A car travels on a circular racetrack of radius 50 m, which is banked at an angle $\theta$. If the car travels at a speed $10~ms^{-1}$, then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be $10~ms^{-2}$, the value of $\theta$ is:

Given below are two statements: Statement I: When any plane passing through the central axis of the body divides the organism into two identical halves, it is called radial symmetry. Statement II: In phylum Echinodermata, both adults and larvae are radially symmetrical. In the light of the above statements, choose the most appropriate answer from the options given below:

Two identical inductors are connected in two different configurations P and Q, where a time varying current $l(t)$ is flowing, as shown in the figure. The induced emf between points a and b for configuration P is $E_{P}$ and that for configuration Q is $E_{Q}$ The ratio $E_{P}/E_{Q}$ is: [Neglect the effect of mutual inductance.] [Image Placeholder]

Which of the following disease is not sexually transmitted?

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]