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41
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 22
Let $A$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $A$, we get a matrix $B$ which has 12 nonzero rows. Which of the following is/are always true? The rank of $A$ is 12. The ranks of $A$ and $B$ are ... . If $v$ is a vector such that $A v=0$ then $B v$ is also 0. The rank of $B$ is at most 11.
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Linear Algebra
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rank-of-matrix
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1-mark
3
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1
answer
42
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 39
For sets $A$ and $B$, let $f: A \rightarrow B$ and $g: B \rightarrow A$ be functions such that $f(g(x))=x$ for each $x \in B$. Which among the following statements is/are correct? The function $f$ must be one-to-one. The function $f$ must be onto. The function g must be one-to-one. The function $g$ must be onto.
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Set Theory & Algebra
Feb 5
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465
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set-theory&algebra
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2
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1
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43
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 48
Consider the quadratic equation $x^2+\dfrac{x}{2}+c=0$, where $c$ is chosen uniformly randomly from the interval $[0,1]$. What is the probability that the given quadratic equation has a real solution? The solutions of $a x^2+b x+c=0$ are given by $x=\dfrac{-b \pm \sqrt{b^2-4 a c}}{2a}$. $1 / 2$ $1 / 4$ $1 / 8$ $1 / 16$
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Probability
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335
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2-marks
6
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2
answers
44
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 49
Consider a $2 \times 2$ matrix M. Which of the following are NOT POSSIBLE for the system of equations $M x=p?$ no solutions for some but not all $\vec{p}$; exactly one solution for all other $\vec{p}$ exactly one solution for ... some $\vec{p}$, exactly one solution for some $\vec{p}$ and more than one solution for some $\vec{p}$
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Linear Algebra
Feb 5
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515
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goclasses2024-mockgate-14
linear-algebra
system-of-equations
multiple-selects
2-marks
6
votes
2
answers
45
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 56
The coefficient of $x^6$ in the expansion of $A(x)$ is, where $ A(x)=\frac{x(1+x)}{(1-x)^3} $
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Combinatory
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501
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6
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1
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46
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 57
A strongly connected component $(\mathrm{SCC})$ of a directed graph $\mathrm{G}=(\mathrm{V}, \mathrm{E})$ ... ; edges in its associated directed acyclic graph $G^{\prime}$ be $A, B$ respectively, then what is $A+B?$
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Graph Theory
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2-marks
11
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2
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47
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 58
Let $\mathrm{F}$ and $\mathrm{G}$ be two propositional formulae. Which of the following is/are True? If $F \vee G$ is a tautology then at least one of $F, G$ is a tautology. If $F \wedge G$ is a contradiction then at ... $G$ is a tautology. If $F \rightarrow G$ is a contradiction then $F$ is a tautology and $G$ is a contradiction.
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Mathematical Logic
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2-marks
2
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1
answer
48
Memory Based GATE DA 2024 | Question: 1
Consider the probability density function \(f(x) = \lambda e^{-\lambda x}\) for \(x \geq 0\) and \(\lambda > 0\). Determine the value of \(\lambda\) such that \(5E(x) = V(x)\).
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Feb 4
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298
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probability
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numerical-answers
1
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2
answers
49
Memory Based GATE DA 2024 | Question: 3
Evaluate the limit: \[ \lim_{{x \to 0}} \frac{\ln \left(\left(x^2+1\right) \cos x\right)}{x^2} \]
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Calculus
Feb 4
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463
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gate2024-da-memory-based
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calculus
limits
numerical-answers
2
votes
2
answers
50
Memory Based GATE DA 2024 | Question: 4
Consider the matrix \[ \mathrm{M} = \begin{bmatrix} 1 & 2 & 3 \\ 3 & 1 & 3 \\ 4 & 3 & 6 \end{bmatrix} \] Find the value of \(|\mathrm{M}^2 + 12M|\).
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Linear Algebra
Feb 4
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452
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gate2024-da-memory-based
goclasses
linear-algebra
determinant
numerical-answers
0
votes
0
answers
51
Memory Based GATE DA 2024 | Question: 5
Consider a matrix \(M \in \mathbb{R}^{3 \times 3}\) and let \(U\) be a 2-dimensional subspace such that \(M\) is a projection onto \(U\). Which of the following statements are true? \(M^3 = M\) \(M^2 = M\) The nullspace of \(M\) is 1-dimensional. The nullspace of \(M\) is 2-dimensional.
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Linear Algebra
Feb 4
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203
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gate2024-da-memory-based
goclasses
linear-algebra
vector-space
0
votes
2
answers
52
Memory Based GATE DA 2024 | Question: 6
Consider the matrix \[ \begin{bmatrix} 2 & -1 \\ 3 & 1 \end{bmatrix} \] What is the nature of the eigenvalues of the given matrix? Both eigenvalues are positive. One eigenvalue is negative. Eigenvalues are complex conjugate pairs. None of the above.
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Feb 4
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247
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eigen-value
0
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1
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53
Memory Based GATE DA 2024 | Question: 7
Consider the function \(f(x) = \frac{1}{1+e^{-x}}\). Determine the derivative \(f^{\prime}(x)\) when \(f(x) = 0.4\).
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Calculus
Feb 4
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282
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gate2024-da-memory-based
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calculus
maxima-minima
numerical-answers
0
votes
0
answers
54
Memory Based GATE DA 2024 | Question: 11
Consider a dataset with a raw score \(x = 75\), a mean \(\mu = 70\), and a standard deviation \(\sigma = 5\). Calculate the Z-score using the formula \(z = \frac{x - \mu}{\sigma}\).
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Probability
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167
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probability
normal-distribution
numerical-answers
0
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2
answers
55
Memory Based GATE DA 2024 | Question: 13
A fair six-sided die is thrown repeatedly. Find the expected number of throws until two consecutive throws show even numbers.
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Probability
Feb 4
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GO Classes
471
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probability
conditional-probability
numerical-answers
0
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1
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56
Memory Based GATE DA 2024 | Question: 14
Consider two events $\mathrm{T}$ and $\mathrm{S}$. Let $\overline{\mathrm{T}}$ denote the complement of event $\mathrm{T}$. The probabilities associated with different events are given as follows: $\mathrm{P}({\mathrm{T}})=0.4$ ... $\mathrm{P}(\mathrm{T}|\mathrm{S})$.
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180
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probability
conditional-probability
numerical-answers
1
vote
0
answers
57
Memory Based GATE DA 2024 | Question: 15
Consider the joint probability density function given by: $ f(x, y)= \begin{cases} 2xy & \text{if } 0 < x < 2 \text{ and } 0 < y < x \\ 0 & \text{otherwise} \end{cases} $ \noindent Determine the conditional expectation $E(Y | X = 1.5)$.
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191
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probability
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1
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58
Memory Based GATE DA 2024 | Question: 28
Consider a function \(f\) with \(f^1(X^*) = 0\) and \(f^{1l}(X^*) > 0\). Based on these conditions, determine the nature of the critical point \(X^*\) for the function \(f(X)\). \(X^*\) is a local maximum \(X^*\) is a local minimum \(X^*\) is a global maximum \(X^*\) is a global minimum
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Calculus
Feb 4
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GO Classes
155
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gate2024-da-memory-based
goclasses
calculus
maxima-minima
0
votes
1
answer
59
Memory Based GATE DA 2024 | Question: 29
Consider the vector \( u = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \\ 5 \end{bmatrix} \), and let \( M = uu^{\top} \). If \( \sigma_1, \sigma_2, \sigma_3, \ldots, \sigma_5 \) are the singular values of \( M \), what is the value of \( \sum_{i=1}^5 \sigma_i \)?
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Linear Algebra
Feb 4
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173
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gate2024-da-memory-based
goclasses
linear-algebra
vector-space
numerical-answers
0
votes
1
answer
60
Memory Based GATE DA 2024 | Question: 30
Consider the function \( F(x) \) defined as follows: \[ F(x) = \left\{ \begin{array}{cc} -x & \text{if } x < -2 \\ ax^2 + bx + c & \text{if } x \in [-2, 2] \\ x & \text{if } x > 2 \end{ ... \] \noindent Determine the values of \( a, b, \) and \( c \) such that \( F(x) \) is continuous and differentiable over its entire domain.
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Calculus
Feb 4
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213
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