AIPMT 2009 Preliminary Mock Test

Consider an electric circuit consisting of two batteries with emfs ${ϵ}_1,{ϵ}_2$ and internal resistances $r_1,r_2$ connected in parallel with an external resistance $R$. If $i_1$ and $i_2$ are currents through the respective branches, which of the following Kirchhoff equations is correct?

A body, under the action of a force $\vec{F}=6\hat{i}-8\hat{j}+10\hat{k}$, acquires an acceleration of $1{\text{m/s}}^2$. The mass of this body must be:

The symbolic representations of four logic gates are given. The symbols for OR, NOT and NAND gates are respectively:

If $\vec{F}$ is the force acting on a particle having position vector $\vec{r}$ and $\vec{\tau }$ be the torque of this force about the origin, then:

The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_1$ and $T_2$ ($T_1>T_2$). The rate of heat transfer, $\frac{dQ}{dt}$, through the rod in a steady state is given by: