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Recent questions in Engineering Mathematics
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151
GATE 2022 | MATHS | Q-32
If the function \( f(x, y) = x^2 + xy + y^2 + \frac{1}{x} + \frac{1}{y} \), \( x \neq 0, y \neq 0 \), attains its local minimum value at the point \((a, b)\), then the value of \(a^3 + b^3\) is _________(rounded off to TWO decimal places).
rajveer43
asked
in
Calculus
Jan 10
by
rajveer43
74
views
calculus
0
votes
0
answers
152
GATE 2022 | MATHS | Q-27
The number of subgroups of a cyclic group of order 12 is ______________________
rajveer43
asked
in
Set Theory & Algebra
Jan 10
by
rajveer43
47
views
discrete-mathematics
0
votes
0
answers
153
GATE 2022 | MATHS | Q-25
Consider the linear system of equations \(Ax = b\) with \[ A = \begin{bmatrix} 3 & 1 & 1 \\ 1 & 4 & 1 \\ 2 & 0 & 3 \\ \end{bmatrix} \] and \[ b = \begin{bmatrix} 2 \\ 3 \\ 4 \\ \end ... for any initial vector. (C) The Gauss-Seidel iterative method converges for any initial vector. (D) The spectral radius of the Jacobi iterative matrix is less than 1.
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
71
views
linear-algebra
matrix
0
votes
0
answers
154
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
by
rajveer43
62
views
linear-algebra
0
votes
1
answer
155
GATE 2022 | MATHS | LINEAR ALGEBRA
Suppose that the characteristic equation of \( M \in \mathbb{C}^{3 \times 3} \) is \[ \lambda^3 + \alpha \lambda^2 + \beta \lambda - 1 = 0, \] where \( \alpha, \beta \in \mathbb{C} \) with \( \alpha + \beta \neq 0 \). Which of the following statements is TRUE? (A) \( M(I ... 1} (M^{-1} + \beta I) = M - \alpha I \) (D)\( M^{-1} (M^{-1} - \beta I) = M + \alpha I \)
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
101
views
linear-algebra
0
votes
0
answers
156
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
by
rajveer43
67
views
linear-algebra
1
vote
1
answer
157
GATE 2023 | MATHS | Question 59
Let \(A\) be a \(3 \times 3\) real matrix with \(\text{det}(A + iI) = 0\), where \(i = \sqrt{-1}\) and \(I\) is the \(3 \times 3\) identity matrix. If \(\text{det}(A) = 3\), then the trace of \(A^2\) is \(\underline{\hspace{1cm}}\).
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
97
views
linear-algebra
0
votes
1
answer
158
GATE 2023 | Maths | Sample Ques for CS-IT
Let \(G\) be an abelian group and \(\Phi: G \rightarrow (\mathbb{Z}, +)\) be a surjective group homomorphism. Let \(1 = \Phi(a)\) for some \(a \in G\). Consider the following statements: \(P\): For every \(g \in G\), there exists an \(n \in \ ... following statements is/are correct? (A) \(P\) is TRUE (B) \(P\) is FALSE (C) \(Q\) is TRUE (D) \(Q\) is FALSE
rajveer43
asked
in
Set Theory & Algebra
Jan 10
by
rajveer43
59
views
set-theory
discrete-mathematics
0
votes
1
answer
159
GATE 2023 | Maths | Problems for DA Paper
Consider the linear system \(Mx = b\), where \[ M = \begin{bmatrix} 2 & -1 \\ -4 & 3 \end{bmatrix} \] and \[ b = \begin{bmatrix} -2 \\ 5 \end{bmatrix} \]. Suppose \(M = LU\), where \(L\) and \(U\) are lower triangular and upper ... (A) both 𝑃 and 𝑄 are TRUE (B) 𝑃 is FALSE and 𝑄 is TRUE (C) 𝑃 is TRUE and 𝑄 is FALSE (D) both 𝑃 and 𝑄 are FALSE
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
92
views
linear-algebra
0
votes
1
answer
160
GATE 2023 | Maths | Linear Alegbra
Let \( M = \begin{bmatrix} 3 & -1 & -2 \\ 0 & 2 & 4 \\ 0 & 0 & 1 \end{bmatrix} \) and \( I = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \). If \( 6M^{-1} = M^2 - 6M + \alpha I \) for some \( \alpha \in \mathbb{R} \), then the value of \( \alpha \) is equal to \(\underline{\hspace{1cm}}\).
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
81
views
linear-algebra
0
votes
0
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
65
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) $𝑃$ 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
by
rajveer43
94
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
88
views
probability
0
votes
0
answers
164
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
by
rajveer43
88
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 $𝑋$ 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
by
rajveer43
69
views
probability
0
votes
0
answers
166
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
by
rajveer43
76
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 $𝑋$ 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
by
rajveer43
78
views
statistics
0
votes
0
answers
168
GATE 2021 | Statistics | Q-3
rajveer43
asked
in
Probability
Jan 10
by
rajveer43
34
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 $P(X≥10)≤0.9$ B) $E(1X+1)<0.1$ and $P(X≥10)≤0.9$ C) $E(1X+1)>0.1$ and $P(X≥10)>0.9$ D) $E(1X+1)<0.1 and P(X≥10)>0.9$
rajveer43
asked
in
Probability
Jan 10
by
rajveer43
83
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
106
views
probability
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