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3 votes
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81
Gate 2011
How to calculate fraction power. (40)^1.2
How to calculate fraction power.(40)^1.2
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2 votes
0 answers
86
Gate Overflow site issue
Why Gate Overflow Answer Writing template changed ? Previously there was separate Text editor section where we could add equation, different different colours and fonts and mathematical formulas. But now in the new template those are not there.
Why Gate Overflow Answer Writing template changed ? Previously there was separate Text editor section where we could add equation, different different colours and fonts a...
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2 votes
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87
#c #cprogram
#include<stdio.h> int main() { int i; for(i =-1;i<sizeof(i);i++) printf("%d",i); } The output of the code is didn't enter to the loop and prints nothing. Can anyone explain
#include<stdio.h>int main() {int i;for(i =-1;i<sizeof(i);i++)printf("%d",i);}The output of the code is didn't enter to the loop and prints nothing.Can anyone explain
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2 votes
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89
TIFR Mathematics 2023 | Part B | Question: 2
Answer whether the following statements are True or False. Suppose $f, g: \mathbb{R} \rightarrow \mathbb{R}$ are continuous functions such that $f^{2}+g^{2}$ is uniformly continuous. Then at least one of the two functions $f$ and $g$ is uniformly continuous.
Answer whether the following statements are True or False.Suppose $f, g: \mathbb{R} \rightarrow \mathbb{R}$ are continuous functions such that $f^{2}+g^{2}$ is uniformly ...
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2 votes
1 answer
92
TIFR Mathematics 2023 | Part B | Question: 5
Answer whether the following statements are True or False. Let $v_{1}, v_{2}, w_{1}, w_{2}$ be nonzero vectors in $\mathbb{R}^{2}$. Then there exists a $2 \times 2$ real matrix $A$ such that $A v_{1}=v_{2}$ and $A w_{1}=w_{2}.$
Answer whether the following statements are True or False.Let $v_{1}, v_{2}, w_{1}, w_{2}$ be nonzero vectors in $\mathbb{R}^{2}$. Then there exists a $2 \times 2$ real m...
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2 votes
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94
TIFR Mathematics 2023 | Part B | Question: 7
Answer whether the following statements are True or False. Given any monic polynomial $f(x) \in \mathbb{R}[x]$ of degree $n,$ there exists a matrix $A \in \mathrm{M}_{n}(\mathbb{R})$ such that its characteristic polynomial equals $f$.
Answer whether the following statements are True or False.Given any monic polynomial $f(x) \in \mathbb{R}[x]$ of degree $n,$ there exists a matrix $A \in \mathrm{M}_{n}(\...
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2 votes
1 answer
95
TIFR Mathematics 2023 | Part B | Question: 8
Answer whether the following statements are True or False. If $A \in \mathrm{M}_{4}(\mathbb{Q})$ is such that its characteristic polynomial equals $x^{4}+1,$ then $A$ is diagonalizable in $\mathrm{M}_{4}(\mathbb{C})$.
Answer whether the following statements are True or False.If $A \in \mathrm{M}_{4}(\mathbb{Q})$ is such that its characteristic polynomial equals $x^{4}+1,$ then $A$ is d...
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2 votes
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96
TIFR Mathematics 2023 | Part B | Question: 9
Answer whether the following statements are True or False. If $A \in \mathrm{M}_{n}(\mathbb{R})$ is such that $A B=B A$ for all invertible matrices $B \in \mathrm{M}_{n}(\mathbb{R})$, then $A=\lambda \cdot \text{Id}$ for some $\lambda \in \mathbb{R}.$
Answer whether the following statements are True or False.If $A \in \mathrm{M}_{n}(\mathbb{R})$ is such that $A B=B A$ for all invertible matrices $B \in \mathrm{M}_{n}(\...
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2 votes
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97
TIFR Mathematics 2023 | Part B | Question: 10
Answer whether the following statements are True or False. There exists a homeomorphism $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $f(2 x)=3 f(x)$ for all $x \in \mathbb{R}.$
Answer whether the following statements are True or False.There exists a homeomorphism $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $f(2 x)=3 f(x)$ for all $x \in \ma...
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2 votes
0 answers
98
TIFR Mathematics 2023 | Part B | Question: 11
Answer whether the following statements are True or False. There exists a continuous bijection from $[0,1] \times[0,1]$ to $\left\{(x, y) \in \mathbb{R}^{2} \mid x^{2}+y^{2} \leq 1\right\}$, which is not a homeomorphism.
Answer whether the following statements are True or False.There exists a continuous bijection from $[0,1] \times[0,1]$ to $\left\{(x, y) \in \mathbb{R}^{2} \mid x^{2}+y^{...
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2 votes
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100
TIFR Mathematics 2023 | Part B | Question: 13
Answer whether the following statements are True or False. A connected metric space with at least two points is uncountable.
Answer whether the following statements are True or False.A connected metric space with at least two points is uncountable.
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