A conducting loop of finite resistance lies on the $x-y$ plane. There is a constant magnetic field in the z direction. The area of the loop varies with time t, as $A=A_{0}(1+\sin t)$ in appropriate units. The figure that correctly indicates the qualitative behaviour of the power P dissipated in the loop as a function of time is: [Image Placeholder]

Two moles of an ideal gas undergo free expansion from 10 L to 100 L at 300 K. The values of $\Delta S_{system}$ and $\Delta S_{surroundings}$ are (R is universal gas constant)

The temperature of a metallic sphere of radius R is increased by a small amount $\Delta T.$ If the linear coefficient of thermal expansion of the metal is $\alpha$, the approximate increase in the volume of the sphere is:

A ray of light with wavelength $\lambda$ is incident on three different photoelectric cells namely 1, 2 and 3. The threshold wavelength of these photoelectric cells are $\lambda_{1}$, $\lambda_{2},$ and $\lambda_{3,}$ respectively and the magnitude of stopping potentials of these cells are $V_{1}$, $V_{2}$ and $V_{3},$ respectively. The relation between $\lambda$ and threshold wavelengths are $\lambda_{1}\lambda$ and $\lambda_{3}>>\lambda$. The correct option is:

Given below are two statements: Statement I: trans-But-2-ene upon treatment with $Br_{2}$ in $CCl_{4}$ gives the following product. [Image Placeholder] Statement II: cis-But-2-ene upon treatment with alkaline $KMnO_{4}$ gives the following product. [Image Placeholder] In the light of the above statements, choose the most appropriate answer from the options given below.