JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Continuity and Differentiability

Let $\mathbb{R}$ denote the set of all real numbers. Let $f:\mathbb{R}\to \mathbb{R}$ be an arbitrary function and let $g:\mathbb{R}\to \mathbb{R}$ be the function defined by

Then which of the follo …

Consider the function $f:\left(-\frac{\pi }{2},\frac{\pi }{2}\right)\to (-\infty ,\infty )$ defined by

where [x sin x] is the greatest integer less than or equal to x …

For a real number $\alpha$, let $[\alpha ]$ denote the greatest integer less than or equal to $\alpha$. For a finite set S , let $|\mathrm{S}|$ denote the number of elements in the set S .

Consider the functions $f:(-3,3)\to (-\infty ,\infty )$ and …

Let $\mathbb{R}$ denote the set of all real numbers. For a real number $x$, let $[x]$ denote the greatest integer less than or equal to $x$. Let $n$ denote a natural number.
Match each entry in List-I to the correct entry in List-II and choose the correct option.

| | L …

Let $x_0$ be the real number such that $e^{x_0}+x_0=0$. For a given real number $\alpha$, define

for all real numbers $x$.
Then which one of the following statements is TRUE?

Let $\mathbb{R}$ denote the set of all real numbers. Let $f:\mathbb{R}\to \mathbb{R}$ and $g:\mathbb{R}\to (0,4)$ be functions defined by

Define the composite function …