AIEEE 2013 PYQ Mock Test

If $x,y,z$ are in A.P. and ${\tan }^{-1}x,{\tan }^{-1}y$ and ${\tan }^{-1}z$ are also in A.P., then:

If $\int f(x)dx=\Psi (x)$, then $\int x^{5}f(x^3)dx$ is equal to:

The equation of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$, and having centre at $(0,3)$ is:

The $x$ -coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $(0,1)$, $(1,1)$ and $(1,0)$ is:

The intercepts on $x$ -axis made by tangents to the curve $y={\int }_0^x|t|dt$, $x\in \mathbb{R}$, which are parallel to the line $y=2x$, are equal to: