AIEEE 2007 PYQ Mock Test

The half-life period of a radioactive element $X$ is same as the mean lifetime of another radioactive element $Y$. Initially they have the same number of atoms. Then:

A Carnot engine, having an efficiency of $\eta =1/10$ as a heat engine, is used as a refrigerator. If the work done on the system is $10\text{J}$, the amount of energy absorbed from the reservoir at lower temperature is:

Carbon, silicon and germanium have four valence electrons each. At room temperature which one of the following statements is most appropriate?

A charged particle with charge $q$ enters a region of constant, uniform and mutually orthogonal fields $\vec{E}$ and $\vec{B}$ with a velocity $\vec{v}$ perpendicular to both $\vec{E}$ and $\vec{B}$, and comes out without any change in magnitude or direction of $\vec{v}$. Then:

The potential at a point $x$ (measured in $\mu \text{m}$) due to some charges situated on the $x$ -axis is given by $V(x)=20/(x^2-4)$ Volts. The electric field $E$ at $x=4\mu \text{m}$ is given by: