AIEEE 2009 PYQ Mock Test

This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement 1: The temperature dependence of resistance is usually given as $R=R_0(1+\alpha \Delta t)$. The resistance of a wire changes from $100\Omega$ to $150\Omega$ when its temperature is increased from $27^{\circ }\text{C}$ to $227^{\circ }\text{C}$. This implies that $\alpha =2.5\times 10^{-3}{/}^{\circ }\text{C}$.
Statement 2: $R=R_i(1+\alpha \Delta T)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta R=(R-R_0)\ll R_0$.

A current loop $ABCD$ is held fixed on the plane of the paper. The arcs $BC$ (radius $=b$) and $DA$ (radius $=a$) of the loop are joined by two straight wires $AB$ and $CD$. A steady current $I$ is flowing in the loop. Angle made by $AB$ and $CD$ at the origin $O$ is $30^{\circ }$. The magnitude of the magnetic field ($B$) due to loop $ABCD$ at the origin ($O$) is:

Referring to the loop $ABCD$ in the previous question, a straight thin wire with steady current $I_1$ flowing out of the plane of the paper is kept at the origin. Due to the presence of the current $I_1$ at the origin:

A mixture of light, consisting of wavelength $590\text{nm}$ and an unknown wavelength, illuminates Young’s double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the $4^{th}$ bright fringe of the unknown light. From this data, the wavelength of the unknown light is:

Two points $P$ and $Q$ are maintained at the potentials of $10\text{V}$ and $-4\text{V}$ respectively. The work done in moving $100$ electrons from $P$ to $Q$ is: