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Recent questions tagged tifrmaths2018

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31
TIFR-2018-Maths-A: 16
True/False Question : Let $G$ be a finite group with a normal subgroup $H$ such that $G/H$ has order $7$. Then $G\cong H\times G/H$.
True/False Question :Let $G$ be a finite group with a normal subgroup $H$ such that $G/H$ has order $7$. Then $G\cong H\times G/H$.
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32
TIFR-2018-Maths-A: 17
True/False Question : The multiplicative group $\mathbb{F}_{7}^{\times }$ is isomorphic to a subgroup of the multiplicative group $\mathbb{F}_{31}^{\times }$.
True/False Question :The multiplicative group $\mathbb{F}_{7}^{\times }$ is isomorphic to a subgroup of the multiplicative group $\mathbb{F}_{31}^{\times }$.
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33
TIFR-2018-Maths-A: 18
True/False Question : Any linear transformation $A:\mathbb{R}^{4}\rightarrow \mathbb{R}^{4}$ has a proper non-zero invariant subspace.
True/False Question :Any linear transformation $A:\mathbb{R}^{4}\rightarrow \mathbb{R}^{4}$ has a proper non-zero invariant subspace.
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34
TIFR-2018-Maths-A: 19
True/False Question : Let $A, B \in M_{n}\left ( \mathbb{R} \right )$ be such that$A+B=AB$. Then $AB=BA$.
True/False Question :Let $A, B \in M_{n}\left ( \mathbb{R} \right )$ be such that$A+B=AB$. Then $AB=BA$.
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35
TIFR-2018-Maths-A: 20
True/False Question : Let $A\in M_{n}\left ( \mathbb{R} \right )$ be upper triangular with all diagonal entries $1$ such that $A\neq I$. Then $A$ is not diagonalizable.
True/False Question :Let $A\in M_{n}\left ( \mathbb{R} \right )$ be upper triangular with all diagonal entries $1$ such that $A\neq I$. Then $A$ is not diagonalizable.
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36
TIFR-2018-Maths-A: 21
True/False Question : A countable group can have only countably many distinct subgroups.
True/False Question :A countable group can have only countably many distinct subgroups.
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37
TIFR-2018-Maths-A: 22
True/False Question : There exists a continuous surjection from $\mathbb{R}^{3}-S^{2}$ to $\mathbb{R}^{2}-\left \{ \left ( 0,0 \right ) \right \}$ (here $S^{2}\subset \mathbb{R}^{3}$ denotes the unit sphere defined by the equation $x^{2}+y^{2}+z^{2}=1$).
True/False Question :There exists a continuous surjection from $\mathbb{R}^{3}-S^{2}$ to $\mathbb{R}^{2}-\left \{ \left ( 0,0 \right ) \right \}$ (here $S^{2}\subset \mat...
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38
TIFR-2018-Maths-A: 23
True/False Question : The permutation group $S_{10}$ has an element of order $30$.
True/False Question :The permutation group $S_{10}$ has an element of order $30$.
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39
TIFR-2018-Maths-A: 24
True/False Question : Let $G$ be a finite group and $g \in G$ an element of even order. Then we can colour the elements of $G$ with two colours in such a way that $x$ and $gx$ have different colours for each $x \in G$.
True/False Question :Let $G$ be a finite group and $g \in G$ an element of even order. Then we can colour the elements of $G$ with two colours in such a way that $x$ and...
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40
TIFR-2018-Maths-A: 25
True/False Question : Let $f(x)$ and $g(x)$ be uniformly continuous functions from $\mathbb{R}$ to $\mathbb{R}$. Then their pointwise product $f(x)g(x)$ is uniformly continuous.
True/False Question :Let $f(x)$ and $g(x)$ be uniformly continuous functions from $\mathbb{R}$ to $\mathbb{R}$. Then their pointwise product $f(x)g(x)$ is uniformly conti...
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