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Search results for tifrmaths2014
1
votes
0
answers
21
TIFR-2014-Maths-A-12
There exists a map $f : \mathbb{Z} \rightarrow \mathbb{Q}$ such that $f$ Is bijective and increasing Is onto and decreasing Is bijective and satisfies $f(n) \geq 0$ if $n \leq 0$ Has uncountable image
There exists a map $f : \mathbb{Z} \rightarrow \mathbb{Q}$ such that $f$ Is bijective and increasing Is onto and decreasing Is bijective and satisfies $f(n) \geq 0$ if $n...
makhdoom ghaya
314
views
makhdoom ghaya
asked
Dec 17, 2015
Set Theory & Algebra
tifrmaths2014
functions
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–
1
votes
0
answers
22
TIFR-2014-Maths-A-13
Let $S$ be the set of all tuples $(x, y)$ with $x, y$ non-negative real numbers satisfying $x + y = 2n$, for a fixed $n \in \mathbb{N}$. Then the supremum value of $x^{2}y^{2}(x^{2}+y^{2})$ on the set $S$ is $3n^{6}$ $2n^{6}$ $4n^{6}$ $n^{6}$
Let $S$ be the set of all tuples $(x, y)$ with $x, y$ non-negative real numbers satisfying $x + y = 2n$, for a fixed $n \in \mathbb{N}$. Then the supremum value of$x^{2}y...
makhdoom ghaya
313
views
makhdoom ghaya
asked
Dec 17, 2015
Set Theory & Algebra
tifrmaths2014
set-theory&algebra
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–
1
votes
0
answers
23
TIFR-2014-Maths-B-8
Let $X$ be a non-empty topological space such that every function $f : X \rightarrow \mathbb{R}$ is continuous. Then $X$ has the discrete topology $X$ has the indiscrete topology $X$ is compact $X$ is not connected
Let $X$ be a non-empty topological space such that every function $f : X \rightarrow \mathbb{R}$ is continuous. Then $X$ has the discrete topology $X$ has the indiscrete ...
makhdoom ghaya
307
views
makhdoom ghaya
asked
Dec 17, 2015
Linear Algebra
tifrmaths2014
vector-space
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1
votes
0
answers
24
TIFR-2014-Maths-A-20
Let $C$ denote the cube $\left[-1, 1\right]^{3} \subset \mathbb{R}^{3}$. How many rotations are there in $\mathbb{R}^{3}$ which take $C$ to itself? 6 12 18 24
Let $C$ denote the cube $\left[-1, 1\right]^{3} \subset \mathbb{R}^{3}$. How many rotations are there in $\mathbb{R}^{3}$ which take $C$ to itself? 6 12 18 24
makhdoom ghaya
305
views
makhdoom ghaya
asked
Dec 17, 2015
Quantitative Aptitude
tifrmaths2014
+
–
1
votes
0
answers
25
TIFR-2014-Maths-A-7
Let $f_{n}(x)$, for $n \geq 1$, be a sequence of continuous non negative functions on $[0, 1]$ such that $\displaystyle \lim_{n \rightarrow \infty} \int_{0}^{1} f_{n}(x) \text{d}x$ ... $0$ point-wise $f_{n}$ will converge point-wise and the limit may be non-zero $f_{n}$ is not guaranteed to have a point-wise limit
Let $f_{n}(x)$, for $n \geq 1$, be a sequence of continuous non negative functions on $[0, 1]$ such that $\displaystyle \lim_{n \rightarrow \infty} \int_{0}^{1} f_{n}(x) ...
makhdoom ghaya
325
views
makhdoom ghaya
asked
Dec 14, 2015
Set Theory & Algebra
tifrmaths2014
convergence
non-gate
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1
votes
0
answers
26
TIFR-2014-Maths-B-9
Let $f : X \rightarrow Y$ be a continuous map between metric spaces. Then $f(X)$ is a complete subset of $Y$ if The space $X$ is compact The space $Y$ is compact The space $X$ is complete The space $Y$ is complete
Let $f : X \rightarrow Y$ be a continuous map between metric spaces. Then $f(X)$ is a complete subset of $Y$ if The space $X$ is compact The space $Y$ is compact The spac...
makhdoom ghaya
317
views
makhdoom ghaya
asked
Dec 17, 2015
Linear Algebra
tifrmaths2014
vector-space
non-gate
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1
votes
0
answers
27
TIFR-2014-Maths-A-2
Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous bounded function, then: $f$ has to be uniformly continuous There exists an $x \in \mathbb{R}$ such that $f(x) = x$ $f$ cannot be increasing $\displaystyle \lim_{x \rightarrow \infty} f(x)$ exists
Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous bounded function, then: $f$ has to be uniformly continuous There exists an $x \in \mathbb{R}$ such that $f(x) ...
makhdoom ghaya
358
views
makhdoom ghaya
asked
Dec 10, 2015
Set Theory & Algebra
tifrmaths2014
continuity
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1
votes
0
answers
28
TIFR-2014-Maths-B-7
$X$ is a topological space of infinite cardinality which is homeomorphic to $X \times X$. Then $X$ is not connected $X$ is not compact $X$ is not homeomorphic to a subset of $R$ None of the above
$X$ is a topological space of infinite cardinality which is homeomorphic to $X \times X$. Then $X$ is not connected $X$ is not compact $X$ is not homeomorphic to a subset...
makhdoom ghaya
266
views
makhdoom ghaya
asked
Dec 17, 2015
Linear Algebra
tifrmaths2014
vector-space
non-gate
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–
1
votes
0
answers
29
TIFR-2014-Maths-B-2
Let $f:\mathbb{R}^{2}\rightarrow \mathbb{R}$ be a continuous map such that $f(x) = 0$ for only finitely many values of $x$. Which of the following is true? Either $f(x)\leq 0$ for all $x$, or, $f(x) \geq 0$ for all $x$ The map $f$ is onto The map $f$ is one-to-one None of the above
Let $f:\mathbb{R}^{2}\rightarrow \mathbb{R}$ be a continuous map such that $f(x) = 0$ for only finitely many values of $x$. Which of the following is true?Either $f(x)\le...
makhdoom ghaya
235
views
makhdoom ghaya
asked
Dec 17, 2015
Set Theory & Algebra
tifrmaths2014
functions
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–
1
votes
0
answers
30
TIFR-2014-Maths-A-4
Let $f$ be the real valued function on $[0, \infty)$ defined by $f(x) = \begin{cases} x^{\frac{2}{3}}\log x& \text {for x > 0} \\ 0& \text{if x=0 } \end{cases}$ Then $f$ is discontinuous at $x = 0$ $f$ ... $f$ is uniformly continuous on $[0, \infty)$ $f$ is not uniformly continuous on $[0, \infty)$, but uniformly continuous on $(0, \infty)$
Let $f$ be the real valued function on $[0, \infty)$ defined by$f(x)= \begin{cases} x^{\frac{2}{3}}\log x& \text {for x 0} \\ 0& \text{if x=0 } \end{cases}$Then$f$ is d...
makhdoom ghaya
382
views
makhdoom ghaya
asked
Dec 10, 2015
Calculus
tifrmaths2014
continuity
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