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TIFR Mathematics 2024 | Part A | Question: 16
What is the number of distinct subfields of $\mathbb{C}$ isomorphic to $\mathbb{Q}[\sqrt[3]{2}]$? $1$ $2$ $3$ Infinite
What is the number of distinct subfields of $\mathbb{C}$ isomorphic to $\mathbb{Q}[\sqrt[3]{2}]$?$1$$2$$3$Infinite
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64
TIFR Mathematics 2024 | Part A | Question: 17
Let $\mathbb{F}_{3}$ denote the finite field with 3 elements. What is the number of one dimensional vector subspaces of the vector space $\mathbb{F}_{3}^{5}$ over $\mathbb{F}_{3}$? $5$ $121$ $81$ None of the remaining three options
Let $\mathbb{F}_{3}$ denote the finite field with 3 elements. What is the number of one dimensional vector subspaces of the vector space $\mathbb{F}_{3}^{5}$ over $\mathb...
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66
TIFR Mathematics 2024 | Part A | Question: 19
Consider the complex vector space $V=\{f \in \mathbb{C}[x] \mid f$ has degree at most 50 , and $f(i x)=-f(x)$ for all $x \in \mathbb{C}\}$. Then the dimension of $V$ equals $50$ $25$ $13$ $47$
Consider the complex vector space$V=\{f \in \mathbb{C}[x] \mid f$ has degree at most 50 , and $f(i x)=-f(x)$ for all $x \in \mathbb{C}\}$.Then the dimension of $V$ equals...
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70
GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 39
Consider a matrix $\left[\begin{array}{lll}0 & 1 & 0 \\ a & 2 & d \\ b & 3 & c\end{array}\right]$. The matrix cannot have rank. $0$ $1$ $2$ $3$
Consider a matrix $\left[\begin{array}{lll}0 & 1 & 0 \\ a & 2 & d \\ b & 3 & c\end{array}\right]$. The matrix cannot have rank.$0$$1$$2$$3$
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72
TIFR CSE 2024 | Part A | Question: 8
A palindrome is a string that reads the same in reverse (e.g. ABBA or KAYAK or MALAYALAM). How many strings of length 5 using the letters from $\{A, B, C, D, E\}$ have no palindromic substring of length at least 2? $243$ $405$ $540$ $675$ $1280$
A palindrome is a string that reads the same in reverse (e.g. ABBA or KAYAK or MALAYALAM).How many strings of length 5 using the letters from $\{A, B, C, D, E\}$ have no ...
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73
TIFR CSE 2024 | Part A | Question: 2
Let $\sigma$ be a uniform random permutation of $\{1, \ldots, 100\}$. What is the probability that $\sigma(1)<\sigma(2)<\sigma(3)$ ... $\frac{3}{100 !}$ $\frac{3 !}{100 !}$ $\frac{6}{100}$ $\frac{1}{6}$ $\frac{1}{3}$
Let $\sigma$ be a uniform random permutation of $\{1, \ldots, 100\}$. What is the probability that $\sigma(1)<\sigma(2)<\sigma(3)$ (i.e., what is the probability that the...
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77
GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 25
Two eigenvalues of $3 \times 3$ matrix $\mathbf{X}$ are $(1+i)$ and $2$. The determinant of the text matrix $\mathrm{X}$ is __________.
Two eigenvalues of $3 \times 3$ matrix $\mathbf{X}$ are $(1+i)$ and $2$. The determinant of the text matrix $\mathrm{X}$ is __________.
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80
GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 48
Consider the matrix $\mathbf{X}$ whose eigenvalues are $1,-1$ and $3$. Then Trace of $\mathbf{X}^{3}-3 \mathbf{X}^{2}$ is __________.
Consider the matrix $\mathbf{X}$ whose eigenvalues are $1,-1$ and $3$. Then Trace of $\mathbf{X}^{3}-3 \mathbf{X}^{2}$ is __________.
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