AIEEE 2013 PYQ Mock Test

The circle passing through $(1,-2)$ and touching the axis of $x$ at $(3,0)$ also passes through the point:

$\text{ABCD}$ is a trapezium such that $\text{AB}$ and $\text{CD}$ are parallel and $\text{BC}\perp \text{CD}$. If $\angle \text{ADB}=\theta$, $\text{BC}=p$ and $\text{CD}=q$, then $\text{AB}$ is equal to:

Given: A circle, $2x^2+2y^2=5$ and a parabola, $y^2=4\sqrt{5}x$.Statement - I: An equation of a common tangent to these curves is $y=x+\sqrt{5}$.Statement - II: If the line $y=mx+\frac{\sqrt{5}}{m}$ ($m\ne 0$) is their common tangent, then $m$ satisfies $m^4-3m^2+2=0$.

A ray of light along $x+\sqrt{3}y=\sqrt{3}$ gets reflected upon reaching $x$ -axis, the equation of the reflected rays is:

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?