What is the decreasing order of reactivity amongst the following compounds towards aromatic electrophilic substitution?
$(i)$ Chlorobenzene
$(ii)$ Benzene
$(iii)$ Anilinium chloride
$(iv)$ Toluene

The angle between the curves $y=\sin x$ and $y=\cos x$ is

$A$ thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net electric field $\vec{E}$ at the center $O$ is:

The distance between two coherent sources is $0.1 \, mm$. The fringe-width on a screen $1.2 \, m$ away from the source is $6.0 \, mm$. The wavelength of light used is $\dots \, \mathring{A}$.

Which of the following pairs is incorrect?

An ideal gas is subjected to a cyclic process involving four thermodynamic states. The amounts of heat $(Q)$ and work $(W)$ involved in each of these states are:
$\begin{aligned} & Q_1=6000 \text{ J}, \quad Q_2=-5500 \text{ J}, \quad Q_3=-3000 \text{ J}, \quad Q_4=3500 \text{ J} \\ & W_1=2500 \text{ J}, \quad W_2=-1000 \text{ J}, \quad W_3=-1200 \text{ J}, \quad W_4=x \text{ J} \end{aligned}$
The ratio of the net work done by the gas to the total heat absorbed by the gas is $\eta$. The values of $x$ and $\eta$ respectively are: