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TIFR2014MathsA2
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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
$\lim_{x \rightarrow \infty} f(x)$ exists.
tifrmaths2014
continuity
asked
Dec 10, 2015
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Set Theory & Algebra
by
makhdoom ghaya
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TIFR2014MathsA6
Let $f:\left[0, 1\right]\rightarrow \mathbb{R}$ be a continuous function. Which of the following statements is always true? $\int_{0}^{1} f^{2}(x) \text{d}x = (\int_{0}^{1} f(x) \text{d}x)^{2}$ $\int_{0}^{1} f^{2}(x) \text{d}x \leq (\int_{0}^{1} f( ... ) \text{d}x)^{2}$ $\int_{0}^{1} f^{2}(x) \text{d}x ≰ (\int_{0}^{1} f(x) \text{d}x)^{2}$
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Dec 14, 2015
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tifrmaths2014
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TIFR2014MathsA4
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 $x = 0$ $f$ ... is uniformly continuous on $[0, \infty)$ $f$ is not uniformly continuous on $[0, \infty)$, but uniformly continuous on $(0, \infty)$.
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Dec 10, 2015
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tifrmaths2014
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TIFR2014MathsB2
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 onetoone None of the above.
asked
Dec 17, 2015
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tifrmaths2014
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Hi Guys, I think this is not correct. ISRO ...
NIELIT specifically mailed that they decided ...
is there any chances of changing the exam date??
ISRO and NIELIT Exam on the same day i.e 17th ...
greatly said @papesh sir
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