Recent questions tagged jee(main)-2019

The value of $\int\limits_0^\pi|\cos x|^3 \mathrm dx$ (1) 2/3 (2) 0 (3) −4/3 (4) 4/3

$\lim\limits_{y\to0} {\sqrt{1+\sqrt{1+y^4}}-\sqrt2\over y^4}$ (1) exists and equals $1\over4\sqrt2$ (2) does not exist (3) exists and equals $1\over2\sqrt2$ (4) exists and equals $1\over2\sqrt2(\sqrt2+1)$

Let $f:R\to R$ be a function defined as : $f(x)=\begin{cases}5,&\text{if}&x\leq1\\a+bx,&\text{if}&1<x<3\\b+5x,&\text{if}&3\leq x<5\\30,&\text{if}&x\geq5\end{cases}$ Then, $f$ is : (1) continuous if $a=5$ and $b=5$ (2) continuous if $a=-5$ and $b=10$ (3) ...