TIFR-2015-Maths-A-2

makhdoom ghaya asked Dec 19, 2015 • edited Aug 17, 2020 by soujanyareddy13

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2 votes

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makhdoom ghaya asked Dec 19, 2015

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TIFR-2015-Maths-A-7
Let $f$ and $g$ be two functions from $[0, 1]$ to $[0, 1]$ with $f$ strictly increasing. Which of the following statements is always correct? If $g$ is continuous, then $f ∘ g$ is continuous If $f$ is continuous, then $f ∘ g$ is continuous If $f$ and $f ∘ g$ are continuous, then $g$ is continuous If $g$ and $f ∘ g$ are continuous, then $f$ is continuous

Let $f$ and $g$ be two functions from $[0, 1]$ to $[0, 1]$ with $f$ strictly increasing. Which of the following statements is always correct?If $g$ is continuous, then $f...

makhdoom ghaya

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makhdoom ghaya asked Dec 19, 2015

2 votes

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makhdoom ghaya asked Dec 21, 2015

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TIFR-2015-Maths-B-12
Let $X \subset \mathbb{R}$ and let $f,g : X \rightarrow X$ be a continuous functions such that $f(X)\cap g(X)=\emptyset$ and $f(X)\cup g(X)= X$. Which one of the following sets cannot be equal to $X$? $[0, 1]$ $(0, 1)$ $[0, 1)$ $\mathbb{R}$

Let $X \subset \mathbb{R}$ and let $f,g : X \rightarrow X$ be a continuous functions such that $f(X)\cap g(X)=\emptyset$ and $f(X)\cup g(X)= X$. Which one of the followin...

makhdoom ghaya

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makhdoom ghaya asked Dec 21, 2015

2 votes

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makhdoom ghaya asked Dec 21, 2015

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TIFR-2015-Maths-B-9
Let $f: \mathbb{R}\rightarrow\mathbb{R}$ be a continuous function and $A \subset \mathbb{R}$ be defined by $A=\left\{ y \in \mathbb{R}:y = \displaystyle \lim_{n \rightarrow \infty} f(x_{n}), \text {for some sequence} x_{n} \rightarrow +\infty\right\}$ Then the set A is necessarily. $A$ connected set $A$ compact set $A$ singleton set None of the above

Let $f: \mathbb{R}\rightarrow\mathbb{R}$ be a continuous function and $A \subset \mathbb{R}$ be defined by$A=\left\{ y \in \mathbb{R}:y = \displaystyle \lim_{n \rightarro...

makhdoom ghaya

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makhdoom ghaya asked Dec 21, 2015

4 votes

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makhdoom ghaya asked Dec 21, 2015

480 views

TIFR-2015-Maths-B-6
Let $f: [0, 1]\rightarrow \mathbb{R}$ be a fixed continuous function such that $f$ is differentiable on $(0, 1)$ and $f(0) = f(1) = 0$. Then the equation $f(x) = f' (x)$ admits. No solution $x \in (0, 1)$ More than one solution $x \in (0, 1)$ Exactly one solution $x \in (0, 1)$ At least one solution $x \in (0, 1)$

Let $f: [0, 1]\rightarrow \mathbb{R}$ be a fixed continuous function such that $f$ is differentiable on $(0, 1)$ and $f(0) = f(1) = 0$. Then the equation $f(x) = f' (x)$ ...

makhdoom ghaya

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makhdoom ghaya asked Dec 21, 2015

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TIFR-2015-Maths-A-2

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