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Recent questions tagged true-false
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91
TIFR-2013-Maths-A: 1
True/False Question : Every countable group $G$ has only countably many distinct subgroups.
True/False Question :Every countable group $G$ has only countably many distinct subgroups.
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2013-Maths-A: 2
True/False Question : Any automorphism of the group $\mathbb{Q}$ under addition is of the form $x\mapsto qx$ for some $q\in \mathbb{Q}$.
True/False Question :Any automorphism of the group $\mathbb{Q}$ under addition is of the form $x\mapsto qx$ for some $q\in \mathbb{Q}$.
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2013-Maths-A: 3
True/False Question : The equation $x^{3}+3x-4=0$ has exactly one real root.
True/False Question :The equation $x^{3}+3x-4=0$ has exactly one real root.
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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94
TIFR-2013-Maths-A: 4
True/False Question : The equation $x^{3}+10x^{2}-100x+1729=0$ has at least one complex root $\alpha$ such that $\left | \alpha \right |> 12.$
True/False Question :The equation $x^{3}+10x^{2}-100x+1729=0$ has at least one complex root $\alpha$ such that $\left | \alpha \right | 12.$
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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95
TIFR-2013-Maths-A: 5
True/False Question : All non-trivial proper subgroups of $\left ( \mathbb{R},+ \right )$ are cyclic.
True/False Question :All non-trivial proper subgroups of $\left ( \mathbb{R},+ \right )$ are cyclic.
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2013-Maths-A: 6
True/False Question : Every inifinte abelian group has at least one element of infinite order.
True/False Question :Every inifinte abelian group has at least one element of infinite order.
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2013-Maths-A: 7
True/False Question : If $A$ band $B$ are similar matrices then every eigenvector of $A$ is an eigenvector of $B$.
True/False Question :If $A$ band $B$ are similar matrices then every eigenvector of $A$ is an eigenvector of $B$.
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2013-Maths-A: 8
True/False Question : If a real square matrix $A$ is similar to a diagonal matrix and satisfies $A^{n}=0$ for some $n$, then $A$ must be the zero matrix.
True/False Question :If a real square matrix $A$ is similar to a diagonal matrix and satisfies $A^{n}=0$ for some $n$, then $A$ must be the zero matrix.
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2013-Maths-A: 9
True/False Question : There is an element of order $51$ in the multiplicative group $\left ( \mathbb{Z}/103\mathbb{Z} \right )^{*}$.
True/False Question :There is an element of order $51$ in the multiplicative group $\left ( \mathbb{Z}/103\mathbb{Z} \right )^{*}$.
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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100
TIFR-2013-Maths-A: 10
True/False Question : Any normal subgroup of order $2$ is contained in the center of the group.
True/False Question :Any normal subgroup of order $2$ is contained in the center of the group.
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 1
True/False Question : Let $f:\left [ 0,1 \right ]\rightarrow \mathbb{R}$ be a continuous function such that $f\left ( x \right )\geq x^{3}$ for all $x \in \left [ 0,1 \right ]$ with $\int_{0}^{1}f\left ( x \right )dx=\frac{1}{4}$. Then $f\left ( x \right )=x^{3}$ for all $x \in \mathbb{R}$.
True/False Question :Let $f:\left [ 0,1 \right ]\rightarrow \mathbb{R}$ be a continuous function such that $f\left ( x \right )\geq x^{3}$ for all $x \in \left [ 0,1 \rig...
soujanyareddy13
120
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 2
True/False Question : Suppose $a, b, c$ are positive real numbers such that $\left ( 1+a+b+c \right )\left ( 1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \right )=16.$ Then $a+b+c=3.$
True/False Question :Suppose $a, b, c$ are positive real numbers such that$$\left ( 1+a+b+c \right )\left ( 1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \right )=16.$$Then $a+b+...
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 3
True/False Question : There exists a function $f:\mathbb{R} \rightarrow \mathbb{R}$ satisfying, $f\left ( -1 \right )=-1, f(1)=1$ and $\left | f\left ( x \right )-f\left ( y \right )\left | \leq \right |x-y \right |^{\frac{3}{2}},$ for all $x,y \in \mathbb{R}.$
True/False Question :There exists a function $f:\mathbb{R} \rightarrow \mathbb{R}$ satisfying,$f\left ( -1 \right )=-1, f(1)=1$ and $\left | f\left ( x \right )-f\left ( ...
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 4
True/Flase Question : Over the real line, $\underset{x\rightarrow \infty }{lim}\: log\left ( 1+\sqrt{4+x} -\sqrt{1+x}\right )=log\left ( 2 \right ).$
True/Flase Question :Over the real line,$$\underset{x\rightarrow \infty }{lim}\: log\left ( 1+\sqrt{4+x} -\sqrt{1+x}\right )=log\left ( 2 \right ).$$
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 5
True/False Question : Suppose $f$ is a continuously differentiable function on $\mathbb{R}$ such that $f\left ( x \right )\rightarrow 1$ and ${f}'\left ( x \right )\rightarrow b$ as $x\rightarrow \infty$. Then $b=1.$
True/False Question :Suppose $f$ is a continuously differentiable function on $\mathbb{R}$ such that $f\left ( x \right )\rightarrow 1$ and ${f}'\left ( x \right )\right...
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 6
True/False Question : If $f:\mathbb{R}\rightarrow \mathbb{R}$ is differentiable and bijective, then $f^{-1}$ is also differentiable.
True/False Question :If $f:\mathbb{R}\rightarrow \mathbb{R}$ is differentiable and bijective, then $f^{-1}$ is also differentiable.
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 7
True/False Question : Let $H_{1},H_{2},H_{3},H_{4}$ be four hyperplanes in $\mathbb{R}^{3}$. The maximum possible number of connected components of $\mathbb{R}^{3}-\left (H_{1}\cup H_{2}\cup H_{3}\cup H_{4} \right )$ is $14.$
True/False Question :Let $H_{1},H_{2},H_{3},H_{4}$ be four hyperplanes in $\mathbb{R}^{3}$. The maximum possible number of connected components of $\mathbb{R}^{3}-\left (...
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 8
True/False Question : Let $n\geq 2$ be a natural number. Let $S$ be the set of all $n\times n$ real matrices whose entries are only $0,1$ or $2$. Then the average determinant of a matrix in $S$ is greater than or equal to $1$.
True/False Question :Let $n\geq 2$ be a natural number. Let $S$ be the set of all $n\times n$ real matrices whose entries are only $0,1$ or $2$. Then the average determin...
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 9
True/False Question : For any metric space $\left ( X,d \right )$ with $X$ finite, there exists an isometric embedding $f:X\rightarrow \mathbb{R}^{4}$.
True/False Question :For any metric space $\left ( X,d \right )$ with $X$ finite, there exists an isometric embedding $f:X\rightarrow \mathbb{R}^{4}$.
soujanyareddy13
116
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 10
True/False Question : There exists a non-negative continuous function $f:\left [ 0,1 \right ]\rightarrow \mathbb{R}$ such that $\int_{0}^{1}f^{n}dx\rightarrow 2$ as $n\rightarrow \infty.$
True/False Question :There exists a non-negative continuous function $f:\left [ 0,1 \right ]\rightarrow \mathbb{R}$ such that $\int_{0}^{1}f^{n}dx\rightarrow 2$ as $n\rig...
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 11
True/False Question : There exists a subset $A$ of $\mathbb{N}$ with exactly five elements such that the sum of any three elements of $A$ is a prime number.
True/False Question :There exists a subset $A$ of $\mathbb{N}$ with exactly five elements such that the sum of any three elements of $A$ is a prime number.
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 12
True/False Question : There exists a finite abelian group $G$ containing exactly $60$ elements of order $2$.
True/False Question :There exists a finite abelian group $G$ containing exactly $60$ elements of order $2$.
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 13
True/False Question : Let $\alpha ,\beta$ be complex numbers with non-positive real parts. Then $\left | e^{\alpha } -e^{\beta }\right |\leq \left | \alpha -\beta \right |.$
True/False Question :Let $\alpha ,\beta$ be complex numbers with non-positive real parts. Then $$\left | e^{\alpha } -e^{\beta }\right |\leq \left | \alpha -\beta \right ...
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 14
True/False Question : Every $2 \times 2$ matrix over $\mathbb{C}$ is a square of some matrix.
True/False Question :Every $2 \times 2$ matrix over $\mathbb{C}$ is a square of some matrix.
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 15
True/False Question : Under the projection map $\mathbb{R}^{2}\rightarrow \mathbb{R}$ sending $\left ( x,y \right )$ to $x$, the image of any closed set is closed.
True/False Question :Under the projection map $\mathbb{R}^{2}\rightarrow \mathbb{R}$ sending $\left ( x,y \right )$ to $x$, the image of any closed set is closed.
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 16
True/False Question : The number of ways a $2\times 8$ rectangle can be tiled with rectangular tiles of size $2\times 1$ is $34$.
True/False Question :The number of ways a $2\times 8$ rectangle can be tiled with rectangular tiles of size $2\times 1$ is $34$.
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 17
True/False Question : Over the real line, $\underset{x\rightarrow \infty }{lim}\left ( \frac{x+log\:9}{x-log\:9} \right )^{x}=81.$
True/False Question :Over the real line, $$\underset{x\rightarrow \infty }{lim}\left ( \frac{x+log\:9}{x-log\:9} \right )^{x}=81.$$
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 18
True/False Question : Let $f:[0,\infty )\rightarrow \mathbb{R}$ be a continuous function with $lim_{x\rightarrow \infty }f\left ( x \right )= 0.$ Then $f$ has a maximum value in $[0,\infty )$
True/False Question :Let $f:[0,\infty )\rightarrow \mathbb{R}$ be a continuous function with $lim_{x\rightarrow \infty }f\left ( x \right )= 0.$ Then $f$ has a maximum va...
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 19
True/False Question : Given a continuous function $f:\mathbb{Q}\rightarrow \mathbb{Q}$, there exists a continuous function $g:\mathbb{R}\rightarrow \mathbb{R}$ such that the restriction of $g$ to $\mathbb{Q}$ is $f$.
True/False Question :Given a continuous function $f:\mathbb{Q}\rightarrow \mathbb{Q}$, there exists a continuous function $g:\mathbb{R}\rightarrow \mathbb{R}$ such that t...
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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TIFR-2017-Maths-A: 20
True/False Question : For all positive integers $m$ and $n$, if $A$ is an $m \times n$ real matrix, and $B$ is an $n \times m$ real matrix such that $AB = I$, then $BA=I$.
True/False Question :For all positive integers $m$ and $n$, if $A$ is an $m \times n$ real matrix, and $B$ is an $n \times m$ real matrix such that $AB ...
soujanyareddy13
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soujanyareddy13
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Aug 30, 2020
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