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TIFR-2018-Maths-B: 12

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soujanyareddy13 asked Aug 29, 2020
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TIFR-2018-Maths-A: 12
True/False Question : If $A \in M_{n}\left ( \mathbb{R} \right )$ ( with $n\geq 2$) has rank $1$, then the minimal polynomial of $A$ has degree $2$.
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TIFR-2018-Maths-B: 1
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soujanyareddy13 asked Aug 30, 2020
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soujanyareddy13 asked Aug 30, 2020
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TIFR-2018-Maths-B: 3
Let $f:\mathbb{R}\rightarrow \mathbb{R}$ ... continuous everywhere except at $0$ $f$ is continuous only at the irrationals $f$ is continuous only at the non-zero rationals $f$ is not continuous anywhere
Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be defined as follows:$$f\left ( x \right )=\left\{\begin{matrix} 1, & if &x=0 \\ 0,&if &x \in \mathbb{R}\setminus \mathbb{Q}, \:...
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