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241

GATE 2022 | Maths | Q-12
Consider $P :$ Let \( M \in \mathbb{R}^{m \times n} \) with \( m > n \geq 2 \). If \( \text{rank}(M) = n \), then the system of linear equations \( Mx = 0 \) has \( x = 0 \) as the only solution. $Q:$ Let \( E \in \mathbb{R}^{n \ ... following statements is TRUE? (A) Both P and Q are TRUE (B) Both P and Q are FALSE (C)P is TRUE and Q is FALSE (D) P is FALSE and Q is TRUE

rajveer43 asked in Linear Algebra Jan 10

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242

GATE 2023 | Maths | Question 60
Let \( A = [a_{ij}]\) be a \(3 \times 3\) real matrix such that \[ A \begin{bmatrix} 1 \\ 2 \\ 1 \end{bmatrix} = 2 \begin{bmatrix} 1 \\ 2 \\ 1 \end{bmatrix}, \quad A \begin{bmatrix} 0 \\ 1 \\ 1 \end{bmatrix} = 2 \begin{bmatrix} 0 \\ 1 ... is the degree of the minimal polynomial of \( A \), then \( a_{11} + a_{21} + a_{31} + m \) equals \(\underline{\hspace{1cm}}\).

rajveer43 asked in Linear Algebra Jan 10

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243

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

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244

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) $𝑃$ is $TRUE$ ... $𝑃$ is $FALSE$ and $𝑄$ is $TRUE$ (C) Both $𝑃$ and $𝑄$ are $FALSE$ (D) Both $𝑃$ and $𝑄$ are $TRUE$

rajveer43 asked in Linear Algebra Jan 10

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245

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

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246

GATE DA - 2024 | Linear Algebra
Let $𝐴$ be an $𝑛 𝑛$ real matrix. Consider the following statements. $(I)$ If $𝐴$ is symmetric, then there exists $𝑐 ≥ 0$ such that $𝐴 + 𝑐𝐼_𝑛$ is symmetric and positive definite, where $𝐼_𝑛$ is the $𝑛 𝑛$ identity matrix $(II)$ If $𝐴$ 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

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247

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 $𝑋$ denotes the minimum number of bulbs that must be tested to find out the two defective bulbs, then $𝑃(𝑋 = 3)$ (rounded off to two decimal places) equals _______________

rajveer43 asked in Probability Jan 10

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248

GATE DA Paper | Practice Problems
Let $𝑌_1 < 𝑌_2 < ⋯ < 𝑌_n$ be the order statistics of a random sample of size $𝑛$ from a continuous distribution, which is symmetric about its mean $𝜇$. Then the smallest value of $𝑛$ (in integer) such that $𝑃(𝑌1 < 𝜇 < 𝑌) ≥ 0.99$, is ______.

rajveer43 asked in Probability Jan 10

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249

Statistics | Poisson Distribution Sample Question | GATE DA
Let $0, 1, 1, 2, 0$ be five observations of a random variable $𝑋$ which follows a Poisson distribution with the parameter $𝜃 > 0$. Let the minimum variance unbiased estimate of $𝑃(𝑋 ≤ 1)$, based on this data, be $𝛼$. Then $5^4𝛼$ (in integer) is equal to _____________

rajveer43 asked in Probability Jan 10

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250

GATE 2021 | Statistics | Q-3

rajveer43 asked in Probability Jan 10

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251

#self doubt
Can someone please explain why no of lineary independent solutions are n-r .… 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

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252

GATE Statistics Question 34

rajveer43 asked in Probability Jan 9

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253

GATE CS Probabilty 2022 statistics paper

rajveer43 asked in Probability Jan 9

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254

GATE 2022 Stat | Question 16 | Linear Algebra

rajveer43 asked in Mathematical Logic Jan 9

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255

GATE 2022 | Linear Algebra | Question 11
Let 𝑴 be a 2 × 2 real matrix such that $(𝑰 + 𝑴)^-1 = 𝑰 − 𝛼𝑴$, where 𝛼 is a non-zero real number and 𝑰 is the 2 × 2 identity matrix. If the trace of the matrix 𝑴 is 3, then the value of 𝛼 is (A) 3/4 (B) 1/3 (C) 1/2 (D) 1/4

rajveer43 asked in Mathematical Logic Jan 9

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256

Topic name:Finding number of Cnadiadte and Super Keys
r=(a1,a2,a3,...a8) assumne that a1a2a3 is a canidate key and other cks we dont know.Then find the number of possible candidate keys and number of superkeys?

supratikde707 asked in Databases Jan 9

by supratikde707

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257

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

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258

Biswajit Kumar asked in CO and Architecture Jan 8

by Biswajit Kumar

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259

ISRO 2024
Consider the context-free grammer $G$ below. There $S$ is the starting non terminal symbol, while $a$ and $b$ are terminal symbols. $S \rightarrow aaSb | T$ $T \rightarrow Tb | a$ Which of the following statments is true about the language $L(G)$ generated by $G$? ... $aaaabb$ does not $aaaabb$ belongs to $L(G)$ but $aabbaabb$ does not $aaabb$ belongs to $L(G)$ but $aaaaabbb$ does not

Ramayya asked in Theory of Computation Jan 7

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260

ISRO 2024
Purpose of priority inheritance protocol in synchronization mechanisms is: To prevent priority inversion in systems having two or lesser priorities for a resource To provide mutual exclusion between threads and prevent data corruption To prevent priority inversion and ensure fairness in resource allocation To allow multiple threads to access any resource simultaneously

Ramayya asked in Operating System Jan 7

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261

ISRO 2024
Which of the following clustering technique is used by K-Means algorithm: Hierarchical Technique Partitional technique Divisive Agglomerative

Ramayya asked in Others Jan 7

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262

ISRO 2024
Match the following and select the correct option: (i) Encryption (P) Manipulation of identification of a host (through NIC identifier) (ii) MAC cloning (Q) Determining version and name of OS and OS utilities (iii) ARP spoofing (R) Protecting the confidentiality (i) Finger printing (S) Poisioning the IP to MAC address ... - (P), (i) - (Q) (i) - (R), (iI) - (Q), (i) - (S), (i) - (P)

Ramayya asked in Computer Networks Jan 7

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263

ISRO 2024
which of the following statements is NOT true? If a language is recursive it complement is recursive If a language is recursive its complement is recursively enumerable If a language and its complement are recursively enumerable it is recursive If a language is recursively enumerable its complement is also recursively enumerable

Ramayya asked in Theory of Computation Jan 7

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264

ISRO 2024
As part of segmentation memory allocation strategy, which of the following assigns a program like code segment and data segment Compiler Assembler Loader Linker A request to the approver.!! This question is asked in ISRO 2024. Due to insufficient points, couldn’t add ‘isro2024’ tag, Please add it.

Ramayya asked in Operating System Jan 7

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265

ISRO 2024
Match the following context of information Secuirty which are closely associated Matching (i) Ingress Filtering (P) Data Leakage Prevention (ii) Egress Filtering (Q) Hiding indentity of systems (iii) NAT (R) Keep Track of TCP/IP connections (iv) Stateful firewall (S) Malicious traffic prevention (i) - (S), (ii) - (P), ... ) - (P), (iv) - (Q) (i) - (R), (ii) - (Q), (iii) - (S), (iv) - (P)

Ramayya asked in Computer Networks Jan 7

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266

#selfdoubt
In CRC, if the dataword is 5 bits and the codeword is 8 bits, how many 0s need to be added to the dataword to make the dividend? What is the size of the remainder? What is the size of the divisor?

Ansh Sinha asked in Computer Networks Jan 7

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267

ISRO 2024
In a vectored interrupt The branch address is assigned to a fixed location in a memory The interrupting source supplies the branch information to the processor The branch address is obtained from a register in the processor None of the above A request to the approver.!! This question is asked in ISRO 2024. Due to insufficient points, couldn’t add ‘isro2024’ tag, Please add it.

Ramayya asked in CO and Architecture Jan 7

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268

ISRO 2024
In Reeverse Polish notation, expression A*B+C*D is written as AB*CD*+ A*BCD*+ AB*CD+* A*B*CD+ A request to the approver.!! This question is asked in ISRO 2024. Due to insufficient points, couldn’t add ‘isro2024’ tag, Please add it.

Ramayya asked in DS Jan 7

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269

UGC NET CSE | June 2008 | Part 2 | Question: 5
In a set of $8$ positive integers, there always exists a pair of numbers having the same remainder when divided by : $7$ $11$ $13$ $15$

admin asked in Others Jan 6

by admin

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270

UGC NET CSE | June 2008 | Part 2 | Question: 9
The characteristic equation of a $\mathrm{T}$ flip flop is given by : $\mathrm{Q}_{\mathrm{N}+1}=\mathrm{TQ}_{\mathrm{N}}$ $\mathrm{Q}_{\mathrm{N}+1}=\mathrm{T}+\mathrm{Q}_{\mathrm{N}}$ $\mathrm{Q}_{\mathrm{N}+1}=\mathrm{T} \oplus \mathrm{Q}_{\mathrm{N}}$ $\mathrm{Q}_{\mathrm{N}+1}=\overline{\mathrm{T}}+\mathrm{Q}_{\mathrm{N}}$

admin asked in Others Jan 6

by admin

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