AIEEE 2007 PYQ Mock Test

Let $A(h,k)$, $B(1,1)$ and $C(2,1)$ be the vertices of a right angled triangle with $AC$ as its hypotenuse. If the area of the triangle is $1$, then the set of values which $k$ can take is given by:

Let $P=(-1,0)$, $Q=(0,0)$ and $R=(3,3\sqrt{3})$ be three points. The equation of the bisector of the angle $PQR$ is:

If one of the lines of $m{y}^2+(1-m^2)xy-m{x}^2=0$ is a bisector of the angle between the lines $xy=0$, then $m$ is:

Let $F(x)=f(x)+f(1/x)$, where $f(x)={\int }_1^x\frac{{\log }_{e}t}{1+t}dt$. Then $F(e)$ equals:

Let $f:\mathbb{R}\to \mathbb{R}$ be a function defined by $f(x)=\min \{x+1,|x|+1\}$. Then which of the following is true?