'Amoebiasis' (amoebic dysentery) is caused by

If the line $ax + by + c = 0$ is a normal to the curve $xy = 1$,then

$A$ proton enters a magnetic field of flux density $1.5 \, Wb/m^2$ with a velocity of $2 \times 10^7 \, m/s$ at an angle of $30^\circ$ with the field. The force on the proton will be

If in a regular polygon,the number of diagonals is $54$,then the number of sides of the polygon is:

If the amplitude of $z - 2 - 3i$ is $\pi / 4$,then the locus of $z = x + iy$ is

The following diagram indicates the energy levels of a certain atom. When the system moves from the $4E$ level to the $E$ level, a photon of wavelength $\lambda_1$ is emitted. The wavelength of the photon produced during its transition from the $\frac{7}{3}E$ level to the $E$ level is $\lambda_2$. The ratio $\frac{\lambda_1}{\lambda_2}$ will be: