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Recent questions tagged tifrmaths2017

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32
TIFR-2017-Maths-A: 22
True/False Question : Let $P$ be a monic, non-zero, polynomial of even degree, and $K>0$. Then the function $P\left ( x \right )-K e^{x}$ has a real zero.
True/False Question :Let $P$ be a monic, non-zero, polynomial of even degree, and $K>0$. Then the function $P\left ( x \right )-K e^{x}$ has a real zero.
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33
TIFR-2017-Maths-A: 23
True/False Question : A $p$ -Sylow subgroup of the underlying additive group of a finite commutative ring $R$ is an ideal in $R$.
True/False Question : A $p$ -Sylow subgroup of the underlying additive group of a finite commutative ring $R$ is an ideal in $R$.
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34
TIFR-2017-Maths-A: 24
True/False Question : Suppose $A$ is an $n \times n$ -real matrix, all whose eigenvalues have absolute value less than $1$. Then for any $v \in \mathbb{R}^{n} ,\left \| Av \right \|\leq \left \| v \right \|.$
True/False Question :Suppose $A$ is an $n \times n$ -real matrix, all whose eigenvalues have absolute value less than $1$. Then for any $v \in \mathbb{R}^{n} ,\left \| Av...
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35
TIFR-2017-Maths-A: 25
True/False Question : For any $x \in \mathbb{R}$, the sequence $\left \{ a_{n} \right \}$, where $a_{1}=x$ and $a_{n+1}=cos\left ( a_{n} \right )$ for all $n$, is convergent.
True/False Question :For any $x \in \mathbb{R}$, the sequence $\left \{ a_{n} \right \}$, where $a_{1}=x$ and $a_{n+1}=cos\left ( a_{n} \right )$ for all $n$, is converge...
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36
TIFR-2017-Maths-A: 26
True/False Question : Suppose $A_{1},\cdots ,A_{m}$ are distinct $n\times n$ real matrices such that $A_{i}A_{j}=0$ for all $i\neq j$. Then $m\leq n.$
True/False Question :Suppose $A_{1},\cdots ,A_{m}$ are distinct $n\times n$ real matrices such that $A_{i}A_{j}=0$ for all $i\neq j$. Then $m\leq n.$
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37
TIFR-2017-Maths-A: 27
True/False Question : In the symmetric group $S_{n}$ any two elements of the same order are conjugate.
True/False Question :In the symmetric group $S_{n}$ any two elements of the same order are conjugate.
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38
TIFR-2017-Maths-A: 28
True/False Question : If a particle moving on the Euclidean line traverses distance $1$ in time $1$ starting and ending at rest, then at some time $t \in \left [ 0,1 \right ]$, at absolute value of its acceleration should be at least $4$.
True/False Question :If a particle moving on the Euclidean line traverses distance $1$ in time $1$ starting and ending at rest, then at some time $t \in \left [ 0,1 \righ...
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39
TIFR-2017-Maths-A: 29
True/False Question : Let $y\left ( t \right )$ be a real valued function defined on the real line such that ${y}'=y \left ( 1-y \right )$, with $y\left ( 0\right ) \in \left [ 0,1 \right ]$. Then $\lim_{t\rightarrow \infty }y\left ( t \right )=1$ .
True/False Question :Let $y\left ( t \right )$ be a real valued function defined on the real line such that ${y}'=y \left ( 1-y \right )$, with $y\left ( 0\right ) \in \l...
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40
TIFR-2017-Maths-A: 30
True/False Question : The matrices $\begin{pmatrix} x &0 \\ 0 & y \end{pmatrix} and \begin{pmatrix} x &1 \\ 0 & y \end{pmatrix}, x\neq y,$ for any $x,y \in \mathbb{R}$ are conjugate in $M_{2}\left ( \mathbb{R} \right )$ .
True/False Question :The matrices $$\begin{pmatrix} x &0 \\ 0 & y \end{pmatrix} and \begin{pmatrix} x &1 \\ 0 & y \end{pmatrix}, x\neq y,$$for any $x,y \in \mathbb{R}$ ar...
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