AIEEE 2010 PYQ Mock Test

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ }$ with each other. When suspended in a liquid of density $0.8{\text{g cm}}^{-3}$, the angle remains the same. If density of the material of the sphere is $16{\text{g cm}}^{-3}$, the dielectric constant of the liquid is:

Two conductors have the same resistance at $0^{\circ }\text{C}$ but their temperature coefficients of resistance are ${\alpha }_1$ and ${\alpha }_2$. The respective temperature coefficients of their series and parallel combinations are nearly:

A point $P$ moves in counter-clockwise direction on a circular path of radius $20\text{m}$. The movement of '$P$ ' is such that it sweeps out a length $s=t^3+5$, where $s$ is in metres and $t$ is in seconds. The acceleration of '$P$ ' when $t=2\text{s}$ is nearly:

Two fixed frictionless inclined planes making an angle $30^{\circ }$ and $60^{\circ }$ with the vertical are shown. Two blocks $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with respect to $B$?

For a particle in uniform circular motion the acceleration $\vec{a}$ at a point $P(R,\theta )$ on the circle of radius $R$ is (here $\theta$ is measured from the $x$ -axis):