variable for all $ a, b $ in $ \mathbf{R} $. Consider the following statements P, Q, R, and S: (P) : $ X $ is a standard normal random variable. (Q) ... 0. Which of the above statements ALWAYS hold TRUE? (A) both P and Q (B) both Q and R (C) both Q and S (D) both P and S

Suppose $ X $ and $ Y $ are two random variables such that $ aX + bY $ is a normal random variable for all $ a, b $ in $ \mathbf{R} $. Consider the following st...

rajveer43

120 views

rajveer43 asked Jan 11

0 votes

1 answer

175

GATE 2016 | MATHS | Q-11
Let $ \mathbf{v}, \mathbf{w}, \mathbf{u} $ be a basis of $ \mathbb{V} $. Consider the following statements P and Q: (P) : $ \{\mathbf{v} + \mathbf{w}, \mathbf{w} + \mathbf{u}, \mathbf{v} - \mathbf{u}\} $ is a basis of $ \mathbb{V} $. ( ... a basis of $ \mathbb{V} $. Which of the above statements hold TRUE? (A) both P and Q (B) only P (C) only Q (D) Neither P nor Q

Let $ \mathbf{v}, \mathbf{w}, \mathbf{u} $ be a basis of $ \mathbb{V} $. Consider the following statements P and Q:(P) : \( \{\mathbf{v} + \mathbf{w}, \mathbf{w} + \m...

rajveer43

152 views

rajveer43 asked Jan 11

0 votes

0 answers

176

GATE 2016 | MATHS | Q-12
Consider the following statements P and Q: (P) : If $ M = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 4 \\ 1 & 3 & 9 \end{bmatrix} $, then M is singular. (Q) : Let S be a diagonalizable matrix. If T is a matrix such that \( ... ), then T is diagonalizable. Which of the above statements hold TRUE? (A) both P and Q (B) only P (C) only Q (D) Neither P nor Q

Consider the following statements P and Q:(P) : If $ M = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 4 \\ 1 & 3 & 9 \end{bmatrix} $, then M is singular.(Q) : Let S be a diagon...

rajveer43

96 views

rajveer43 asked Jan 11

0 votes

0 answers

177

GATE 2016 | MATHS | Q-14
Consider a real vector space $ V $ of dimension $ n $ and a non-zero linear transformation $ T: \mathbb{V} \rightarrow \mathbb{V} $. If $ \text{dim}(T) < n $ and $T^2 = \lambda T$, for some $ \lambda \in \mathbb{R} \backslash \{0\} $, then which ... 0 \) for all $ X \in \mathbb{W} $ (C) $ T $ is invertible (D) $ \lambda$ is the only eigenvalue of $ T $

Consider a real vector space $ V $ of dimension $ n $ and a non-zero linear transformation $ T: \mathbb{V} \rightarrow \mathbb{V} $. If $ \text{dim}(T) < n $ and ...

rajveer43

84 views

rajveer43 asked Jan 11

0 votes

0 answers

178

GATE 2018 | MATH | Q-64
Let $X_1$ and $X_2$ be independent geometric random variables with the same probability mass function given by $P(X = k) = p(1 - p)^{k-1}$, $k = 1, 2, \ldots$. Then the value of $P(X_1 = 2 | X_1 + X_2 = 4)$ correct up to three decimal places is____________

Let $X_1$ and $X_2$ be independent geometric random variables with the same probability mass function given by $P(X = k) = p(1 - p)^{k-1}$, $k = 1, 2, \ldots$. Th...

rajveer43

108 views

rajveer43 asked Jan 11

0 votes

0 answers

179

GATE 2018 | MATHS | Q-63
Let $X$ be the number of heads in 4 tosses of a fair coin by Person 1 and let $Y$ be the number of heads in 4 tosses of a fair coin by Person 2. Assume that all the tosses are independent. Then the value of $P(X = Y )$ correct up to three decimal places is_________

Let $X$ be the number of heads in 4 tosses of a fair coin by Person 1 and let $Y$ be the number of heads in 4 tosses of a fair coin by Person 2. Assume that all the tosse...

rajveer43

103 views

rajveer43 asked Jan 11

0 votes

1 answer

180

GATE 2018 | MATHS | Q-62
Let $X1, X2, X3, X4$ be independent exponential random variables with mean $1, 1/2, 1/3, 1/4,$ respectively. Then $Y = min(X1, X2, X3, X4)$ has exponential distribution with mean equal to

Let $X1, X2, X3, X4$ be independent exponential random variables with mean $1, 1/2, 1/3, 1/4,$ respectively. Then $Y = min(X1, X2, X3, X4)$ has exponential distribution w...

rajveer43

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rajveer43 asked Jan 11

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