The shadow of a tower standing on a level ground is found to be $60 \, m$ longer when the sun's altitude is $30^\circ$ than when it is $45^\circ$. The height of the tower is

$A$ proton (mass $m$ and charge $+e$) and an $\alpha$-particle (mass $4m$ and charge $+2e$) are projected with the same kinetic energy at right angles to a uniform magnetic field. Which one of the following statements is true?

When a certain circuit consisting of a constant $e.m.f.$ $E$, an inductance $L$, and a resistance $R$ is closed, the current in it increases with time according to curve $1$. After one parameter $(E, L, \text{or } R)$ is changed, the increase in current follows curve $2$ when the circuit is closed a second time. Which parameter was changed and in what direction?

Aniline reacts with acetaldehyde to form

The energy levels of a certain atom are $A, B,$ and $C$ in increasing order of energy,i.e.,$E_A < E_B < E_C$. If $\lambda_1, \lambda_2,$ and $\lambda_3$ are the wavelengths of radiation corresponding to transitions $C \to B, B \to A,$ and $C \to A$ respectively,which of the following relations is correct?

In which of the following compounds does nitrogen exhibit the highest oxidation state?