A photon and an electron, each of 20 eV energy, move in free space. The ratio of linear momentum of electron $p_{e}$ to that of photon $p_{Ph}$, $\frac{p_{e}}{p_{Ph}}$ is [Take speed of light $=3\times10^{8}ms^{-1}$ charge of electron $=-1.6\times10^{-19}C$ and mass of electron $=9\times10^{-31}$ kg]

A unit positive point charge is taken slowly through an infinitesimally thin tube that is inside a charged dielectric sphere of radius R, having uniform positive charge density $\rho$, as shown in the figure. The initial and final positions of the charge are marked by A and B at distance 2R and 3R respectively, from the centre of the sphere. In this process, the magnitude of the total work done on the point charge is $\frac{\rho R^{2}}{n\epsilon_{0}}$. The value of n is: ($\epsilon_{0}$ is the permittivity of vacuum) [Image Placeholder]

Consider a particle moving along a straight line, whose position as a function of time is given by $s(t)=\alpha t^{2}-\beta t+\gamma$, where $\alpha=1~ms^{-2}$ $\beta=6~ms^{-1}$ and $\gamma=5m.$ The average speed of the particle, in $ms^{-1}$ from $t=0$ to $t=6$ s is:

In an acidic medium, 10 mL of 0.25 M oxalic acid is titrated with $KMnO_{4}$ solution. If the volume of $KMnO_{4}$ solution required to reach end point is 10 mL, the strength of the $KMnO_{4}$ solution is

Which of the following statements are Correct? (a) Energy flow from producers to consumers is unidirectional (b) Energy pyramid can never be inverted (c) Transfer of energy follows the 1% law Choose the correct answer from the options given below :