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TIFR Mathematics 2024 | Part B | Question: 18
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Let $A, B$ be subsets of $\{0, \ldots, 9\}$. It is given that, on choosing elements $a \in A$ and $b \in B$ at random, $a+b$ takes each of the values $0, \ldots, 9$ with equal probability. Then one of $A$ or $B$ is singleton.
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TIFR Mathematics 2024 | Part A | Question: 18
For a positive integer $n$, let $a_{n}, b_{n}, c_{n}, d_{n}$ be the real numbers such that \[ \left(\begin{array}{ll} 1 & 1 \\ 1 & 0 \end{array}\right)^{n}=\left(\begin{array}{ll} a_{n} & b_{n} \\ c_{n} & ... the following numbers equals $\lim _{n \rightarrow \infty} a_{n} / b_{n}$ ? $1$ $e$ $3 / 2$ None of the remaining three options
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TIFR Mathematics 2024 | Part B | Question: 1
If $\text{G}$ is a group of order $361$, then $\text{G}$ has a normal subgroup $\text{H}$ such that $H \cong G / H$.
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TIFR Mathematics 2024 | Part B | Question: 2
There exists a metric space $\text{X}$ such that the number of open subsets of $\text{X}$ is exactly $2024$.
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TIFR Mathematics 2024 | Part B | Question: 3
The function $d: \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R}$ given by $d(x, y)=\left|e^{x}-e^{y}\right|$ defines a metric on $\mathbb{R}$, and $(\mathbb{R}, d)$ is a complete metric space.
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