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Recent questions in Engineering Mathematics
0
votes
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answers
161
GATE 2023 | Maths | Practice Problem for DA Paper
Let \( T: \mathbb{R}^4 \rightarrow \mathbb{R}^4 \) be a linear transformation, and the null space of \( T \) be the subspace of \( \mathbb{R}^4 \) given by \[ \{ (x_1, x_2, x_3, x_4) \in \mathbb{R}^4 : 4x_1 + 3x_2 + 2x_3 + x_4 = 0 \}. \] If \( \text{Rank}(T - 3I) = ... \( x(x - 3) \) (B) \( x(x - 3)^3 \) (C) \( x^3(x - 3) \) (D) \( x^2(x - 3)^2 \)
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
72
views
linear-algebra
0
votes
0
answers
162
GATE 2023 | MATHS | Practice Problem for DA Paper
Let \(M = \begin{bmatrix} 4 & -3 \\ 1 & 0 \end{bmatrix}\). Consider the following statements: \(P:\ M^8 + M^{12}\) is diagonalizable. \(Q:\ M^7 + M^9\) is diagonalizable. Which of the following statements is correct? (A) $π$ is $TRUE$ ... $π$ is $FALSE$ and $π$ is $TRUE$ (C) Both $π$ and $π$ are $FALSE$ (D) Both $π$ and $π$ are $TRUE$
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
100
views
linear-algebra
0
votes
0
answers
163
GATE 2022 | Statistics | GATE-DA Sample Question
A company sometimes stops payments of quarterly dividends. If the company pays the quarterly dividend, the probability that the next one will be paid is $0.7$. If the company stops the quarterly dividend, the probability that the next ... (rounded off to three decimal places) that the company will not pay quarterly dividend in the long run is ______.
rajveer43
asked
in
Probability
Jan 10
by
rajveer43
92
views
probability
0
votes
0
answers
164
GATE DA - 2024 | Linear Algebra
Let $π΄$ be an $π π$ real matrix. Consider the following statements. $(I)$ If $π΄$ is symmetric, then there exists $π β₯ 0$ such that $π΄ + ππΌ_π$ is symmetric and positive definite, where $πΌ_π$ is the $π π$ identity matrix $(II)$ If $π΄$ is symmetric and ... above statements is/are true? (A) Only (I) (B) Only (II) (C) Both (I) and (II) (D) Neither (I) nor (II)
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
96
views
linear-algebra
0
votes
0
answers
165
GATE Practice Problem | Probability
Two defective bulbs are present in a set of five bulbs. To remove the two defective bulbs, the bulbs are chosen randomly one by one and tested. If $π$ denotes the minimum number of bulbs that must be tested to find out the two defective bulbs, then $π(π = 3)$ (rounded off to two decimal places) equals _______________
rajveer43
asked
in
Probability
Jan 10
by
rajveer43
74
views
probability
0
votes
0
answers
166
GATE DA Paper | Practice Problems
Let $π_1 < π_2 < β― < π_n$ be the order statistics of a random sample of size $π$ from a continuous distribution, which is symmetric about its mean $π$. Then the smallest value of $π$ (in integer) such that $π(π1 < π < π) β₯ 0.99$, is ______.
rajveer43
asked
in
Probability
Jan 10
by
rajveer43
82
views
statistics
probability
0
votes
0
answers
167
Statistics | Poisson Distribution Sample Question | GATE DA
Let $0, 1, 1, 2, 0$ be five observations of a random variable $π$ which follows a Poisson distribution with the parameter $π > 0$. Let the minimum variance unbiased estimate of $π(π β€ 1)$, based on this data, be $πΌ$. Then $5^4πΌ$ (in integer) is equal to _____________
rajveer43
asked
in
Probability
Jan 10
by
rajveer43
83
views
statistics
0
votes
0
answers
168
GATE 2021 | Statistics | Q-3
rajveer43
asked
in
Probability
Jan 10
by
rajveer43
40
views
statistics
probability
0
votes
1
answer
169
GATE 2021 | Statistics | Q-11
Let $X$ be a non constant positive random variable such that $E(X)=9$. Then which of the following statements is correct A) $E(1X+1)>0.1$ and $P(Xβ₯10)β€0.9$ B) $E(1X+1)<0.1$ and $P(Xβ₯10)β€0.9$ C) $E(1X+1)>0.1$ and $P(Xβ₯10)>0.9$ D) $E(1X+1)<0.1 and P(Xβ₯10)>0.9$
rajveer43
asked
in
Probability
Jan 10
by
rajveer43
88
views
statistics
0
votes
1
answer
170
GATE 2022 | Statistics | Q- 57
In a laboratory experiment, the behavior of cats are studied for a particular food preference between two foods $A$ and $B$ . For an experiment, 70% of the cats that had food A will prefer food A, and 50% of the cats that had food ... experiment, then the percentage (rounded off to one decimal place) of cats those will prefer food A in the third experiment, is ______
rajveer43
asked
in
Probability
Jan 10
by
rajveer43
115
views
probability
0
votes
0
answers
171
#self doubt
Can someone please explain why no of lineary independent solutions are n-r .β¦ My confusion is if in 3*3 Matrix rank is 2 means 2 lineary independent rows right? How solution is getting calculated as 3-2=1?
Dknights
asked
in
Linear Algebra
Jan 10
by
Dknights
56
views
linear-algebra
engineering-mathematics
0
votes
2
answers
172
GATE 2022 | Statistics | Question 47
Let π΄ be any 3 Γ 3 symmetric matrix with eigenvalues 1, 2 and 3. Let π΅ be any 3 Γ 3 matrix with real eigenvalues such that $π΄π΅ + π΅^Tπ΄ = 3π°$, where π° is the 3 Γ 3 identity matrix. Then which of the following cannot be eigenvalue(s) of the matrix π΅ ? (A) 1/4 (B) 3/4 (C) 1/2 (D) 7/4
rajveer43
asked
in
Linear Algebra
Jan 9
by
rajveer43
164
views
linear-algebra
0
votes
0
answers
173
GATE Statistics Question 34
rajveer43
asked
in
Probability
Jan 9
by
rajveer43
55
views
probability
0
votes
0
answers
174
GATE CS Probabilty 2022 statistics paper
rajveer43
asked
in
Probability
Jan 9
by
rajveer43
54
views
probability
0
votes
0
answers
175
GATE 2022 Stat | Question 16 | Linear Algebra
rajveer43
asked
in
Mathematical Logic
Jan 9
by
rajveer43
43
views
linear-algebra
1
vote
0
answers
176
GATE 2022 | Linear Algebra | Question 11
Let π΄ be a 2 Γ 2 real matrix such that $(π° + π΄)^-1 = π° β πΌπ΄$, where πΌ is a non-zero real number and π° is the 2 Γ 2 identity matrix. If the trace of the matrix π΄ is 3, then the value of πΌ is (A) 3/4 (B) 1/3 (C) 1/2 (D) 1/4
rajveer43
asked
in
Mathematical Logic
Jan 9
by
rajveer43
81
views
linear-algebra
0
votes
0
answers
177
Linear Algebra, Eigen Vales & Eigen Vectors
$If \ A = \begin{pmatrix} 1&1 \\ 1&0 \end{pmatrix},\ \alpha M_1+\beta M_2+\gamma M_3,\ where \ M_1 = L_{2x2},\ M_2 = \begin{pmatrix} 0&1 \\ 1&1 \end{pmatrix}\ and \ M_3 = \begin{pmatrix} 1&1 \\ 1&1 \end{pmatrix} \ then \ -$ ... $\alpha = 1,\ \beta = -1,\ \gamma = 2$ D. $\alpha = -1,\ \beta = 1,\ \gamma = 2$
Debargha Mitra Roy
asked
in
Linear Algebra
Jan 8
by
Debargha Mitra Roy
109
views
engineering-mathematics
linear-algebra
eigen-value
matrix
1
vote
1
answer
178
selfdoubt combinatory
In how many ways can you distribute 4 different choclates to 3 people such that each gets atleast 1 choclate.
nihal_chourasiya
asked
in
Combinatory
Jan 7
by
nihal_chourasiya
187
views
self-doubt
made-easy-test-series
0
votes
1
answer
179
ISRO 2024
Maximum number of Simple graphs possible with $n$ vertices $2^{n(n-1)/2}$ $2^{(n-1)/2}$ $2^{n(n+1)/2}$ $2^{n(n+1)}$
Ramayya
asked
in
Graph Theory
Jan 7
by
Ramayya
182
views
isro-2024
graph-theory
discrete-mathematics
0
votes
1
answer
180
ISRO 2024
If there are five faces and nine vertices in an undirected planar graph, then number of edges is 14 6 12 None of the above
Ramayya
asked
in
Graph Theory
Jan 7
by
Ramayya
265
views
isro-2024
graph-theory
graph-planarity
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